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Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 1.2 Problem Solving to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 1.1 Adding and Subtracting Whole Numbers

Solve

Question 1.
Christine spent 24 minutes on Monday painting for her art project. She painted for 88 minutes on Tuesday, 45 minutes on Wednesday, and 55 minutes on Friday. How many minutes, in total, did she spend working on her art project?
Answer:
212 minutes
Explanation:
Christine spent 24 minutes on Monday painting for her art project.
She painted for 88 minutes on Tuesday, 45 minutes on Wednesday,
and 55 minutes on Friday.
Total minutes she spend working on her art project

Question 2.
Carl scored 114,564 points on the first level of his computer game. He scored 113,098 on the second level, and 125,888 on the third level. How many points, in total, did he score on all three levels?
Answer:
353550 points
Explanation:
Carl scored 114,564 points on the first level of his computer game.
He scored 113,098 on the second level, and 125,888 on the third level.
Total points she score on all three levels,

Question 3.
Jane has 175 stamps in her stamp collection, Stella has 133 stamps in her collection, and their cousin Penny has 212 stamps in hers. If Jane and Stella combine their stamp collections, how many more stamps will they have than Penny?
Answer:
96 stamps
Explanation:
Jane has 175 stamps in her stamp collection,
Stella has 133 stamps in her collection, and their cousin Penny has 212 stamps in hers.
If Jane and Stella combine their stamp collections,
Number of more stamps will they have than Penny,

Question 4.
The student council helped organize a jump rope competition for the school. During the competition, Team A jumped rope 1,339 times in 20 minutes. Team B jumped rope 1,448 times in 22 minutes, and Team C jumped rope 1,552 times in 23 minutes. What is the total number of times that the students jumped rope?
Answer:
4339 times
Explanation:
Team A jumped rope 1,339 times in 20 minutes.
Team B jumped rope 1,448 times in 22 minutes,
Team C jumped rope 1,552 times in 23 minutes.
Total number of times that the students jumped rope,

Question 5.
Larry spent Saturday afternoon reading his book. If he started the day on page 256, and stopped on page 539, how many pages did he read on Saturday?
Answer:
283 pages
Explanation:
Larry started the day on page 256, and stopped on page 539,
Number of pages did he read on Saturday

Question 6.
The average baby rhinoceros weighs 143 pounds at birth. Fully grown, the average weight of a rhinoceros is 3,950 pounds. How much weight will the average rhinoceros gain in its lifetime?
Answer:
3807
Explanation:
The average baby rhinoceros weighs 143 pounds at birth.
The average weight of fully grown rhinoceros is 3,950 pounds.
Total average weight gain by rhinoceros in its lifetime,

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 1.1 Adding and Subtracting Whole Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 1.1 Adding and Subtracting Whole Numbers

Exercises Add

Question 1.

Answer:
292
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 2.

Answer:
1320
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 3.

Answer:
726
Explanation:
Line up all the addends according to their place values.
Then the sum of the addends are as shown below,

Question 4.

Answer:
1273
Explanation:
Line up all the addends according to their place values.
Then the sum of the addends is 1273 as shown.

Question 5.

Answer:
1406
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 6.

Answer:
603
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 7.

Answer:
675
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 8.

Answer:
11001
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 9.

Answer:
11007
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 10.

Answer:
1092
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 11.

Answer:
1182976
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 12.

Answer:
507382
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 13.
Beatrice works the weekend shift at the local nature park. 325 people visited the park on Saturday morning. During the afternoon, another 455 people visited the nature park. That evening, another 175 people attended. How many people, in total, visited the park on Saturday?
Answer:
955
Explanation:
325 people visited the park on Saturday morning.
During the afternoon, another 455 people visited the nature park.
That evening, another 175 people attended.
Total people visited the park on Saturday,

Question 14.
Trevor is calculating the batting statistics for his baseball team. They hit 145 home runs, 117 triples, 612
doubles, and 543 singles. Using these statistics, how many times did Trevor’s team hit the ball?
Answer:
1417
Explanation:
Baseball hit 145 home runs, 117 triples, 612 doubles, and 543 singles.
Total number of times Trevor’s team hit the ball,

Exercises Subtract

Question 1.

Answer:
919
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 2.

Answer:
893
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 3.

Answer:
7084
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 4.

Answer:
1589
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 5.

Answer:
1038
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 6.

Answer:
560
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 7.

Answer:
1188
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 8.

Answer:
657889
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 9.

Answer:
3062
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 10.

Answer:
194566
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 11.

Answer:
276292
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 12.

Answer:
141685
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 13.
The U.S. Forest Service estimated that lašt year Williams Canyon was home to 325,000 deciduous trees. This season an insect infestation killed 125,889 trees. How many trees are flow left standing?
Answer:
199111
Explanation:
Last year Williams Canyon home has 325,000 deciduous trees.
This season an insect infestation killed 125,889 trees.
Total number of trees are flow left standing,

Question 14.
During a recent hurricane, 1,385 of Oak Island’s 3,034 inhabitants evacuated the island by ferry. How many of the inhabitants stayed behind during the storm?
Answer:
1649
Explanation:
During a recent hurricane, 1,385 of Oak Island’s and
3,034 inhabitants evacuated the island by ferry.
Total number of the inhabitants stayed behind during the storm,

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 9-12 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 9-12 Answer Key

Round to the nearest tenth.

Question 1.
3406.997 _____
Answer:
3407.0
Explanation:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number.
It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.,
So, 3406.997 is round off to 3407.

Question 2.
334,782.099 _______
Answer:
334,782.1
Explanation:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number.
It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.,
So, 334,782.099  is round off to 334,782.1.

Question 3.
65,529.0887 _____
Answer:
65,529.1
Explanation:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number.
It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.,
So, 65,529.0887 is round off to 65,529.1

Question 4.
12.94996 _______
Answer:
12.9
Explanation:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number.
It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.,
So, 12.94996 is round off to 12.9

Round to the nearest hundredth.

Question 5.
2,467,891.3554 ________
Answer:
2,467,891.36
Explanation:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number.
It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.,
So, 2,467,891.3554 is round off to 2,467,891.36

Question 6.
12.4532 __________
Answer:
12.45
Explanation:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number.
It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.,
12.4532 is round to the nearest hundredth 12.45

Question 7.
97.009 ___________
Answer:
97.01
Explanation:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number.
It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.,
So, 97.009 is round to the nearest hundredth 97.01

Question 8.
17.61093 _________
Answer:
17.61
Explanation:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number.
It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc
So, 17.61093 is round to the nearest hundredth 17.61

Round to the nearest ten thousandth.

Question 9.
467,001.35545 ____
Answer:
467,001.3555
Explanation:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number.
It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.,
So, 467,001.35545 is round off the nearest ten thousandth 467,001.3555.

Question 10.
199.11115 _________
Answer:
199.1112
Explanation:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number.
It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.,
So, 199.11115 is round off the nearest ten thousandth 199.1112.

Question 11.
1,683,679.57344 _____
Answer:
1,683,679.5734
Explanation:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number.
It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.,
So, 1,683,679.57344 is round off the nearest ten thousandth 1,683,679.5734.

Question 12.
8.194301 _________
Answer:
8.1943
Explanation:
Rounding off means a number is made simpler by keeping its value intact but closer to the next number.
It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.,
So, 8.194301 is round off the nearest ten thousandth 8.1943.

Convert decimals to fractions.

Question 13.
.8 _______
Answer:
\(\frac{4}{5}\)
Explanation:
multiply 0.8 by 10 and dividing be 10 to convert in to p/q format.
= \(\frac{8}{10}\)
= \(\frac{4}{5}\)

Question 14.
.875 ____
Answer:
\(\frac{7}{8}\)
Explanation:
multiply 0.875 by 1000 and dividing be 1000 to convert in to p/q format.
= \(\frac{875}{1000}\)
= \(\frac{7 X125}{8 X 125}\)
= \(\frac{7}{8}\)

Question 15.
.08 ____
Answer:
\(\frac{2}{25}\)
Explanation:
multiply 0.08 by 100 and dividing be 100 to convert in to p/q format.
= \(\frac{8}{100}\)
= \(\frac{2 X 4}{25 X 4}\)
= \(\frac{2}{25}\)

Question 16.
.625 ____
Answer:
\(\frac{5}{8}\)
Explanation:
multiply 0.625 by 1000 and dividing be 1000 to convert in to p/q format.
= \(\frac{625}{1000}\)
= \(\frac{5 X 125}{8 X 125}\)
= \(\frac{5}{8}\)

Convert fractions to decimals.

Question 17.
\(\frac{3}{5}\) _______
Answer:
0.6
Explanation:
To convert a fraction to a decimal. In a fraction, the fraction bar means divided by (÷).
\(\frac{3}{5}\)
Every fraction represents its numerator with its denominator.
3 ÷ 5
= 3 x 2 ÷ 5 x 2
= 6 ÷ 10
= 0.6

Question 18.
\(\frac{8}{15}\) _______
Answer:
0.5333
Explanation:
To convert a fraction to a decimal. In a fraction, the fraction bar means divided by (÷).
\(\frac{8}{15}\)
Every fraction represents its numerator with its denominator.
8 ÷ 15
= 3 x 2 ÷ 5 x 2
= 6 ÷ 10
= 0.6

Question 19.
\(\frac{3}{16}\) _______
Answer:
0.1875
Explanation:

Question 20.
6\(\frac{1}{8}\) _______
Answer:
6.125
Explanation:
6\(\frac{1}{8}\)
= \(\frac{6 x 8 + 1}{8}\)
= \(\frac{49}{8}\)

Put the decimals in order from greatest to least.

Question 21.
.122, .1145, .616, .6165, .513, .3132, .2126, .819
________________________
Answer:
0.819, 0.6165, 0.616, 0.513, 0.3132, 0.2126, 0.122, 0.1145
Explanation:
When comparing the numbers with the decimal numbers,
always compare the whole numbers first.
If two whole numbers are same then moving right to the decimal of the numbers,
we compare as shown above.

Question 22.
.217, .0217, .0133, .0487, .1243, .20413, .5257, .05257, .05205
Answer:
0.5257, 0.217, 0.20413, 0.1243, 0.05257, 0.05205, 0.0487, 0.0217, 0.0133
Explanation:
When comparing the numbers with the decimal numbers,
always compare the whole numbers first.
If two whole numbers are same then moving right to the decimal of the numbers,
we compare as shown above.

Add or Subtract.

Question 23.

Answer:
3.472817
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 24.

Answer:
6.53518656
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 25.

Answer:
6.660933
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 26.

Answer:
1.91916
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 27.

Answer:
1.428711
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 28.

Answer:
2.24946656
Explanation:
Arrange the given numbers according to their place value,
starting from ones, tens and so on..
Then subtract the bigger number from the smaller,
If required borrow one from the next column to find the difference.

Question 29.

Answer:
$6.75
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Question 30.

Answer:
$2.78
Explanation:
Line up all the addends according to their place values.
If the sum of the place value has 2 digits,
then write the second digit and carry the first digit to the next column.

Multiply or Divide.

Question 31.

Answer:
36.297
Explanation:
Line up all the numbers according to the place values,
then multiply with ones place first and then move to the next place.
Always write zeros in place holders.

Question 32.

Answer:
2119.175
Explanation:
Line up all the numbers according to the place values,
then multiply with ones place first and then move to the next place.
Always write zeros in place holders.

Question 33.

Answer:
$0.1068
round off to
$0.11
Explanation:

Question 34.

Answer:
7.48935
Explanation:
Line up all the numbers according to the place values,
then multiply with ones place first and then move to the next place.
Always write zeros in place holders.

Question 35.

Answer:
$0.92
Explanation:
Line up all the numbers according to the place values,
then multiply with ones place first and then move to the next place.
Always write zeros in place holders.
0.9184 is round off to 0.92

Question 36.

Answer:
2.9768005
Explanation:
Line up all the numbers according to the place values,
then multiply with ones place first and then move to the next place.
Always write zeros in place holders.

Question 37.

Answer:
$6.88
Explanation:
Line up all the numbers according to the place values,
then multiply with ones place first and then move to the next place.
Always write zeros in place holders.
6.875 is round off to 6.88

Question 38.

Answer:
1.478625
Explanation:

Question 39.

Answer:
6.380989
Explanation:
2.24 x 100 = 224
14.293415 x 100 = 1429.3415

6.38098883 is round off to 6.380989

Question 40.

Answer:
$11.70
Explanation:
.23 x 100 = 23
2.69 x 100 = 269

11.6956 is round off to 11.70

Question 41.

Answer:
23.22
Explanation:
0.025 x 1000 = 25
0.5805 x 1000 = 580.5

Question 42.

Answer:
1.4189
Explanation:

Estimate, then multiply or divide.

Question 43.

Answer:
Estimate: 0.09
Product: 0.106575
Explanation:
Round each factor to its highest place values,
and then multiply the rounded amounts.
0.3 x 0.3 = 0.9

Question 44.

Answer:
Estimate: 0.6
Quotient: 0.6362
Explanation:
Ignore the decimals first.
143143 ÷ 225
then place the decimals in the quotient as shown below,

0.636191111 is round off to the nearest 0.6362

Question 45.

Answer:
Estimate: 300
Product: 303.50
Explanation:
Round each factor to its highest place values,
and then multiply the rounded amounts.
1200 x 25 = 300

Question 46.

