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Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 19.2 Types of Angles: Supplementary, Complementary, Interior, and Exterior to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 19.2 Types of Angles: Supplementary, Complementary, Interior, and Exterior

Exercises

IDENTIFY

Question 1.
From the figure below, give examples of two complementary, two supplementary and two vertical angles.
Complementary ________________
Supplementary ________________
Vertical ________________

Answer:
Complementary angles are CD, FG,
Supplementary angles are AD, CF,
Vertical angles are BE, AD,

Explanation:
Complementary: Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees. Vertical angles are angles opposite each other where two lines cross.
Vertical angles are angles that are opposite each other when two lines intersect
each other. The two pairs of opposite angles are equal to each other.
The two pairs of neighboring angles are supplementary, meaning they
add up to 180 degrees. Therefore given Complementary angles are CD,
FG, Supplementary angles are AD, CF, Vertical angles are BE, AD.

Question 2.
For the figure below, list all complementary and supplementary angles.

Complementary ________________
Supplementary ________________
Answer:
Complementary angles : Angle AC, Angle CE,
Supplementary: Angle AE or Angle EA,

Explanation:
Complementary: Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

Question 3.

Are angle DOB and angle DOC complementary? Explain.
Answer:
Yes, Complementary,

Explanation:
Yes angle DOB and angle DOC are complementary as there sum of angles of
DOB and DOC  is 90 degrees.

Question 4.
In the figure below, a line is intersecting two parallel lines. Fill in the missing information:

∠a = ∠_________ = ∠_________ = ∠___________
Answer:
∠a = ∠e = ∠d = ∠h,

Explanation:
The missing information a line is intersecting two parallel lines are
∠a = ∠e = ∠d = ∠h.

Question 5.
In the figure below, a line is intersecting two parallel lines. Fill in the missing angle measurements:

∠a = _________;
∠b = _________;
∠c = _________;
∠d = _________;
∠e = _________;
∠f = _________;
∠h = _________;
Answer:
∠a = 125 degrees;
∠b = 55 degrees;
∠c = 125 degrees;
∠d = 55 degrees;
∠e = 125 degrees;
∠f = 55 degrees;
∠g= 125 degrees,
∠h = 55 degrees,

Explanation:
Given line is intersecting two parallel lines. The missing angle measurements are
∠a = 125 degrees;
∠b = 55 degrees;
∠c = 125 degrees;
∠d = 55 degrees;
∠e = 125 degrees;
∠f = 125 degrees;
∠h = 55 degrees as ∠a  + ∠b = 180 degrees,
∠c + ∠d = 180 degrees and ∠d = 55 degrees so ∠c = 180 – 55 = 125 degrees,
as ∠a = ∠c = 125 degrees, ∠b = 180 – 125 = 55 degrees,
∠e + ∠f = 180 degrees,
∠g + ∠h = 180 degrees and ∠g = 125 degrees so ∠h = 180 – 125 = 55 degrees,
as ∠e = ∠g = 125 degrees, ∠f = 180 – 125 = 55 degrees,

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 19.1 Measuring and Naming Angles to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 19.1 Measuring and Naming Angles

Exercises

IDENTIFY

Identify the angle as acute, right, or obtuse.

Question 1.

Answer:
Acute angle,

Explanation:
An angle which is measuring less than 90 degrees is called an acute angle. The given ∠46^o angle is smaller than the right angle (which is equal to 90 degrees).

Question 2.

Answer:
Right angle,

Explanation:
An angle that is measuring equal to 90 degrees is called a right angle. The given ∠90^o angle is the right angle (which is equal to 90 degrees).

Question 3.

Answer:
Acute angle,

Explanation:
An angle which is measuring less than 50 degrees is called an acute angle. The given ∠50^o angle is smaller than the right angle (which is equal to 90 degrees).

Question 4.

Answer:
Obtuse angle,

Explanation:
An obtuse angle is an angle that is greater than 90° and less than 180°.
In other words, an obtuse angle is between a right angle and a straight angle.
So the given ∠131^o angle is an obtuse angle.

Question 5.

Answer:
Acute angle,

Explanation:
An angle which is measuring less than 30 degrees is called an acute angle. The given ∠30^o angle is smaller than the right angle (which is equal to 90 degrees).

Question 6.

Answer:
Obtuse angle,

Explanation:
An obtuse angle is an angle that is greater than 90° and less than 180°.
In other words, an obtuse angle is between a right angle and a straight angle.
So the given ∠120^o angle is an obtuse angle.