Answer:
Estimate: 13750
Quotient: 13755
Explanation:
Ignore the decimals first.
5502 ÷ 4
then place the decimals in the quotient as shown below,

Question 47.

Answer:
Estimate: 90
Product: 90.75
Explanation:
Round each factor to its highest place values,
and then multiply the rounded amounts.
6 x 15 = 90

Question 48.

Answer:
Estimate: 50
Quotient: 45.61818
Explanation:
Ignore the decimals first.
2509 ÷ 55
then place the decimals in the quotient as shown below,

Question 49.

Answer:
Estimate: 320
Product: 308.01465
Explanation:
Round each factor to its highest place values,
and then multiply the rounded amounts.
80 x 4 = 320

Question 50.

Answer:
Estimate: 60
Quotient: 55.419
Explanation:
Ignore the decimals first.
184545 ÷ 333
then place the decimals in the quotient as shown below,

Question 51.
Flora went to the stationery store to buy tools for her art class. She spent $2.50 on colored pencils, $7.05 on a set of artist pallets, $4.59 for a used straight edge, $2.09 for a lined memo pad, and $5.28 for a new water bottle. How much did she spend altogether? ________
If Flora only brought thirty dollars with her, did she have enough money?
If so, how much change should she get back? ___________
If not, how much more money does she need? _________
Answer:
Total amount spent = $21.51
Yes, she has enough money.
Change she gets back = $8.49
Total amount she need = Not required.
Explanation:
Flora spent $2.50 on colored pencils,
$7.05 on a set of artist pallets,
$4.59 for a used straight edge,
$2.09 for a lined memo pad and
$5.28 for a new water bottle.
Total amount she spend altogether ,
$2.50 + $7.05 + $4.59 + $2.09 + $5.28 = $21.51
If Flora only brought thirty dollars with her,
Yes, she have enough money because she need to spend only $21.51
Total change she get back $30 – $21.51 = $8.49
She don’t need any extra amount.

Question 52.
Thad and his chess club raised a total of $563.75 for the local homeless shelter. There are 11 people in the chess club. If each member raised the same amount of money, how much did each member raise?
Answer:
$51.25
Explanation:
Thad and his chess club raised a total of $563.75 for the local homeless shelter.
There are 11 people in the chess club.
If each member raised the same amount of money,
Total amount each member raise is $563.75 ÷ 11 = $51.25

Question 53.
Jane went to the store to buy food for a party of 8 friends. She spent $3.75 on each person for soup, $1.15 each for a warm beverage, and $.76 each for a piece of fruit. How much did she spend in total to buy the food?
She brought two $20-bills with her. ______
Did she have enough money? ________
Answer:
Total amount to buy the food = $45.28
No, she didn’t have enough money.
Explanation:
Jane went to the store to buy food for a party of 8 friends.
She spent $3.75 on each person for soup,
$1.15 each for a warm beverage and
$.76 each for a piece of fruit.
Total amount spent to buy on food,
3.75 + 1.15 + 0.76 = 5.66
food for a party of 8 friends
5.66 x 8 = 45.28
She brought two $20-bills with her.
No, she didn’t have enough money.

Question 54.
Evelyn drives 14.25 miles each way to visit her aunt. What is the total distance she drives if she visits
her aunt 3 times?
Answer:
85.5 miles
Explanation:
Evelyn drives 14.25 miles each way to visit her aunt,
if she visits her aunt 3 times then,
14.25 x 2 = 28.5 per one visit.
The total distance she drives if she visits her aunt 3 times
28.5 x 3 = 85.5

Question 55.
A drilling rig can drill to -5 meters below the ground in an hour. At that speed, how far has the rig dug in a week? __________
Answer:
– 840 meters.
Explanation:
A drilling rig can drill to -5 meters below the ground in an hour.
24 hours a day
– 5 X 24 = -120 meters per day
At that speed, how far has the rig dug in a week,
7 days a week
– 120 x 7 = – 840 meters per week

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 6-8 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 6-8 Answer Key

Change to mixed numbers.

Question 1.
\(\frac{17}{7}\)
Answer:
2\(\frac{3}{7}\)
Explanation:
Any fraction greater than 1 is an improper fraction can be be changed to mixed number,
which is a part of whole number and fraction.
\(\frac{17}{7}\)
= 2\(\frac{3}{7}\)

Question 2.
\(\frac{29}{6}\)
Answer:
4\(\frac{5}{6}\)
Explanation:
Any fraction greater than 1 is an improper fraction can be be changed to mixed number,
which is a part of whole number and fraction.
\(\frac{29}{6}\)
= 4\(\frac{5}{6}\)

Question 3.
\(\frac{102}{17}\)
Answer:
6
Explanation:
Any fraction greater than 1 is an improper fraction can be be changed to mixed number,
which is a part of whole number and fraction.
\(\frac{102}{17}\)
= 6

Question 4.
\(\frac{350}{33}\)
Answer:
10\(\frac{20}{33}\)
Explanation:
Any fraction greater than 1 is an improper fraction can be be changed to mixed number,
which is a part of whole number and fraction.
\(\frac{350}{33}\)
= 10\(\frac{20}{33}\)

Change to improper fractions.

Question 5.
7\(\frac{6}{11}\)
Answer:
\(\frac{83}{11}\)
Explanation:
To convert mixed fraction to improper fraction,
7\(\frac{6}{11}\)
Multiply the whole number by denominator of fraction.
7 x 11 = 77
Then add the numerator to the product.
77 + 6 = 83
Place the total over denominator,
\(\frac{83}{11}\)

Question 6.
5\(\frac{4}{13}\)
Answer:
\(\frac{69}{13}\)
Explanation:
To convert mixed fraction to improper fraction,
5\(\frac{4}{13}\)
Multiply the whole number by denominator of fraction.
5 x 13 = 65
Then add the numerator to the product.
65 + 4 = 69
Place the total over denominator,
\(\frac{69}{13}\)

Question 7.
4\(\frac{15}{19}\)
Answer:
\(\frac{91}{19}\)
Explanation:
To convert mixed fraction to improper fraction,
4\(\frac{15}{19}\)
Multiply the whole number by denominator of fraction.
4 x 19 = 76
Then add the numerator to the product.
76 + 15 = 91
Place the total over denominator,
\(\frac{91}{19}\)

Question 8.
7\(\frac{7}{16}\)
Answer:
\(\frac{119}{16}\)
Explanation:
To convert mixed fraction to improper fraction,
7\(\frac{7}{16}\)
Multiply the whole number by denominator of fraction.
7 x 16 = 112
Then add the numerator to the product.
112 + 7 = 119
Place the total over denominator,
\(\frac{119}{16}\)

Add or subtract, and reduce to simplest form.

Question 9.
1\(\frac{3}{4}\) + \(\frac{3}{4}\)
Answer:
2\(\frac{1}{2}\)
Explanation:
1\(\frac{3}{4}\) + \(\frac{3}{4}\)
= \(\frac{7}{4}\) + \(\frac{3}{4}\)
Add the numerators 7 + 3 = 10
Then place over denominators.
\(\frac{10}{4}\) = \(\frac{5}{2}\)
Reduce to the simplest form as,
= 2\(\frac{1}{2}\)

Question 10.
\(\frac{17}{49}\) – \(\frac{11}{49}\)
Answer:
\(\frac{6}{49}\)
Explanation:
\(\frac{17}{49}\) – \(\frac{11}{49}\)
Subtract the numerators 17 – 11 = 6
Then place over denominators.
\(\frac{6}{49}\)

Question 11.
1\(\frac{5}{11}\) + \(\frac{3}{11}\)
Answer:
1\(\frac{8}{11}\)
Explanation:
1\(\frac{5}{11}\) + \(\frac{3}{11}\)
= \(\frac{16}{11}\) + \(\frac{3}{11}\)
Add the numerators 16 + 3 = 19
Then place over denominators.
\(\frac{19}{11}\)
Reduce to the simplest form as,
= 1\(\frac{8}{11}\)

Question 12.
2\(\frac{23}{39}\) + \(\frac{24}{39}\)
Answer:
3\(\frac{8}{39}\)
Explanation:
2\(\frac{23}{39}\) + \(\frac{24}{39}\)
= \(\frac{101}{39}\) + \(\frac{24}{39}\)
Add the numerators 101 + 24 = 125
Then place over denominators.
\(\frac{125}{39}\)
Reduce to the simplest form as,
= 3\(\frac{23}{39}\)

Question 13.
\(\frac{34}{41}\) – \(\frac{13}{41}\)
Answer:
\(\frac{21}{41}\)
Explanation:
\(\frac{34}{41}\) – \(\frac{13}{41}\)
Subtract the numerators 34 – 13 = 21
Then place over denominators.
\(\frac{21}{41}\)

Question 14.
\(\frac{11}{32}\) + \(\frac{19}{32}\)
Answer:
\(\frac{15}{16}\)
Explanation:
\(\frac{11}{32}\) + \(\frac{19}{32}\)
Add the numerators 11 + 19 = 30
Then place over denominators.
\(\frac{30}{32}\) = \(\frac{15}{16}\)

Question 15.
\(\frac{55}{93}\) – \(\frac{28}{93}\)
Answer:
\(\frac{9}{31}\)
Explanation:
\(\frac{55}{93}\) – \(\frac{28}{93}\)
Subtract the numerators 55 – 28 = 27
Then place over denominators.
\(\frac{27}{93}\) = \(\frac{9}{31}\)

Question 16.
\(\frac{36}{74}\) + \(\frac{33}{74}\)
Answer:
\(\frac{69}{74}\)
Explanation:
\(\frac{36}{74}\) + \(\frac{33}{74}\)
Add the numerators 36 + 33 = 69
Then place over denominators.
\(\frac{69}{74}\)

Question 17.
5\(\frac{3}{17}\) – 4\(\frac{2}{17}\)
Answer:
1\(\frac{1}{17}\)
Explanation:
5\(\frac{3}{17}\) – 4\(\frac{2}{17}\)
= \(\frac{88}{17}\) + \(\frac{70}{17}\)
Subtract the numerators 88 – 70 = 18
Then place over denominators.
\(\frac{18}{17}\)
Reduce to the simplest form as,
= 1\(\frac{1}{17}\)

Question 18.
4\(\frac{23}{33}\) + \(\frac{17}{24}\)
Answer:
5\(\frac{107}{264}\)
Explanation:
4\(\frac{23}{33}\) + \(\frac{17}{24}\)
= \(\frac{155}{33}\) + \(\frac{17}{24}\)
Find a common multiple for both the denominators is 264
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{155 X 8}{33 X 8}\) + \(\frac{17 X 11}{24 X 11}\)
= \(\frac{1240}{264}\) + \(\frac{187}{264}\)
Add the numerators 1240 + 187 = 1427
Then place over denominators.
\(\frac{1427}{264}\)
Reduce to the simplest form as,
= 5\(\frac{107}{264}\)

Question 19.
\(\frac{4}{9}\) + \(\frac{4}{15}\)
Answer:
\(\frac{32}{45}\)
Explanation:
\(\frac{4}{9}\) + \(\frac{4}{15}\)
Find a common multiple for both the denominators is 135
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{4 X 15}{9 X 15}\) + \(\frac{4 X 9}{15 X 9}\)
= \(\frac{60}{135}\) + \(\frac{32}{135}\)
Add the numerators 60 + 36 = 96
Then place over denominators.
\(\frac{96}{135}\)
Reduce to the simplest form as,
= \(\frac{32}{45}\)

Question 20.
\(\frac{14}{25}\) – \(\frac{13}{35}\)
Answer:
\(\frac{33}{175}\)
Explanation:
\(\frac{14}{25}\) – \(\frac{13}{35}\)
Find a common multiple for both the denominators is 175.
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{14 X 7}{25 X 7}\) – \(\frac{13 X 5}{35 X 5}\)
= \(\frac{98}{175}\) – \(\frac{65}{175}\)
Subtract the numerators 98 – 65 = 33
Then place over denominators.
\(\frac{33}{175}\)

Question 21.
1\(\frac{5}{9}\) + \(\frac{3}{11}\)
Answer:
1\(\frac{82}{99}\)
Explanation:
1\(\frac{5}{9}\) + \(\frac{3}{11}\)
= \(\frac{14}{9}\) + \(\frac{3}{11}\)
Find a common multiple for both the denominators is 99.
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{14 X 11}{9 X 11}\) + \(\frac{3 X 9}{11 X 9}\)
= \(\frac{154}{99}\) + \(\frac{27}{99}\)
Add the numerators 154 + 27 = 181
Then place over denominators.
\(\frac{181}{99}\)
Reduce to its simplest f form,
1\(\frac{82}{99}\)

Question 22.
1\(\frac{7}{19}\) – \(\frac{2}{7}\)
Answer:
1\(\frac{11}{133}\)
Explanation:
1\(\frac{7}{19}\) – \(\frac{2}{7}\)
= \(\frac{26}{19}\) – \(\frac{2}{7}\)
Find a common multiple for both the denominators is 133.
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{26 X 7}{19 X 7}\) – \(\frac{2 X 19}{7 X 19}\)
= \(\frac{182}{133}\) – \(\frac{38}{133}\)
Subtract the numerators 182 – 38 = 144
Then place over denominators.
\(\frac{144}{133}\)
Reduce to its simplest f form,
1\(\frac{11}{133}\)

Question 23.
\(\frac{3}{4}\) – \(\frac{19}{41}\)
Answer:
\(\frac{47}{164}\)
Explanation:
\(\frac{3}{4}\) – \(\frac{19}{41}\)
Find a common multiple for both the denominators is 164.
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{3 X 41}{4 X 41}\) – \(\frac{19 X 4}{41 X 4}\)
= \(\frac{123}{164}\) – \(\frac{76}{164}\)
Subtract the numerators 123 – 76 = 47
Then place over denominators.
\(\frac{47}{164}\)

Question 24.
2\(\frac{8}{13}\) + \(\frac{9}{17}\)
Answer:
3\(\frac{32}{221}\)
Explanation:
2\(\frac{8}{13}\) + \(\frac{9}{17}\)
= \(\frac{34}{13}\) + \(\frac{9}{17}\)
Find a common multiple for both the denominators is 221.
Multiply both the numerator and denominator,
that will make the denominator equal to common multiple.
\(\frac{34 X 17}{13 X 17}\) + \(\frac{9 X 13}{17 X 13}\)
= \(\frac{578}{221}\) + \(\frac{117}{221}\)
Add the numerators 578 + 117 = 695
Then place over denominators.
\(\frac{695}{117}\)
Reduce to its simplest f form,
3\(\frac{32}{221}\)

Estimate, then add or subtract.

Question 25.
2\(\frac{14}{25}\) – 1\(\frac{17}{21}\)
Answer:
\(\frac{394}{525}\)
Explanation:
2\(\frac{14}{25}\) – 1\(\frac{17}{21}\)
= \(\frac{(2 X 25) + 14}{25}\) – \(\frac{(1 X 21) + 17}{21}\)
= \(\frac{64}{25}\) – \(\frac{38}{21}\)
= \(\frac{(64 X 21) – (38 X 25)}{525}\)
= \(\frac{1344 – 950}{525}\)
\(\frac{394}{525}\)

Question 26.
9\(\frac{22}{63}\) + 25\(\frac{43}{63}\)
Answer:
35\(\frac{2}{63}\)
Explanation:
9\(\frac{22}{63}\) + 25\(\frac{43}{63}\)
= 9\(\frac{(9 X 63) + 22}{63}\) + 25\(\frac{(25 x 63) + 43}{63}\)
= \(\frac{589}{63}\) + \(\frac{1618}{63}\)
= \(\frac{2207}{63}\)
= 35\(\frac{2}{63}\)

Question 27.
12\(\frac{23}{29}\) + 11\(\frac{17}{29}\)
Answer:
24\(\frac{11}{29}\)
Explanation:
12\(\frac{23}{29}\) + 11\(\frac{17}{29}\)
= latex]\frac{(12 X 29) + 23}{29}[/latex] + latex]\frac{(11 X 29) + 17}{29}[/latex]
= latex]\frac{371}{29}[/latex] + latex]\frac{336}{29}[/latex]
= latex]\frac{371 + 336}{29}[/latex]
= latex]\frac{707}{29}[/latex]
= 24\(\frac{11}{29}\)

Question 28.
18\(\frac{3}{7}\) + 5\(\frac{1}{4}\)
Answer:
23\(\frac{19}{28}\)
Explanation:
18\(\frac{3}{7}\) + 5\(\frac{1}{4}\)
= \(\frac{(7 X 18) + 3}{7}\) + \(\frac{(4 X 5) + 1}{4}\)
= \(\frac{129}{7}\) + \(\frac{21}{4}\)
= \(\frac{(129 X 4) + 21 x 7}{28}\)
= \(\frac{516 + 147 }{28}\)
= \(\frac{663}{28}\)
= 23\(\frac{19}{28}\)

Multiply or divide, and reduce to simplest form.

Question 29.
3 × 3\(\frac{2}{11}\)
Answer:
9\(\frac{6}{11}\)
Explanation:
3 × 3\(\frac{2}{11}\)
convert mixed fraction to improper fraction,
3 × \(\frac{35}{11}\)
Multiply the whole number by numerator,
3 × 35 = 105
Place your answer over denominator.
= \(\frac{105}{11}\)
Reduce to the simplest form,
9\(\frac{6}{11}\)

Question 30.
\(\frac{1}{2}\) × 55
Answer:
27\(\frac{1}{2}\)
Explanation:
\(\frac{1}{2}\) x 55
Multiply the whole number by numerator,
1 × 55 = 55
Place your answer over denominator.
= \(\frac{55}{2}\)
Reduce to the simplest form,
27\(\frac{1}{2}\)

Question 31.
\(\frac{3}{4}\) × 24
Answer:
18
Explanation:
\(\frac{3}{4}\) x 24
Multiply the whole number by numerator,
3 × 24 = 72
Place your answer over denominator.
= \(\frac{72}{4}\)
Reduce to the simplest form as 18.

Question 32.
\(\frac{14}{18}\) × \(\frac{11}{28}\)
Answer:
\(\frac{11}{36}\)
Explanation:
\(\frac{14}{18}\) x \(\frac{11}{28}\)
Multiply the numerators and denominators,
14 x 11 = 154
18 x 28 = 504
Place your answer over denominator.
= \(\frac{154}{504}\)
Reduce to the simplest form,
\(\frac{11}{36}\)

Question 33.
\(\frac{1}{3}\) × 4\(\frac{7}{9}\)
Answer:
1\(\frac{16}{27}\)
Explanation:
\(\frac{1}{3}\) x 4\(\frac{7}{9}\)
Convert mixed fraction into improper fraction,
\(\frac{1}{3}\) x \(\frac{43}{9}\)
Multiply the numerators and denominators,
1 x 43 = 43
3 x 9 = 27
Place your answer over denominator.
= \(\frac{43}{117}\)
Reduce to the simplest form,
1\(\frac{16}{27}\)

Question 34.
16 × \(\frac{3}{11}\)
Answer:
4\(\frac{4}{11}\)
Explanation:
16 × \(\frac{3}{11}\)
Multiply the whole number by numerator,
16 × 3 = 48
Place your answer over denominator.
= \(\frac{48}{11}\)
Reduce to the simplest form,
4\(\frac{4}{11}\)

Question 35.
\(\frac{16}{29}\) ÷ 48
Answer:
\(\frac{1}{87}\)
Explanation:
\(\frac{16}{29}\) ÷ 48
Multiply the whole number by denominator,
48 x 29 = 1392
place the numerator over denominator,
\(\frac{16}{1392}\)
Reduce to the simplest form,
\(\frac{1}{87}\)

Question 36.
\(\frac{51}{47}\) ÷ 17
Answer:
\(\frac{3}{47}\)
Explanation:
\(\frac{51}{47}\) ÷ 17
Multiply the whole number by denominator,
17 x 47 = 799
place the numerator over denominator,
\(\frac{51}{799}\)
Reduce to the simplest form,
\(\frac{3}{47}\)

Question 37.
\(\frac{7}{3}\) ÷ 42
Answer:
\(\frac{1}{18}\)
Explanation:
\(\frac{7}{3}\) ÷ 42
Multiply the whole number by denominator,
42 x 3 = 126
place the numerator over denominator,
\(\frac{7}{126}\)
Reduce to the simplest form,
\(\frac{1}{18}\)

Question 38.
\(\frac{4}{27}\) ÷ 3
Answer:
\(\frac{4}{81}\)
Explanation:
\(\frac{4}{27}\) ÷ 3
Multiply the whole number by denominator,
27 x 3 = 81
place the numerator over denominator,
\(\frac{4}{81}\)

Question 39.
\(\frac{75}{83}\) ÷ 15
Answer:
\(\frac{5}{83}\)
Explanation:
\(\frac{75}{83}\) ÷ 15
Multiply the whole number by denominator,
83 x 15 = 1245
place the numerator over denominator,
\(\frac{75}{1245}\)
Reduce to the simplest form,
\(\frac{5}{83}\)

Question 40.
39 ÷ \(\frac{6}{7}\)
Answer:
45\(\frac{1}{2}\)
Explanation:
39 ÷ \(\frac{6}{7}\)
Multiply the whole number by denominator,
39 x 7 = 273
place the numerator over denominator,
\(\frac{6}{273}\)
Reduce to the simplest form,
45\(\frac{1}{2}\)

Question 41.
125 ÷ \(\frac{25}{44}\)
Answer:
220
Explanation:
125 ÷ \(\frac{25}{44}\)
Multiply the whole number by denominator,
125 x 44 = 5500
place the numerator over denominator,
\(\frac{25}{5500}\) = 220

Question 42.
\(\frac{3}{4}\) ÷ \(\frac{16}{27}\)
Answer:
1\(\frac{17}{64}\)
Explanation:
\(\frac{3}{4}\) ÷ \(\frac{16}{27}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{3}{4}\) x \(\frac{27}{16}\)
Multiply the numerators and denominators,
3 x 27 = 81
4 x 16 = 64
place the numerator over denominator,
\(\frac{81}{64}\)
Reduce to the simplest form,
1\(\frac{17}{64}\)

Question 43.
\(\frac{24}{17}\) ÷ \(\frac{17}{24}\)
Answer:
1
Explanation:
\(\frac{24}{17}\) ÷ \(\frac{17}{24}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{24}{17}\) x \(\frac{24}{17}\)
Multiply the numerators and denominators,
24 x 17 = 408
24 x 17 = 408
place the numerator over denominator,
\(\frac{408}{408}\) = 1

Question 44.
\(\frac{39}{76}\) ÷ \(\frac{52}{57}\)
Answer:
\(\frac{9}{16}\)
Explanation:
\(\frac{39}{76}\) ÷ \(\frac{52}{57}\)
Multiply the first fraction by the reciprocal of the second fraction,
\(\frac{39}{76}\) x \(\frac{57}{52}\)
Multiply the numerators and denominators,
39 x 57 = 2223
76 x 52 = 3952
place the numerator over denominator,
\(\frac{2223}{3952}\)
Reduce to the simplest form,
1\(\frac{9}{16}\)

Question 45.
Elena jogs at a constant rate of 5\(\frac{1}{3}\) miles per hour. How far does she jog in 3 hours?
Answer:
16 miles
Explanation:
Elena jogs at a constant rate of 5\(\frac{1}{3}\) miles per hour.
she jog in 3 hours = 3 x 5\(\frac{1}{3}\)
= 3 × \(\frac{16}{3}\)
Multiply the whole number by numerator,
16 × 3 = 48
Place your answer over denominator.
= \(\frac{48}{3}\)
= 16 miles.

Question 46.
To plant his vegetable garden, Randy needs to dig 24 holes that are each 4\(\frac{1}{2}\) inches deep.
How many total inches does he have to dig?
Answer:
108 inches.
Explanation:
Randy needs to dig 24 holes that are each 4\(\frac{1}{2}\) inches deep.
Total inches he need to dig,
24 x 4\(\frac{1}{2}\)
convert mixed fraction to improper fraction,
24 x \(\frac{9}{2}\)
Multiply the whole number by numerator,
24 x 9 = 216
place the numerator over denominator,
\(\frac{216}{2}\)
= 108 inches.

Question 47.
Cassie has \(\frac{5}{6}\) pound of sunflower seeds. She wants to divide the seeds among 3 people.
How many pounds will each person get?
Answer:
\(\frac{5}{18}\) pounds.
Explanation:
Cassie has \(\frac{5}{6}\) pound of sunflower seeds.
She wants to divide the seeds among 3 people.
Number of pounds will each person get,
\(\frac{5}{6}\) ÷ 3
Multiply the whole number by denominator,
6 x 3 = 18
place the numerator over denominator,
\(\frac{5}{18}\) pounds.

Question 48.
The temperature on Tuesday was -3°F.On Wednesday the temperature was 4°F.What is the average temperature for the two days? On which day was the temperature closer to 0°F?
Answer:
\(\frac{1}{2}\)°F;
Tuesday.
Explanation:
The temperature on Tuesday was -3°F.
On Wednesday the temperature was 4°F.
The average temperature for the two days,
\(\frac{ -3 + 4}{2}\)
= \(\frac{1}{2}\)°F.

Question 49.
A cookie recipe calls for \(\frac{3}{4}\) cup of sugar. If Aaron wants to make one half batches of cookies, how many cups of sugar will he need?
Answer:
1\(\frac{1}{8}\) cups
Explanation:
A cookie recipe calls for \(\frac{3}{4}\) cup of sugar.
If Aaron wants to make one half batches of cookies,
how many cups of sugar will he need
\(\frac{3}{4}\) + 1\(\frac{1}{2}\)
= \(\frac{3}{4}\) + 1\(\frac{2}{4}\)
= \(\frac{3}{4}\) + \(\frac{6}{4}\)
= \(\frac{9}{8}\)
= 1\(\frac{1}{8}\) cups.

Question 50.
Vivi steps off a 10-foot-high diving board and goes 7\(\frac{3}{8}\) feet below the surface of the swimming pool, then back up to the surface. How far does she travel together?
Answer:
24\(\frac{3}{4}\)
Explanation:
10 + 7\(\frac{3}{8}\) + 7\(\frac{3}{8}\)
= 10 + \(\frac{59}{8}\) + \(\frac{59}{8}\)
= 10 + \(\frac{118}{8}\)
= \(\frac{80 +118}{8}\)
= \(\frac{198}{8}\)
= 24 \(\frac{6}{8}\)
= 24 \(\frac{3}{4}\)

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 24–26 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 24–26 Answer Key

Identify each angle as obtuse, acute or right.