Question 7.

Answer:
Right angle,

Explanation:
Explanation:
An angle which is measuring equal to 90 degrees is called a right angle. The given ∠90^o angle is the right angle (which is equal to 90 degrees).

Question 8.

Answer:
Obtuse angle,

Explanation:
An obtuse angle is an angle which is greater than 90° and less than 180°.
In other words, an obtuse angle is between a right angle and a straight angle.
So the given ∠175^o angle is obtuse angle.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Unit Test Lessons 1–6 to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Unit Test Lessons 1–6 Answer Key

Solve.

Question 1.
Edie’s local newspaper has 4,476 pages of advertising each year. If the magazine is published once a week, about how many pages of advertising are in each issue? (Calculate using 52 weeks in a year.) How many pages exactly?
Answer:
90,86
Explanation:
4,476 pages of advertising each year
the magazine is published once a week and there are 52 weeks in a year
\(\frac{4476}{52}\)
= 86.0769
86 to 90 pages for each issue

Add or subtract.

Question 2.

Answer:
41606
Explanation:
Start by lining up the number, to add by place value.
Add up each place value, starting in the ones place.
If the total of a place value has 2 digits,
write the second digit and carry the first digit to the next column.

Question 3.

Answer:
236137
Explanation:
Start by lining up the number, to add by place value.
Add up each place value, starting in the ones place.
If the total of a place value has 2 digits,
write the second digit and carry the first digit to the next column.

Question 4.

Answer:
1511691
Explanation:
Start by lining up the number, to add by place value.
Add up each place value, starting in the ones place.
If the total of a place value has 2 digits,
write the second digit and carry the first digit to the next column.

Question 5.

Answer:
193
Explanation:
Line up the numbers according to their place values.
Subtract each value, starting from ones place.
Regroup the numbers and borrow one ten from the next place value.

Question 6.

Answer:
1389
Explanation:
Line up the numbers according to their place values.
Subtract each value, starting from ones place.
Regroup the numbers and borrow one ten from the next place value.

Question 7.

Answer:
120109
Explanation:
Line up the numbers according to their place values.
Subtract each value, starting from ones place.
Regroup the numbers and borrow one ten from the next place value.

Question 8.

Answer:
91785
Explanation:
Line up the numbers according to their place values.
Subtract each value, starting from ones place.
Regroup the numbers and borrow one ten from the next place value.

Question 9.
\(\frac{31}{4}\) + \(\frac{3}{4}\)
Answer:
8\(\frac{1}{2}\)
Explanation:
\(\frac{31}{4}\) + \(\frac{3}{4}\)
As both the denominators are same,
numerators can be added directly.
\(\frac{31 + 3}{4}\)
= \(\frac{34}{4}\)
= 8\(\frac{1}{2}\)

Question 10.
\(\frac{19}{43}\) – \(\frac{13}{43}\)
Answer:
\(\frac{6}{43}\)
Explanation:
\(\frac{19}{43}\) – \(\frac{13}{43}\)
As both the denominators are same,
numerators can be added directly.
\(\frac{19 – 13}{4}\)
= \(\frac{6}{43}\)

Question 11.
4\(\frac{5}{11}\) + 5\(\frac{6}{11}\)
Answer:
10
Explanation:
4\(\frac{5}{11}\) + 5\(\frac{6}{11}\)
Convert the mixed fraction in to improper fraction.
\(\frac{49}{11}\) + \(\frac{61}{11}\)
As both the denominators are same,
numerators can be added directly.
\(\frac{49 + 61}{11}\)
= \(\frac{110}{11}\)
= 10

Question 12.
2\(\frac{23}{39}\) + \(\frac{24}{39}\)
Answer:
3\(\frac{8}{39}\)
Explanation:
2\(\frac{23}{39}\) + \(\frac{24}{39}\)
Convert the mixed fraction in to improper fraction.
\(\frac{101}{39}\) + \(\frac{24}{39}\)
As both the denominators are same,
numerators can be added directly.
\(\frac{101 + 24}{39}\)
= \(\frac{125}{39}\)
= 3\(\frac{8}{39}\)

Question 13.
\(\frac{12}{61}\) – \(\frac{3}{61}\)
Answer:
\(\frac{9}{61}\)
Explanation:
\(\frac{12}{61}\) – \(\frac{3}{61}\)
As both the denominators are same,
numerators can be subtracted directly.
\(\frac{12 – 3{61}\)
= \(\frac{9}{61}\)

Change each to a mixed number.