Question 1.

Answer:
Obtuse Angle
Explanation:
Any angle that is greater than 90° but less than 180° is known as obtuse angle.

Question 2.

Answer:
Right Angle.
Explanation:
If the angle formed between two rays is exactly 90° then it is called a Right Angle.

Question 3.

Answer:
Acute Angle
Explanation:
If two rays intersect at a vertex, forming an angle that is less than 90° is known as Acute Angle.

Question 4.

Answer:
Acute Angle
Explanation:
If two rays intersect at a vertex, forming an angle that is less than 90° is known as Acute Angle.

Question 5.

Answer:
Obtuse Angle
Explanation:
Any angle that is greater than 90° but less than 180° is known as obtuse angle.

Identify each pair of angles as supplementary, complementary, vertical, or not any of these. Explain why.

Question 6.

Answer:
Complementary Angle;
Sum of the angle measures are 90°.
Explanation:
If the sum of two angles is 90 degrees,
then they are said to be complementary angles, and they form a right angle together.
52 ° + 38 ° = 90 °

Question 7.

Answer:
Supplementary Angle;
Sum of the angles is 180°.
Explanation:
If the sum of two angles is 180 degrees,
then they are said to be supplementary angles, which form a linear angle together.
66 ° + 114 ° = 180 °

Question 8.

Answer:
Complementary Angle;
Sum of the angle measures are 90°.
Explanation:
If the sum of two angles is 90 degrees,
then they are said to be complementary angles, and they form a right angle together.
66 ° + 24 ° = 90 °

Question 9.

Answer:
Neither Complementary nor Supplementary Angle;
Sum of the angles are 89°.
Explanation:
If the sum of two angles is 90 degrees,
then they are said to be complementary angles, and they form a right angle together.
But the sum of the two angles in the given figure is less than 90 degrees.
So, it is neither Complementary nor Supplementary Angle.
44 ° + 45 ° = 89 °

Question 10.

Answer:
Neither Complementary or Supplementary Angle;
Sum of the angles are 169°.
Explanation:
If the sum of two angles is 180 degrees,
then they are said to be supplementary angles, which form a linear angle together.
But the sum of the two angles in the given figure is less than 180 degrees.
So, it is neither Complementary nor Supplementary Angle.
144 ° + 25 ° = 169 °

Identity the following triangles as scalene, equilateral, or isosceles.

Question 11.

Answer:
Equilateral Triangle.
Explanation:
An equilateral triangle is a triangle with all three sides of equal length.

Question 12.

Answer:
Scalene Triangle.
Explanation:
All angles of a scalene triangle are unequal, all are of different size and length.

Question 13.

Answer:
Isosceles Triangle.
Explanation:
An Isosceles triangle is a triangle with two equal sides.

Question 14.

Answer:
Scalene Triangle.
Explanation:
All angles of a scalene triangle are unequal, all are of different size and length.

Question 15.

Answer:
Equilateral Triangle.
Explanation:
An equilateral triangle is a triangle with all three sides of equal length.

Question 16.

Answer:
Isosceles Triangle.
Explanation:
An Isosceles triangle is a triangle with two equal sides.

Identify the following triangles as obtuse, right, or acute.

Question 17.

Answer:
Right Angle.
Explanation:
If the angle formed between two rays is exactly 90° then it is called a Right Angle.

Question 18.

Answer:
Acute Angle.
Explanation:
If two rays intersect at a vertex, forming an angle that is less than 90° is known as Acute Angle.

Question 19.

Answer:
Acute Angle.
Explanation:
If two rays intersect at a vertex, forming an angle that is less than 90° is known as Acute Angle.

Question 20.

Answer:
Acute Angle.
Explanation:
If two rays intersect at a vertex, forming an angle that is less than 90° is known as Acute Angle.

Question 21.

Answer:
Obtuse Angle.
Explanation:
Any angle that is greater than 90° but less than 180° is known as obtuse angle.

Question 22.

Answer:
Right Angle.
Explanation:
If the angle formed between two rays is exactly 90° then it is called a Right Angle.

Answer the following questions by looking at the figure on the right.

Question 23.
Name the center point
Answer:
Point A
Explanation:
The center of a circle is the point equidistant from the points on the edge.

Question 24.
Which segments are chords?
Answer:
\(\overline{HC}\),\(\overline{BD}\), \(\overline{BC}\), \(\overline{CD}\)
Explanation:
The chord of a circle is the line segment joining any two points on the circumference of the circle.

Question 25.
Which segment is the diameter?
Answer:
\(\overline{HG}\)
Explanation:
The diameter is the length of the line through which the center touches two points on the edge of the circle.

Question 26.
Which segments are radii?
Answer:
\(\overline{AG}\),\(\overline{AD}\), \(\overline{AH}\)
Explanation:
Radius of a circle is the distance from the center of the circle to any point on it’s circumference.

Identify the figures and fill in the missing information.

Question 27.

Figure _____________
Base is _____________
Number of faces _____________
Number of edges _____________
Number of vertices _____________
Answer:
Figure is Cube,
Base is Square,
Number of faces 6,
Number of edges 12,
Number of vertices 8.
Explanation:
A Cube is a solid three-dimensional figure,
which has 6 square faces, 8 vertices and 12 edges.
Base of a cube is has four sides looks like square.
It is also said to be a regular hexahedron.

Question 28.

Figure _____________
Base is _____________
Number of faces _____________
Number of edges _____________
Number of vertices _____________
Answer:
Figure is Rectangular solid,
Base is Rectangle,
Number of faces 6,
Number of edges 12,
Number of vertices 8.
Explanation:
A Rectangular solid is also known as Cuboid.
Rectangular solids are 3D shapes with six rectangle sides all meeting perpendicularly.
Number of faces of a rectangular solid are 6, edges 12 and vertices 8.

Question 29.

Figure _____________
Base is _____________
Number of faces _____________
Number of edges _____________
Number of vertices _____________
Answer:
Figure is Rectangular Pyramid,
Base is Rectangle,
Number of faces 5,
Number of edges 8,
Number of vertices 5.
Explanation:
Pyramids are three-dimensional structures having triangle faces with a polygon shape at its base.
If the base of a pyramid is rectangular, then it is called a rectangular pyramid.
It has 5 faces, 8 edges and 5 vertices.

Question 30.

Figure _____________
Base is _____________
Number of faces _____________
Number of edges _____________
Number of vertices _____________
Answer:
Figure is Cone,
Base is Circle,
Number of faces 1,
Number of edges – no Edges,
Number of vertices 1.
Explanation:
A Cone always passes through a fixed point  or the vertex.
Cone has circular base with no edges.
It has one circular face and one vertex (corner).

Question 31.

Figure _____________
Base is _____________
Number of faces _____________
Number of edges _____________
Number of vertices _____________
Answer:
Figure is Triangular Pyramid,
Base is Triangle,
Number of faces 4,
Number of edges 6,
Number of vertices 4.
Explanation:
A triangular pyramid is a pyramid with a triangular base.
All triangular-based pyramids, either regular or irregular, have four vertices and faces.
Triangular-based pyramids have 6 edges.

Question 32.

Figure _____________
Base is _____________
Number of faces _____________
Number of edges _____________
Number of vertices _____________
Answer:
Figure is Triangular Prism,
Base is Triangle,
Number of faces 5,
Number of edges 9,
Number of vertices 6.
Explanation:
A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides.
It is a three-dimensional shape that has three side faces and two base faces,
connected to each other through nine edges.
Base of a triangular prism is triangle with 6 vertices.

Identify the figures.

Question 33.

Answer:
Pentagon.
Explanation:
Penta denotes five and gon denotes angle.
A pentagon is a simple polygon, which has five sides and five angles.

Question 34.

Answer:
Hexagon.
Explanation:
Hexa means six and gona means angles.
A hexagon is a closed two-dimensional polygon with six sides.
Hexagon has 6 vertices and 6 angles.

Question 35.

Answer:
Heptagon.
Explanation:
Hepta means seven and gon means sides.
A Heptagon is a polygon with seven sides and seven angles.
It has seven straight sides and seven corners or vertices.

Question 36.

Answer:
Octagon.
Explanation:
An Octagon is an 8-sided polygon, also called 8-gon, in a two-dimensional plane.
Octagon is a polygon that has 8 sides and 8 angles.
The number of vertices and edges of an octagon is 8.

Question 37.

What is the circumference of the circle? (Use 3.14 for π). What is the area of the circle?
Answer:
Circumference = 18.84 cm;
Area = 28.26 sq units.
Explanation:
A = π r2
r = 3 cm
A = 3.14 x 3 x 3
A = 28.26 sq cm
The circumference of the circle (Use 3.14 for π)
C = 2πr
C = 2 x 3.14 x 3
C = 18.84 cm

Question 38.

Jerome bought a present that came in a box that looked like the figure above. If he wants to wrap the present before he gives it to his sister, how much wrapping paper will he need to wrap the present?
Answer:
148 sq cm
Explanation:
TSA – Total Surface Area to be calculated
the surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA = 2lw + 2lh + 2hw, to find the surface area
TSA = 2(5 x 6 + 6 x 4 + 4 x 5)
TSA = 2(30 + 24 + 20)
TSA = 2 x 74
TSA = 148 sq cm

Question 39.

How many 1-inch cube wooden blocks can fit in the box shown in the figure?
Answer:
120 wooden blocks.
Explanation:
The formula for the volume of the cuboid can be derived from the concept explained on rectangular sheets.
Let the area of a rectangular sheet of paper be ‘A’,
the height up to which they are stacked be ‘h’ and the volume of the cuboid be ‘V’.
Then, the volume of the cuboid is given by multiplying the base area and height.
The volume of cuboid = Base area × Height
The base area for cuboid = l × b
Hence, the volume of a cuboid, V = l × b × h = lbh
Volume of a cuboid = (length × breadth × height) cubic units.
= (l × b × h) cubic units.
= (10 x 6 x 2) cubic units
= 120 cubic units

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 21–23 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 21–23 Answer Key

Review the graph and answer the following questions.

Question 1.
Is there more trash on the beach due to plastic or paper?
Answer:
Plastic
Explanation:
Observe the graph of Trash on Beach,
Plastic is more than paper.
Total amount of plastic is 5000 and paper less than it.

Question 2.
Which material accounts for more than twice as much trash on the beach as Styrofoam?
Answer:
Cigarettes
Explanation:
Observe the graph of Trash on Beach,
Styrofoam is around 7000,
Cigarettes is around 14000,
So, Cigarettes are as twice as much trash on the beach as Styrofoam.

Question 3.
What material accounts for the least amount of trash on the beach?
Answer:
Wood
Explanation:
Observe the graph of Trash on Beach,
The least amount of trash is wood i.e., around 2000.

Use data from the graphs to answer the following questions.

Question 4.
Which city has the highest average temperature in the summer? ____________
The lowest? ____________________________
Answer:
Highest temperature is Orlando,
Lowest temperature is Omaha.
Explanation:
The above chart shows the U.S city summer temperatures.
When compared with all the city temperatures,
Highest temperature is Orlando more than 80 °F,
Lowest temperature is Omaha below 70 °F.

Question 5.
The average temperature of Chicago is 4 degrees warmer than Cleveland, true or false? ___________
Answer:
True
Explanation:
The above chart shows the U.S city summer temperatures.
When compared with the average temperature of Chicago it is 4 degrees warmer than Cleveland.

Question 6.
Which city is cooler during the summertime, San Francisco or Milwaukee?
Answer:
San Francisco
Explanation:
The above chart shows the U.S city summer temperatures.
When compared with the average temperature of San Francisco and Milwaukee,
San Francisco is cooler during summer time.

Question 7.
On what day did Jason practice his guitar the most? __________
The least? ___________________
Answer:
Jason practice his guitar the most on Thursday.
The least on Monday.
Explanation:
Observe the above chart of Jason’s Guitar practice schedule.
On Thursday he practiced more number of hours rather than other days.
On Monday he practiced less hours.

Question 8.
Jason practices 2.5 hours more on Thursday than on what other day?
Answer:
Monday.
Explanation:
Observe the above chart of Jason’s Guitar practice schedule.
On Thursday he practiced he practiced for 3.5 hours
On Monday he practiced for one hour.
3.5 – 1 = 2.5
So, Jason practices 2.5 hours more on Thursday than on Monday.

Question 9.
What is the total number of hours that Jason practices from Monday to Saturday?
Answer:
13\(\frac{1}{2}\) or 13.5 hours.
Explanation:
Observe the above chart of Jason’s Guitar practice schedule.
On Monday he practiced for 1 hour.
On Tuesday he practiced for 1.5 hours.
On Wednesday he practiced for 3 hours.
On Thursday he practiced for 3.5 hours.
On Friday he practiced for 2 hours.
On Saturday he practiced for 2.5 hours.
The total number of hours that Jason practices from Monday to Saturday is,
1 + 1.5 + 3 + 3.5 + 2 + 2.5 = 13.5 hours
13\(\frac{1}{2}\) hours.

Question 10.
In what year did Rocco hit more home runs than doubles?
Answer:
2009
Explanation:
From the above given chart of Rocco’s Baseball Statistics,
Rocco hit more home runs than doubles in 2006.

Question 11.
One year, Rocco injured his leg sliding into second base and missed some games while he recovered. What year do you think that was?
Answer:
2006
Explanation:
From the above given chart of Rocco’s Baseball Statistics,
In 2006 his score is less than compared with other years.
So, Rocco injured his leg sliding into second base and missed some games while he recovered.

Question 12.
Fredo is planning the menu for his restaurant. He conducted a survey of restaurant guests and converted that information into a circle graph. Based on the data, what is the most popular type of entree that Fredo’s restaurant serves?

Answer:
Chicken
Explanation:
The above chart shows the Meal Entree Orders of Fredo’s Restaurant.
The most popular type of entree that Fredo’s restaurant serves is chicken.

Question 13.
Based on the data, which is more popular as an entree, fish or meat?
Answer:
Fish
Explanation:
The above chart shows the Meal Entree Orders of Fredo’s Restaurant.
When compared with the fish or meat serves in the entree of Fredo’s restaurant is Fish.

Question 14.
Fredo would like to add more vegetarian entrees, but he won’t until at least 10% of the patrons want them. Should Fredo add more vegetarian entrees, and why?
Answer:
Yes, 17% ordered vegetarian meals.
Explanation:
The above chart shows the Meal Entree Orders of Fredo’s Restaurant.
Yes, Fredo would add more vegetarian entrees,
because 17% ordered vegetarian meals.

Question 15.
Look at the following data group: 2, 3, 5, 8, 8, 9, 16, 24, 28, 40, 44
What is the median of the data group? ____________________
What is the mean? ______________________
What is the range? ____________________
Answer:
Median = 9
Mean = 17
Range = 42
Explanation:
First Range of data is the difference between the highest and the lowest values of the data
data group: 2, 3, 5, 8, 8, 9, 16, 24, 28, 40, 44
Range = 44 – 2 = 42
Mean:
Find the sum of the values by adding them all up.
Divide the sum by the number of values in the data set.
Mean = \(\frac{2+3+5+8+8+9+16+24+28+40+44}{11}\)
= \(\frac{187}{11}\) = 17
Median:
 First, arrange the given data in ascending order.

Next, we need to pick the middlemost data.
For the odd number of data points, there is only one middle data point,
we can take it as the median of the data as 9 as rounded shown in the

Question 16.
Put the following data into a stem-and-leaf plot:
19, 22, 22, 25, 26, 27, 28, 30, 34, 36, 37, 44, 44, 44, 45, 48, 48, 49, 50, 53, 55, 57, 58, 64, 67
What is the mode of the set of data? ___________________
What is the median? ___________________
What is the mean? ___________________
Answer:
Mode = 44
Median = 44
Mean = 41.3
Explanation:
a stem-and-leaf plot:

The mode is the number or numbers that occur the most frequently.
44 is occur most frequently
as per the above stem leaf plot
mode of the above data is 44
Median:
 First, arrange the given data in ascending order.

Next, we need to pick the middlemost data.
For the odd number of data points, there is only one middle data point,
we can take it as the median of the data as 44 as rounded shown in the
Mean:
Find the sum of the values by adding them all up.
Divide the sum by the number of values in the data set.
Mean = \(\frac{19, 22, 22, 25, 26, 27, 28, 30, 34, 36, 37, 44, 44, 44, 45, 48, 48, 49, 50, 53, 55, 57, 58, 64, 67}{25}\)
= \(\frac{1032}{25}\) = 41.3

Question 17.
What is the approximate range of the third quartile?

What is the median of the data? ___________________
What is the range of the data? ___________________
Answer:
Third quartile range = 14
Median = 22
Range of data = 45
Explanation:

First Range of data is the difference between the highest and the lowest values of the data
max – min = 50 – 5 = 45
Median = 22 is the Q2 center of the data given in the picture
Third quartile range = Q3 – Q2 = 36 – 22 = 14

Question 18.
How many of the outcomes in this tree diagram result in having less than two tails?

Answer:
4
Explanation:

Less then two tails combination are rounded in the above picture, total 4 combinations are identified

Question 19.
James conducted a survey of students in his class. He found that out of the 50 people he surveyed, 35 used a backpack to carry their books and 28 carried calculators. If 13 students carried a calculator and a backpack, how many students carry only a backpack?

Fill in the Venn Diagram to model the problem.
Answer:
22

Explanation:
As in the above venn diagram yellow circle 22 students used backpack to carry their books.
A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits. Venn diagrams help to visually represent the similarities and differences between two concepts.

Question 20.
What does this Venn Diagram tell you?

Answer:
7 people liked both volleyball and football;
47 people in total were surveyed;
20 people liked only volleyball and
20 people only liked football.
Explanation:
As in the above venn diagram
7 people liked both volleyball and football;
47 people in total were surveyed;
20 people liked only volleyball and
20 people only liked football.
A Venn diagram is an illustration that uses circles to show the relationships among things or finite groups of things. Circles that overlap have a commonality while circles that do not overlap do not share those traits.

Question 21.
You have a bag of 20 markers, 5 of which are green, 3 of which are red, 7 of which are yellow, 3 of which are blue, and 2 of which are orange. What is the chance of reaching into the bag and pulling out a yellow marker? _________________
Anything but a green marker? _________________
Answer:
Yellow marker \(\frac{7}{20}\);
Green marker \(\frac{15}{20}\) or \(\frac{3}{4}\)
Explanation:
First sample space ={5(green)+3(red)+7(yellow)+3(blue)+2(orange)} = 20 markers,
means if we pic one marker we can get either of the 5 of which are green, 3 of which are red, 7 of which are yellow, 3 of which are blue, and 2 of which are orange marker.
the chance of reaching into the bag and pulling out a yellow marker is the probability of yellow marker
Yellow marker = \(\frac{7}{20}\)
any market except Green marker = all markers – green markers divided by total markers
= \(\frac{20 – 5}{20}\)
= \(\frac{15}{20}\) or \(\frac{3}{4}\)

Question 22.
A grocery store did a taste test of 3 brands of cookies. In a random survey of 50 people walking down the street in front of the store, 20 people said they preferred Brand A, 14 people preferred Brand B, and 16 people preferred Brand C. Which of the following is the most valid conclusion?
(a) The grocery store should stop selling Brand B.
(b) Brands B and C have roughly the same popularity.
(c) Brand A is twice as popular as Brand B.
Answer:
B
Explanation:
A taste test of 3 brands of cookies in a random survey of 50 people walking down the street in front of the store, 20 people said they preferred brand A,
14 people preferred brand B,
and 16 people preferred brand C
brands B and C have roughly the same popularity.

Question 23.
Find the mean absolute deviation for the values below.

Answer:
MAD = 8
Explanation:
Average = \(\frac{sum of the scores}{number of the scores}\)
= \(\frac{84 + 68 + 92 + 76}{4}\)
= \(\frac{320}{4}\) = 80
finding the difference between score and average score
I 84 – 80 I = 4
I 68 – 80 I = 12
I 92 – 80 I = 12
I 76 – 80 I = 4
average of the differences,
= \(\frac{4 + 12 + 12 + 4}{4}\)
= \(\frac{32}{4}\) = 8
mean absolute deviation (MAD) = 8.

Question 24.
Andy did a random survey to find out what type of pet is most popular in his town. 17 people chose dogs, 18 people chose cats, and 6 people chose fish. Complete the probability model.

Answer:

Explanation:
The probability model total samples are 17 + 18 + 6 = 41
probability of 17 people chose dogs out of 41 samples is
P(Dog) = \(\frac{Number of Dogs}{total samples}\)
= \(\frac{17}{41}\)
= 0.41
probability of 18 people chose cats out of 41 samples is
P(Dog) = \(\frac{Number of Cats}{total samples}\)
= \(\frac{18}{41}\)
= 0.44
probability of 6 people chose dogs out of 41 samples is
P(Dog) = \(\frac{Number of fish}{total samples}\)
= \(\frac{6}{41}\)
= 0.15

Question 25.
Alex rolls a pair of six-sided dice. What is the probability that he will roll a 2 and a 6?
Answer:
\(\frac{1}{36}\)
Explanation:
Alex rolls a pair of six-sided dice,
Probability of two dies with 6 sides.
6 x 6 = 36 samples
only one time we can see the combination that he will roll a 2 and a 6
as all combinations are given below.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 18–20 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 18–20 Answer Key

Question 1.
Armando is going to replace the trim around all of the doors in his house. The outside of each door measures 18 \(\frac{1}{2}\) feet. If he has 9 doors, how many inches of trim does he need to replace?
Answer:
1998 inches of trim.
Explanation:
18\(\frac{1}{2}\) convert in to inches
18 x 12 + \(\frac{1}{2}\) x 12
= 216 + 6
= 222
So, 222 x 9 = 1998 inches of trim.

Question 2.
Ashley wants to empty her fish tank before she cleans it. The fish tank holds 34 gallons. She is using a one-quart container to empty the tank by hand. How many full containers will she need to empty the tank?
Answer:
136 quarter containers need to empty the tank.
Explanation:
1 gallon = 4 quarters
The fish tank holds 34 gallons,
= 4 x 34 = 136 quarters
136 quarter containers need to empty the tank.

Question 3.
Annika weighed boxes for shipping books to customers. The first box weighed 160 ounces, the second box 3 weighed 10 \(\frac{3}{8}\) pounds, and the third box weighed \(\frac{1}{200}\) ton. Which box weighed the most?
Answer:
Second box weighed the most.
Explanation:

To compare the three boxes all should be of same units,
first convert the weights are in one unit pounds,
first box weighed 160 ounces = 10 pounds,
the second box 3 weighed 10 \(\frac{3}{8}\) pounds,
the third box weighed \(\frac{1}{200}\) ton = 1 pound,
Second box weighed the most.

Question 4.
Mandie wants to fence in her corral, and needs to know how much fencing to purchase. The corral has an irregular shape, with sides of 25 \(\frac{1}{4}\) feet, 330 inches, 6 yards, one foot, \(\frac{3}{160}\) of a mile, and 9 feet. How much fence material will she need?
________________ feet
Answer:
179.75 ft
Explanation:
All measures are converted in to one units as feet.
25 \(\frac{1}{4}\) feet = 25.25ft
330 inches = 27.5 ft
6 yards = 18 ft
one foot = 1
\(\frac{3}{160}\) of a mile = 99 ft
9 feet = 9 ft
25 \(\frac{1}{4}\) feet, 330 inches, 6 yards,
one foot, \(\frac{3}{160}\) of a mile, and 9 feet.
= 25.25 + 27.50 + 18 + 1 + 99 + 9
= 179.75 ft

Question 5.
What is the area of a rectangle with a length of 20 feet and a width of 144 inches?

_____________ square feet
Answer:
240 square feet.
Explanation:
144 in to be converted in to ft by dividing 12.
144/12 = 12 ft
the area of a rectangle = length x width.
A = l x w
A = 20 x 12
A = 240 sq ft

Question 6.
What is the area of a right triangle with sides of 6 feet, 8 feet, and 120 inches?

_____________ square feet
Answer:
24 sq ft.
Explanation:
120 in to be converted in to ft by dividing 12.
120/12 = 10 ft
the area of a triangle = (1/2) base x height,
A = (1/2) b x h
A = 0.5 x 6 x 8
A = 24 sq ft.

Question 7.
What is the volume of a rectangular box with sides of 48 inches and 3 \(\frac{1}{2}\) feet, and a height of 30 inches?

______________ cubic feet
Answer:
V = 35cu ft
Explanation:
To be converted in to ft by divide by 12.
30/12 = 2.5 ft
48/12 = 4 ft
Volume of a rectangular box V = l x b x h
V = 3.5 x 2.5 x 4
V = 35cu ft

Question 8.
A modern spacecraft must travel 8.1 miles per second in order to reach the planet Mars. How far does the spacecraft travel in a minute?
in an hour? ______________
in a day? ______________
Answer:
486 miles in a minute,
160 miles in an hour,
699,840 miles in a day.
Explanation:
8.1 miles per second.
1 minute = 60 seconds.
8.1 x 60 = 486 miles in a minute.
1 hour = 60 minutes.
486 x 60 = 29,160 miles in an hour.
1 day = 24 hours.
29,160 x 24 = 699,840 miles in a day.

Question 9.
If the distance to the moon from the earth is 248,000 miles, how long does it take the spacecraft in the previous exercise to travel to the moon? How many times a day could the spacecraft go back and forth between the moon and the earth?
Answer:
8.5 hours and 3 times.
Explanation:
The distance to the moon from the earth is 248,000 miles.
A modern spacecraft must travel 8.1 miles per second in order to reach the planet Mars,
486 x 60 = 29,160 miles in an hour.
248,000/29,160 = 8.5 hours.
8 x 3 = 24 hours.
Number of times in a day the spacecraft could go back and forth between the moon and the earth,
24 / 8.5 = 2.8 or 3 times.

Question 10.
The world record for the shot put is 23.12 meters. The world record for the discus throw is 74.08 meters. How many centimeters longer is the record for the discus throw than the record for the shot put?
Answer:
5096 cm
Explanation:
The shot put is 23.12 meters.
The discus throw is 74.08 meters.
Difference between disc throw and shot put,
74.08 – 23.12 = 50.96 meters.
1 meter = 100 cm.
50.96 x 100 = 5096 cm.

Question 11.
Stacey is measuring fabric for her grandmother, who is going to make a rectangular banner for the school. The banner will be 6.5 meters in length and 2,350 millimeters in width. How much fabric will Stacey’s grandmother need to buy?
______________ sq cm
Answer:
152,750sq cm
Explanation:
The banner will be 6.5 meters in length and 2,350 millimeters in width.
In the above given information, both units are of different to be converted to one unit.
Lets convert in to centimeters as below,
length = 6.5 meter x 100 cm = 650 cm
width = 2,350millimeters /10 = 235.0 cm
Area of a rectangle = Length x width
A = 650 x 235
A = 152,750 sq cm.

Question 12.
Sharon has three cans of latex paint to recycle. One can holds 2,957 milliliters of paint, the second can holds 105.6 centiliters of paint, and the third can holds 3.9 liters of paint. How much paint, in total, will Sharon be recycling?
______________ liters
Answer:
7.913 liters
Explanation:
In the given information all are of different units,
which are to be converted in to one unit as below to find out the total paint recycling.
One can holds 2,957 milliliters = 2.957 liters of paint,
the second can holds 105.6 centiliters =1.056 liters of paint,
and the third can holds 3.9 liters of paint.
paint, in total, will Sharon be recycling = 2.957 + 1.056 + 3.9
= 7.913 liters.

Question 13.
What is the area of a triangle with sides of 8 cm, 8 cm, a base of 4 cm, and a height of 6 cm?

_______________ sq cm
Answer:
12 sq cm
Explanation:
The area of a triangle with  a base of 4 cm, and a height of 6 cm.
A = (1/2) x base x height
A = 0.5 x 4 x 6
A = 12 sq cm.

Question 14.
Jerrie walked around the entire rectangular school parking lot, which measures 106 meters by 7,500 centimeters. How far did Jerrie walk?
______________ meters
Answer:
Jerrie walks 362 meters.
Explanation:
In the given information all are of different units,
which are to be converted in to one unit as shown below.
Rectangular school parking lot, measures 106 meters long and 7,500 centimeters.
1 meter = 100 cm
7500 ÷ 100 =75 meters wide.
The perimeter of a rectangular park to be calculate as shown below.
P = 2(Length + Width)
P = 2 (106 + 75)
P = 2 (181)
P = 362 meters
So, Jerrie walks 362 meters.

Question 15.
How much topsoil can fit into a rectangular dump truck that measures 3.6 meters in width, 6.5 meters in length, and 3.5 meters high?
______________ cu meters
Answer:
81.9 cu meters.
Explanation:
The given information to find out the volume of the rectangular cuboid is,
3.6 meters in width, 6.5 meters in length, and 3.5 meters high.
Volume V = Length x Width x Height
V = 3.6 x 6.5 x 3.5
V = 81.9 cu meters

Question 16.
The average player on the soccer team measures 5 feet, 11 inches tall. About how tall is that in centimeters?
Answer:
180.34 cm
Explanation:
In the given information all are of different units,
which are to be converted in to one unit as shown below.
player on the soccer team measures 5 feet, 11 inches tall.
5 feet x 30 cm = 152.4 cm
11 inches x 2.5 = 27.94 cm
5 feet, 11 inches = 152.4 + 27.94
= 180.34 cm

Question 17.
The average taxicab has a gas tank that holds 85 liters of gasoline. How much is that in quarts?
______________ quarts
In gallons?
______________ quarts
Answer:
89.8 quarts;
22.45 gallons.
Explanation:
we know,
1 quart = 1.0567 liters
A gas tank holds 85 liters of gasoline.
85 x 1.0567 = 89.8 quarts,
1 gallon = 4 quarters = 3.7854 liters
85 /3.7854 = 22.45 gallons

Question 18.
Pauline measured a rectangular box and found that its dimensions were 55 inches by 32 inches by 20 inches tall. What is the total outside surface area in square inches?
_______________ sq in
In square feet? ______________ sq ft
Answer:
7000 sq in;
48.61 sq ft.
Explanation:
To find the surface area of a cuboid, add the areas of all 6 faces.
Dimensions were length 55 inches, width 32 inches and height 20 inches.
We can also label the length (l), width (w), and height (h) of the prism and use the formula as,
the surface area SA = 2lw + 2lh + 2hw
SA = 2 (55 x 32 + 32 x 20 + 20 x 55)
SA = 2 x (1760 + 640 +1100 )
SA = 2 x 3500
SA = 7000 sq in
To convert square in to sq foot by multiplying by 0.006944.
SA = 7000 sq in
SA = 7000 x 0.006944 = 48.61 sq ft.

Question 19.
A body temperature of 103.6° F is considered an extremely high fever. What temperature is that in Celsius?
Answer:
C = 39.7738° C
Explanation:
To convert temperatures in degrees Fahrenheit to Celsius,
subtract 32 and multiply by 0.5555 (or 5/9).
The notation C represents the temperature in Celsius, and F is the temperature in Fahrenheit.
C = 5/9 x (F – 32)
C = 0.5555 x (103.6 – 32)
C = 0.5555 x (71.6)
C = 39.7738° C

Question 20.
In track and field, the standard middle distance event is the 5,000 meters. About how many feet is 5,000 meters?
_____________ feet
Answer:
16,404 ft.
Explanation:
1 meter = 3.28 feet
5,000 meters = 5000 x 3.2808 ft
= 16,404 ft.

Question 21.
What is the volume of the rectangular pyramid?

Answer:
35 cu cm.
Explanation:
Area of rectangular base = length x width
B = 7 x 3 = 21 sq cm
volume of the rectangular pyramid = 1/3 x B x h
V = (1/3) x 21 x 5 = 35 cu cm.

Question 22.
What is the volume of the triangular solid?

Answer:
144 cubic in.
Explanation:
Volume of the triangular solid = Bh (Area of base x height)
B = Area of base = 1/2 bxh
B = 1/2 x 6 x 8 = 24 sq in
Volume V = Bh
V = 24 x 6
V = 144 cubic in

Question 23.
The air conditioning company suggests that people keep the temperature in their homes between 23 and 26 degrees Celsius during the summer. What is that range in degrees Fahrenheit?
Answer:
73.4 – 78.8 degrees Fahrenheit.
Explanation:
To convert temperatures in degrees Celsius to Fahrenheit,
add 32 and multiply by 1.8 (or 9/5).
The notation C represents the temperature in Celsius, and F is the temperature in Fahrenheit.
F = 9/5 x (C + 32)
If C = 23
F = 9/5 x (23 + 32)
F = \(\frac{9 X 23}{5}\) + 32
F = \(\frac{207}{5}\) + 32
F = 41.4 + 32
F = 73.4° F
If C = 26
F = 9/5 x (26 + 32)
F = \(\frac{9 X 26}{5}\) + 32
F = \(\frac{234}{5}\) + 32
F = 46.8 + 32
F = 78.8° F

Question 24.
The distance of a flight from Boston to Chicago is about 1,200 miles. The average ground speed for a commercial airliner is about 850 kilometers per hour. About how long will it take to fly from Boston to Chicago?
_______________ hours
Answer:
2\(\frac{1}{4}\)
Explanation:
Converting kilometers per hour in to miles per hour.
By multiplying the kilometer number with 0.62137 to get in miles.
850 x 0.62137 = 528.1645 miles per hour
Distance = Speed x Time
to calculate, how long will it take to fly from Boston to Chicago
Time = distance / speed
Time = 1200/528.1645 = 2.27 hours or 2\(\frac{1}{4}\) hours.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 16–17 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 16–17 Answer Key

Restate in exponential form then calculate.

Question 1.
8 × 8 × 2 + 3 × 3 × 3
Answer:
155
Explanation:
8 × 8 × 2 + 3 × 3 × 3
= 8²× 2 + 3³
= 155
Question 2.
2 × 2 × 4 × 4 – 3 × 3 × 3
Answer:
37
Explanation:
2 × 2 × 4 × 4 – 3 × 3 × 3
= 2² × 4² – 3³
= 2² x 2² × 2² – 3³
= 2⁶ – 3³
= 64 – 27
=37
Question 3.
5 × 25 × 2 × 2 × 4 × 4 + 7 × 7 – 5 × 5
Answer:
8024
Explanation:
5 × 25 × 2 × 2 × 4 × 4 + 7 × 7 – 5 × 5
=5³ × 2² x 4² x 7² – 5²
=125 x 4 x 16 x 49 – 25
= 8024

Restate using scientific notation.

Question 4.
13,654,764.011
Answer:
1.3654764011 x 10⁷
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10.
b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number.
1.3654764011 x 10⁷

Question 5.
28,397.01
Answer:
2.839701 x 10⁴
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Such that the absolute value of a is greater than or equal to one and less than ten or,
1 ≤ |a| < 10.
b is the power of 10 required,
so that the scientific notation is mathematically equivalent to the original number.

Question 6.
.100745
Answer:
1.00745 x 10^-1
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Such that the absolute value of a is greater than or equal to one and less than ten or,
1 ≤ |a| < 10.
b is the power of 10 required,
so that the scientific notation is mathematically equivalent to the original number.

Question 7.
21,194,668,041.1
Answer:
2.11946680411 x 10¹⁰
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Such that the absolute value of a is greater than or equal to one and less than ten or,
1 ≤ |a| < 10.
b is the power of 10 required,
so that the scientific notation is mathematically equivalent to the original number.

Question 8.
813.056
Answer:
8.13056 x 10²
Explanation:
The proper format for scientific notation is a x 10^b where a is a number or decimal number.
Such that the absolute value of a is greater than or equal to one and less than ten or,
1 ≤ |a| < 10.
b is the power of 10 required,
so that the scientific notation is mathematically equivalent to the original number.

Calculate.

Question 9.
3³
Answer:
aⁿ = a x a x a ….a(n times)
3³ = 3 x 3 x 3
= 27
Question 10.
8⁴
Answer:
4096
Explanation:
aⁿ = a x a x a ….a(n times)
8⁴ = 8 x 8 x 8 x 8
= 4096

Question 11.
2³ × 2^-2
Answer:
2
Explanation:
a^m + aⁿ = a^m+n
2³ × 2^-2
= 2^3-2
= 2
Question 12.
10^-8 ÷ 10^-9
Answer:
Explanation:
10^-8 ÷ 10^-9
a^m ÷ aⁿ = a^m-n
10^-8 ÷ 10^-9
= 10^-8 × 10⁹
= 10^{9 – 8}
= 10

Question 13.
15¹¹ × 15^-11
Answer:
Explanation:
a^m + aⁿ = a^m+n
15¹¹ × 15^-11
= 15^{11 – 11}
= 15⁰
= 1  (a⁰ = 1)

Question 14.
\(\sqrt{49}\)
Answer:
7
Explanation:
\(\sqrt{49}\)
= \(\sqrt{7 X 7}\)
= 7

Question 15.
\(\sqrt{64}\)
Answer:
8
Explanation:
\(\sqrt{64}\)
= \(\sqrt{8 X 8}\)
= 8

Question 16.
\(\sqrt{16}\)
Answer:
4
Explanation:
\(\sqrt{16}\)
= \(\sqrt{4 X 4}\)
= 4

Question 17.
\(\sqrt{1}\)
Answer:
1
Explanation:
\(\sqrt{1}\)
= \(\sqrt{1 X 1}\)
= 1

Question 18.
\(\sqrt{25}\)
Answer:
5
Explanation:
\(\sqrt{25}\)
= \(\sqrt{5 X 5}\)
= 5

Solve for x.

Question 19.
x – 15 ≤ 23
Answer:
x ≤ 38
Explanation:
x – 15 ≤ 23
x ≤ 23 + 15
x ≤ 38

Question 20.
3 + x ≥ 4
Answer:
x ≥ 1
Explanation:
3 + x ≥ 4
x ≥ 4 – 3
x ≥ 1

Question 21.
5x < 650
Answer:
x < 130
Explanation:
5x < 650
x < 650/5
x < 130

Question 22.
3x – 6 > 36
Answer:
x > 14
Explanation:
3x – 6 > 36
3x > 36 + 6
3x > 42
x >42 / 3
x > 14

Question 23.
\(\frac{x}{4}\) ≤ 8
Answer:
x ≤ 32
Explanation:
\(\frac{x}{4}\) ≤ 8
x ≤ 8 x 4
x ≤ 32

Question 24.
6 + x = 13
Answer:
x = 7
Explanation:
6 + x = 13
x = 13 – 6
x = 7

Question 25.
x – 15 = 22
Answer:
x = 7
Explanation:
x – 15 = 22
x = 22 – 15
x = 7

Question 26.
39 – x = 25
Answer:
x = 14
Explanation:
39 – x = 25
39 – 25 = x
x = 14

Question 27.
x + 60 = 90
Answer:
x = 30
Explanation:
x + 60 = 90
x = 90 – 60
x = 30

Question 28.
6x + 3 = 33
Answer:
x = 5
Explanation:
6x + 3 = 33
6x = 33 – 3
6x = 30
x = 30/6
x = 5

Question 29.
4x – 5 = 19
Answer:
x = 6
Explanation:
4x – 5 = 19
4x = 19 + 5
4x = 24
x = 24/4
x = 6

Question 30.
6x + 3 = 45
Answer:
x = 7
Explanation:
6x + 3 = 45
6x = 45 – 3
6x = 42
x = 42/6
x = 7

Question 31.
2x + 14 = 42
Answer:
14
Explanation:
2x + 14 = 42
2x = 42 – 14
2x = 28
x = 28/2
x = 14

Question 32.
4 – 4x = -48
Answer:
x = 13
Explanation:
4 – 4x = -48
– 4x = -48 – 4
– 4x = -52
x = 52/4
x = 13

Question 33.
\(\frac{x}{6}\) + 3 = 12
Answer:
x = 54
Explanation:
\(\frac{x}{6}\) + 3 = 12
\(\frac{x}{6}\) = 12 – 3
x = 9 x 6
x = 54

Question 34.
\(\frac{x}{2}\) – 5 = 30
Answer:
x = 70
Explanation:
\(\frac{x}{2}\) – 5 = 30
\(\frac{x}{2}\) = 30 + 5
\(\frac{x}{2}\) = 35
x = 35 x 2
x = 70

Question 35.
\(\frac{1}{3}\)x – 4 = 16
Answer:
x = 60
Explanation:
\(\frac{1}{3}\)x – 4 = 16
\(\frac{1}{3}\)x = 16 + 4
\(\frac{1}{3}\)x = 20
x = 60

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 13–15 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 13–15 Answer Key

Determine if the following proportions are equal. (Write Yes or No.)

Question 1.
\(\frac{5}{4}\) = \(\frac{24}{16}\)
Answer:
NO
Explanation:
LHS = \(\frac{5}{4}\) x \(\frac{4}{4}\)
= \(\frac{20}{16}\)
LHS is not equal to RHS

Question 2.
\(\frac{21}{12}\) = \(\frac{7}{36}\)
Answer:
NO
Explanation:
LHS = \(\frac{21}{12}\) x \(\frac{3}{3}\)
= \(\frac{7}{4}\)
LHS is not equal to RHS

Question 3.
\(\frac{12}{19}\) = \(\frac{36}{57}\)
Answer:
YES
Explanation:
LHS = \(\frac{12}{19}\) x \(\frac{3}{3}\)
= \(\frac{36}{57}\) = RHS
LHS = RHS

Question 4.
\(\frac{1}{4}\) = \(\frac{6}{24}\)
Answer:
YES
Explanation:
LHS = \(\frac{1}{4}\) x \(\frac{6}{6}\)
= \(\frac{6}{24}\) = RHS
LHS = RHS

Solve for x.

Question 5.
\(\frac{x}{10}\) = \(\frac{30}{20}\)
Answer:
x = 15
Explanation:
\(\frac{x}{10}\) = \(\frac{30}{20}\)
x = \(\frac{30}{20}\) x 10
x =\(\frac{30 X 10}{20}\)
x =15

Question 6.
\(\frac{25}{x}\) = \(\frac{40}{100}\)
Answer:
x = 62.5
Explanation:
\(\frac{25}{x}\) = \(\frac{40}{100}\)
x = \(\frac{25}{40}\) x 100
x = 0.625 x 100
x = 62.5

Question 7.
\(\frac{33}{96}\) = \(\frac{11}{x}\)
Answer:
x = 32
Explanation:
\(\frac{33}{96}\) = \(\frac{11}{x}\)
by cross multiplying
33 x = 96 x 11
x = \(\frac{96 X 11}{33}\)
x = 32

Question 8.
\(\frac{1}{10}\) = \(\frac{20}{x}\)
Answer:
x = 200
Explanation:
\(\frac{1}{10}\) = \(\frac{20}{x}\)
by cross multiplying
1 x = 20 x 10
x = \(\frac{20 X 10}{1}\)
x = 200

Solve.

Question 9.
Create a ratio to compare the length of the side of a barn (140 ft) to the width of the barn (64 ft).
Answer:
\(\frac{35}{16}\) or 35 : 16
Explanation:
\(\frac{Length}{width}\)
= \(\frac{140}{64}\)
by dividing both numerator and denominator by 4 for simplification
we get = \(\frac{35}{16}\)

Question 10.
Create a ratio to compare the amount of unsaturated fat in salad dressing (5 grams) to the amount of carbohydrates (9 grams).
Answer:
\(\frac{5}{9}\) or 5 : 9
Explanation:
The amount of unsaturated fat in salad dressing (5 grams),
The amount of carbohydrates (9 grams).
= \(\frac{unsaturated fat in salad dressing (5 grams)}{carbohydrates (9 grams)}\)
= \(\frac{5}{9}\)

Question 11.
Wallace rides his bicycle at an average speed of 18 miles per hour. How many miles does he travel in 3 \(\frac{1}{3}\) hours?
Answer:
60 miles
Explanation:
Distance = Speed x Time
Distance = 18 x 3\(\frac{1}{3}\)
D = 18 x 3.33
D = 60 miles

Question 12.
Jermaine can make 29 loaves of bread for every 3 batches he bakes. How many batches of bread does he need to bake in order to make 232 loaves?
Answer:
24 batches
Explanation:
\(\frac{29}{3}\) = \(\frac{232}{x}\)
= \(\frac{3}{29}\) X \(\frac{232}{x}\)
x = \(\frac{232 X 3}{29}\)
x =8 x 3
x = 24

Question 13.
Phyllis drinks \(\frac{3}{4}\) of a pint of water after each mile she walks. How many pints of water will she drink if she walks 5 \(\frac{3}{4}\) miles?
Answer:
4\(\frac{5}{16}\)
Explanation:
\(\frac{3}{4}\) = 1 pints of water she drinks
5\(\frac{3}{4}\) = let x pints of water
x \(\frac{3}{4}\) = 5\(\frac{3}{4}\)
x = \(\frac{3}{4}\) x \(\frac{23}{4}\)
x = \(\frac{3 X 23}{4 x 4}\)
x = \(\frac{69}{16}\)
x= 4\(\frac{5}{16}\)

Question 14.
Ginny needs to check the air in her tires every 750 miles. How many times will she need to check her tires if she is taking a trip that is 6,750 miles in length?
Answer:
9 times
Explanation:
Ginny needs to check the air in her tires every 750 miles.
Number of times she need to check her tires,
if she is taking a trip that is 6,750 miles in length.
= \(\frac{6,750}{750}\)
= 9 times  (750 x 9 = 6,750)

Calculate.

Question 15.
30% of 1 \(\frac{2}{5}\)
Answer:
\(\frac{21}{50}\)
Explanation:
30% of 1 \(\frac{2}{5}\)
= 1 \(\frac{2}{5}\) x \(\frac{30}{100}\)
= \(\frac{7}{5}\) x \(\frac{3}{10}\)
= \(\frac{7 X 3}{5 X 10}\)
= \(\frac{21}{50}\)

Question 16.
40% of 440
Answer:
176
Explanation:
40% of 440
= 440 x \(\frac{40}{100}\)
= 4.4 x 40
= 176

Question 17.
\(\frac{1}{4}\) of 48%
Answer:
12%
Explanation:
\(\frac{1}{4}\) of 48%
= \(\frac{1}{4}\) x \(\frac{48}{100}\)
= 0.25 x 48%
= 12%

Question 18.
\(\frac{2}{5}\) of 70%
Answer:
28%
Explanation:
\(\frac{2}{5}\) of 70%
= 0.4 x 70%
= 28%

Question 19.
\(\frac{3}{8}\) of 340%
Answer:
127.5%
Explanation:
\(\frac{3}{8}\) of 340%
= 0.375 x 340%
= 127.5%

Question 20.
43% of 0.705
Answer:
0.30315
Explanation:
43% of 0.705
= \(\frac{43}{100}\) of 0.705
= 0.705 x 0.43
= 0.30315

Question 21.
84% of 1.906
Answer:
0.30315
Explanation:
84% of 1.906
= \(\frac{84}{100}\) of 1.906
= 1.906 x 0.84
= 1.60104

Question 22.
75% of .7575
Answer:
0.568125
Explanation:
75% of .7575
= \(\frac{75}{100}\) of 0.7575
= 0.7575 x 0.75
= 0.568125

Question 23.
Jessie deposited $824.25 of his babysitting money into . an account that pays 4.5% interest. How much will he have in his account at the end of one year?
Answer:
$861.35
Explanation:
Jessie deposited $824.25 of his babysitting money into an account that pays 4.5% interest.
SI = PRT/100
SI = 824.25 x 4.5 x 1 = 37.09125
Total amount in his account at the end of one year,
Amount = Principle + interest
Amount = 824.25 + 37.09125
Amount = $861.35

Question 24.
What is the annual rate of interest on a loan of $1,500 if you have paid a total of $120 in interest after two years?
Answer:
4%
Explanation:
The annual rate of interest on a loan of $1,500.
If paid a total of $120 in interest after two years,
SI = PRT/100
120 = 1500.00 x R x 2
R = 120 / 1500 x 2
R = 0.04
R= 4%

Question 25.
Chris bought a jacket that was marked $50 before tax. He paid $53.50 after tax. What percent tax did he pay? ______________
If the jacket was on sale and was originally marked $75, by what percent did the price decrease? ______________
Answer:
7%, 33%
Explanation:
A jacket that was marked $50 before tax.
He paid $53.50 after tax,
53.5 – 50 = 3
3.5/50 = 0.07 = 7%
The jacket was on sale and was originally marked $75,
by what percent did the price decrease.
50/75 x100 = 66.66
100 – 66.66 = 33.33
33% or 33.33%

Provide the ordered pairs for the points plotted on the graph.

Question 26.
A ______________
Answer:
A(1,3)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.
So, A(1,3).

Question 27.
B _______________
Answer:
B(4, 4)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.
So, B(4, 4).

Question 28.
C _______________
Answer:
C(-5, 2)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.
So, C(-5, 2)

Question 29.
D _______________
Answer:
B(4, -4)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, B(4, -4).

Question 30.
E _______________
Answer:
E(-4, -2)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, E(-4, -2).

Question 31.
F _______________
Answer:
F(7, 6)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, F(7, 6).

Question 32.
G _______________
Answer:
G(-2, 5)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, G(-2, 5).

Question 33.
H _______________
Answer:
H(-6, -6)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, H(-6, -6).

Question 34.
I _______________
Answer:
H(-3, 8)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, H(-3, 8).

Question 35.
J _______________
Answer:
J(3,- 8)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, J(3,- 8).

Plot the following points on the grid provided:

Question 36.
A (1, 4)
Answer:

Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, A(1, 4) is marked as above in the x, y plain.

Question 37.
B (4, 1)
Answer:

Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, b(4, 1) is marked as above in the x, y plain.

Question 38.
C (3, 9)
Answer:

Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, C(3, 9) is marked as above in the x, y plain.

Question 39.
D (-9, -3)
Answer:

Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, D(-9, -3) is marked as above in the x, y plain.

Question 40.
E (-4, 4)
Answer:

Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, E(-4, 4) is marked as above in the x, y plain.

Question 41.
F (-1, -4)

Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical line.
So, A(-1, -4) is marked as above in the x, y plain.

Question 42.
A train has 7 cars and can carry 224 people. If the train adds 2 extra cars, how many people can it carry? What is the unit rate per car?
Answer:
32 unit rate per car
64 people can carry
Explanation:
A train has 7 cars and can carry 224 people
one car carry = 224/7 = 32
each car carry 32 people
If the train adds 2 extra cars
7 + 2 = 9 cars
9 cars x 32 = 288
288 – 224 = 64 people.

Question 43.
How fast is Car A going?
Answer:
Speed = 1 mile per minute
Explanation:
Speed = Distance / Time
Speed = 5 / 5
Speed = 1 mile per minute

Question 44.
How fast is Car B going?
Answer:
Speed = 3 miles per minute
Explanation:
Speed = Distance / Time
Speed = 9 / 3
Speed = 3 miles per minute

Question 45.
How far will Car A have gone after 5 minutes?
Answer:
5 miles
Explanation:
Speed = 1 mile per minute
Time = 5 minutes.
Distance = speed x time
Distance = 1 x 5 miles

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Unit Test Lessons 1–5 existing for free of cost.

McGraw-Hill Math Grade 7 Unit Test Lessons 1-5 Answer Key

Add or subtract.

Question 1.

Answer:
311
Explanation:
Add the addends from the ones place,
carry the first number of the digit if any to get the sum.

Question 2.

Answer:
505
Explanation:
Add the addends from the ones place,
carry the first number of the digit if any to get the sum.

Question 3.

Answer:
1573
Explanation:
Add the addends from the ones place,
carry the first number of the digit if any to get the sum.

Question 4.

Answer:
4906
Explanation:
Add the addends from the ones place,
carry the first number of the digit if any to get the sum.

Question 5.

Answer:
652,576
Explanation:
Add the addends from the ones place,
carry the first number of the digit if any to get the sum.

Question 6.

Answer:
838
Explanation:
When the subratend is smaller than the minued,
then borrow from the next place of the number,
to find the difference.

Question 7.

Answer:
1219
Explanation:
When the subratend is smaller than the minued,
then borrow from the next place of the number,
to find the difference.

Question 8.

Answer:
6395
Explanation:
When the subratend is smaller than the minued,
then borrow from the next place of the number,
to find the difference.

Question 9.

Answer:
4889
Explanation:
When the subratend is smaller than the minued,
then borrow from the next place of the number,
to find the difference.

Question 10.

Answer:
379
Explanation:
When the subratend is smaller than the minued,
then borrow from the next place of the number,
to find the difference.

Round to the nearest thousand, then add or subtract.

Question 11.

Answer:
Nearest thousand is 21,000.
sum = 21,022
Explanation:
Nearest thousand to 6234 is 6000,
Nearest thousand to 14788 is 15000.
6000 + 15000 = 21000.
So, 21022 is nearest to 21000.

Question 12.

Answer:
Nearest thousand is 54,000.
sum = 53,931
Explanation:
Nearest thousand to 24573 is 25000,
Nearest thousand to 29358 is 29000.
25000 + 29000 = 54000.
So, 53931 is nearest to 54000.

Question 13.

Answer:
Nearest thousand is 67,000.
sum = 66,587
Explanation:
Nearest thousand to 12661 is 13000,
Nearest thousand to 44867 is 45000.
Nearest thousand to 9059 is 9000.
13000 + 45000 + 9000 = 67000.
So, 66587 is nearest to 67000.

Question 14.

Answer:
Nearest thousand is 71,000.
sum = 70,364
Explanation:
Nearest thousand to 15768 is 16000,
Nearest thousand to 44903 is 45000.
Nearest thousand to 9693 is 10000.
16000 + 45000 + 10000 = 71000.
So, 70364 is nearest to 71000.

Question 15.

Answer:
Nearest thousand is 90,000.
sum = 89,853
Explanation:
Nearest thousand to 79255 is 790000,
Nearest thousand to 5828 is 6000.
Nearest thousand to 4770 is 5000.
79000 + 6000 + 5000 = 90000.
So, 89853 is nearest to 90000.

Question 16.

Answer:
Nearest thousand is 9,000;
Difference = 8,576
Explanation:
Nearest thousand to 9870 is 10000,
Nearest thousand to 1294 is 1000.
10000 – 1000 = 9000.
So, 8576 is nearest to 9000.

Question 17.

Answer:
Nearest thousand is 14,000;
Difference = 13,890
Explanation:
Nearest thousand to 17650 is 18000,
Nearest thousand to 3760 is 4000.
18000 – 4000 = 14000.
So, 13890 is nearest to 4000.

Question 18.

Answer:
Nearest thousand is 10,000;
Difference = 10,263
Explanation:
Nearest thousand to 28735 is 29000,
Nearest thousand to 18472 is 19000.
29000 – 19000 = 10000.
So, 10263 is nearest to 10000.

Question 19.

Answer:
Nearest thousand is 12,000;
Difference = 11,716
Explanation:
Nearest thousand to 22908 is 23000,
Nearest thousand to 11192 is 11000.
23000 – 11000 = 12000.
So, 11716 is nearest to 12000.

Question 20.

Answer:
Nearest thousand is 38,000;
Difference = 37,866
Explanation:
Nearest thousand to 93556 is 94000,
Nearest thousand to 55690 is 56000.
94000 – 56000 = 38000.
So, 37866 is nearest to 38000.

Multiply or divide. Round to the nearest hundredth.

Question 21.

Answer:
Nearest hundredth of 3192 is 3000.
Explanation:

Question 22.

Answer:
Nearest hundredth of 22,356 is 22,000.
Explanation:

Question 23.

Answer:
Nearest hundredth of 21,850 is 22,000.
Explanation:

Question 24.

Answer:
Nearest hundredth of 30,260 is 30,000.
Explanation:

Question 25.

Answer:
Nearest hundredth of 48,766 is 49,000.
Explanation:

Question 26.

Answer:
Nearest hundredth is 14.
Explanation:

Question 27.

Answer:
Nearest hundredth is 21.
Explanation:

Question 28.

Answer:
Nearest hundredth of 58.25 is 58.
Explanation:

Question 29.

Answer:
Nearest hundredth of 18.36 is 18.
Explanation:

Question 30.

Answer:
Nearest hundredth of 13.35 is 13.
Explanation:

Round, then multiply or divide.

Question 31.

Answer:
Nearest number is 72,000;
product = 77,112
Explanation:
Nearest number of 918 is 900.
Nearest number of 84 is 80.
Ignore the zeros and multiply the numbers.
8 x 9 = 72
Then add the number of zeros to the product as 72,000.
So, nearest product of 77,112 is 72,000.

Question 32.

Answer:
Nearest number is 300,000;
product = 297,724
Explanation:
Nearest number of 9604 is 10000.
Nearest number of 31 is 30.
10,000 x 3 = 300,000
So, nearest product of 297,724 is 300,000.

Question 33.

Answer:
Nearest number is 24,000,000;
product = 21,996,652
Explanation:
Nearest number of 77453 is 80000.
Nearest number of 300 is 300.
Ignore the zeros and then multiply the numbers.
8 x 3 = 24
Then add the zeros to the product as 24,000,000.
So, nearest product of 21,996,652 is 24,000,000.

Question 34.

Answer:
Nearest number is 5,600,000;
product = 5,067,270
Explanation:
Nearest number of 13845 is 140000.
Nearest number of 366 is 400.
140,000 x 400 = 5,600,000
So, nearest product of 5,067,270 is 5,600,000.

Question 35.

Answer:
Nearest number is 48,000,000;
product = 46,163,126
Explanation:
Nearest number of 79867 is 80000.
Nearest number of 578 is 600.
80,000 x 600 = 48,000,000
So, nearest product of 46,163,126 is 48,000,000.

Question 36.

Answer:
3.09
Explanation:

3.0887 is round off to 3.09

Question 37.

Answer:
5.86
Explanation:

5.8571 is round off to 5.86

Question 38.

Answer:
16.68
Explanation:

Question 39.

Answer:
121.89
Explanation:

Question 40.

Answer:
1,025.57
Explanation:

Give the place value of the number 7 for questions 41-44.

Question 41.
1,845,732
__________
Answer:
7 is in Hundredth place.
Explanation:
7 is in hundredth place as shown below.

Question 42.
45.357
__________
Answer:
7 is in Thousandth place.
Explanation:
The value of digit depends on the place it occupies.

Question 43.
73,561,132.001
__________
Answer:
7 is in Ten millions place.
Explanation:
The value of digit depends on the place it occupies.

Question 44.
20.075
__________
Answer:
7 is in Hundredths place.
Explanation:
The value of digit depends on the place it occupies.

Question 45.
Parks Commissioner Davis is planning for the town’s upcoming fiscal year. Last year the town had a total of 2,435 visitors to its nature center, 7,693 visitors to its children’s park, and 9,287 visitors to its arboretum. How many visitors did the town’s parks have, in total, last year?
Answer:
19415 visitors
Explanation:
Last year the town had a total of 2,435 visitors to its nature center,
7,693 visitors to its children’s park,
9,287 visitors to its arboretum.
Total number of visitors to the town’s parks last year,
2,435 + 7,693 + 9,287 = 19,415

Question 46.
Last year Trey had 435 coins in his collection. This year Trey added 124 more coins to his collection. How many coins does he now have in his collection?
Answer:
559 coins
Explanation:
Last year Trey had 435 coins in his collection.
This year Trey added 124 more coins to his collection.
Total coins he now have in his collection 435 + 124 = 559 coins.

Question 47.
Edie’s favorite magazine has a total of 1,476 pages of advertising each year. If the magazine is published every month, about how many pages of advertising are in each issue?
__________________
How many pages exactly?
__________________
Answer:
About 120 pages;
123 pages exactly.
Explanation:
Edie’s favorite magazine has a total of 1,476 pages of advertising each year.
If the magazine is published every month,
Total pages of advertising in each issue every month,
1 year has 12 months.
1476 ÷ 12 =123 pages exactly,
about 120 pages every month.

Question 48.
At 1,776 feet in height, the new Freedom Tower in New York will be one of the tallest buildings in the world. What is the height of the building written in expanded form?
Answer:
(1 x 1000) + (7 x 100) + (7 x 100  (6 x 1)
Explanation:
Given height is 1,776 feet ,
In expanded form we write the numbers according to their place values.
1 in thousands place, 7 is in hundreds place, 7 is in tens place and 6 is in ones place.
(1 x 1000) + (7 x 100) + (7 x 100  (6 x 1)

Question 49.
What is the word form of the number 19,238,976?
Answer:
Nineteen million, two hundred thirty eight thousand, nine  hundred seventy six.
Explanation:
Given number 19,238,976
In word form we write the numbers according to their place values.
So, 19,238,976 is written as,
Nineteen million, two hundred thirty eight thousand, nine  hundred seventy six.

Calculate using order of operations (PEMDAS).

Question 50.
5 × (7 – 3)² + (19 — 5) × 2 + (6 – 3) × 2 + 2³
Answer:
122
Explanation:
5 × (7 – 3)² + (19 — 5) × 2 + (6 – 3) × 2 + 2³
= 5 × (4)² + (14) × 2 + (3) × 2 + 8
= 5 x 16 + 28 + 6 + 8
= 80 + 28 + 6 + 8
= 122

Question 51.
29 + (3 × 5) × 2 + (8 – 3)²
Answer:
84
Explanation:
29 + (3 × 5) × 2 + (8 – 3)²
= 29 + (15) × 2 + (5)²
= 29 + (15) × 2 + (5)²
= 29 + 30 +25
= 84

What number property does each expression display?

Question 52.
5 + (4 + 6) = (5 + 4) + 6
Answer:
Associative property of Addition.
Explanation:
a + (b + c) = (a + b) + c
5 + (4 + 6) = (5 + 4) + 6
15 = 15
Question 53.
2(6 + 3) = 2(6) + 2(3)
Answer:
Distributive property of Multiplication over Addition.
Explanation:
a x (b + c) = a x b + a x c
2(6 + 3) = 2(6) + 2(3)
2(9) = 12 + 6
18 = 18

Question 54.
15 + 16 + 18 = 18 + 16 + 15
Answer:
Commutative property of Addition.
Explanation:
Commutative property of Addition
a + b + c = c + b + a
15 + 16 + 18 = 18 + 16 + 15
31 + 18 = 34 + 15
49 = 49

Question 55.
24(1) = 24
Answer:
Identity property of Multiplication.
Explanation:
a x 1 = a
Identity property of Multiplication.
21 x 1 = 24

Question 56.
8 + 0 = 8
Answer:
Identity property of Addition.
Explanation:
Identity property of Addition.
a + 0 = a
Question 57.
20 × 1 = 20
Answer:
Identity property of Multiplication.
Explanation:
a x 1 = a
Identity property of Multiplication.
20 x 1 = 20

Question 58.
4 × (5 × 3) = (4 × 5) × 3
Answer:
Associative property of Multiplication.
Explanation:
a x (b x c) = (a x b) x c
4 × (5 × 3) = (4 × 5) × 3
4 x 15 = 20 x 3
60 = 60
Question 59.
63(0) + (63 + 0) = 0 + 63 = 63
Answer:
Zero property of Addition and Multiplication..
Explanation:
a x 0 + a + 0 = a
Zero property of Addition
a + 0 = a
Zero property of Multiplication.
a x 0 = 0
63(0) + (63 + 0) = 0 + 63 = 63

Solve each equation and indicate the point on the number line that corresponds with the answer.

Question 60.
-6 + 10 – 6 = ____
Answer:
D
Explanation:

-6 + 10 – 6 = 10 – 12 = – 2
Question 61.
-10 + 5 – 4 = ___
Answer:
C
Explanation:

-10 + 5 – 4 = 5 – 14 = – 9

Question 62.
-10 + (-4) + 8 = ___
Answer:
B
Explanation:

-10 + (-4) + 8
= 8 – 14
= – 6

Question 63.
9 – 5 + (-8) = ___
Answer:
A
Explanation:

9 – 5 + (-8)
= 9 – 5 – 8
= 9 – 13
= -4

Calculate.

Question 64.
—5 × 15
Answer:
-75
Explanation:
As -5 is negative integer multiplicand,
the product also negative integer, as below.
– 5 x 15 = – 75

Question 65.
-45 ÷ 9
Answer:
-5
Explanation:
As -45 is negative integer dividend,
the quotient also negative integer, as below.
-45 ÷ 9 = -5

Question 66.
63 ÷ (-7)
Answer:
-9
Explanation:
As -7 is negative integer divisor,
the quotient also negative integer, as below.
63 ÷ (-7) = -9

Question 67.
4 × (-6) ÷ -3
Answer:
8
Explanation:
4 x -6 = -24
-24 ÷ -3
As both the devisor and dividend are negative integers,
the result is positive integer, as shown below.
24 ÷ 3 = 8

Question 68.
Calculate: |-45| + |45| ___________
Answer:
90
Explanation:
45 is a absolute value with mod symbol,
Mod of any symbol get positive.
|-45| + |45| = 45 + 45 = 90

Question 69.
Which is larger: |-134| or |-135|? ________
Answer:
|-135|
Explanation:
|-135| is larger due to the 135 is a absolute value with mod symbol.

Question 70.
If Noah arrives 23 minutes late for an appointment and Matthew arrives 28 minutes early, who arrived closer to the correct time? ________________________________________________
Answer:
Noah
Explanation:

23 is closer to 0
Noah arrived closer to the correct time.