Question 14.
\(\frac{45}{7}\)
Answer:
6\(\frac{3}{7}\)
Explanation:

6\(\frac{3}{7}\)

Question 15.
\(\frac{66}{8}\)
Answer:
8\(\frac{1}{4}\)
Explanation:

= 8\(\frac{1}{4}\)

Question 16.
\(\frac{1}{2}\) × 44
Answer:
22
Explanation:
\(\frac{1}{2}\) × 44
\(\frac{44}{2}\)

Question 17.
\(\frac{1}{4}\) × 22
Answer:
5\(\frac{1}{2}\)
Explanation:
\(\frac{1}{4}\) × 22
\(\frac{22}{4}\)

= 5\(\frac{1}{2}\)

Question 18.
\(\frac{11}{18}\) × \(\frac{11}{22}\)
Answer:
\(\frac{11}{36}\)
Explanation:
\(\frac{11}{18}\) × \(\frac{11}{22}\)
= \(\frac{11 x 11}{18 x 22}\)
= \(\frac{11}{18 x 2}\)
= \(\frac{11}{36}\)

Question 19.
\(\frac{2}{3}\) × 4\(\frac{3}{5}\)
Answer:
3\(\frac{1}{15}\)
Explanation:
\(\frac{2}{3}\) × 4\(\frac{3}{5}\)
Convert the mixed fraction in to improper fraction.
= \(\frac{2}{3}\) × \(\frac{23}{5}\)
= \(\frac{2 x 23}{3 x 5}\)
= \(\frac{46}{15}\)
= 3\(\frac{1}{15}\)

Question 20.
18 × \(\frac{7}{9}\)
Answer:
14
Explanation:
18 × \(\frac{7}{9}\)
= \(\frac{18 x 7}{9}\)
= \(\frac{2 x 7}{1}\)
= 14

Question 21.
\(\frac{15}{29}\) ÷ 45
Answer:
\(\frac{1}{87}\)
Explanation:
\(\frac{15}{29}\) ÷ 45
= \(\frac{15}{45 x 29}\)
= \(\frac{1}{3 x 29}\)
= \(\frac{1}{87}\)

Question 22.
\(\frac{54}{47}\) ÷ 18
Answer:
\(\frac{3}{47}\)
Explanation:
= \(\frac{54}{47}\) ÷ 18
= \(\frac{54}{18 x 47}\)
= \(\frac{3}{47}\)

Question 23.
42 ÷ \(\frac{7}{3}\)
Answer:
18
Explanation:
42 ÷ \(\frac{7}{3}\)
= \(\frac{42 x 3}{7}\)
= 18

Question 24.
\(\frac{4}{27}\) ÷ 3
Answer:
\(\frac{4}{81}\)
Explanation:
\(\frac{4}{27}\) ÷ 3
= \(\frac{4}{3 x 27}\)
= \(\frac{4}{81}\)

Question 25.
\(\frac{75}{83}\) ÷ 15
Answer:
\(\frac{5}{83}\)
Explanation:
\(\frac{75}{83}\) ÷ 15
= \(\frac{75}{15 x 83}\)
= \(\frac{5}{83}\)

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

Question 26.
\(\frac{5}{4}\) = \(\frac{24}{26}\)
Answer:
No
Explanation:
\(\frac{5}{4}\) = \(\frac{24}{26}\)

Question 27.
\(\frac{21}{12}\) = \(\frac{7}{36}\)
Answer:
No
Explanation:
\(\frac{21 x 3}{12 x 3}\) = \(\frac{21}{36}\)
\(\frac{21}{12}\) is not equal to \(\frac{7}{36}\)

Question 28.
\(\frac{12}{19}\) = \(\frac{38}{48}\)
Answer:
No
Explanation:
\(\frac{12 x 3}{19 x 3} \) = \(\frac{36}{57}\)
\(\frac{12}{19}\) is not equal to \(\frac{38}{48}\)

Question 29.
\(\frac{1}{4}\) = \(\frac{6}{24}\)
Answer:
Yes
Explanation:
\(\frac{1}{4}\) = \(\frac{6}{24}\)
\(\frac{1 x 6}{4 x 6}\) = \(\frac{6}{24}\)
\(\frac{1}{4}\) = \(\frac{6}{24}\)
So, both the proportions equal.

Solve for x.

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

Question 31.
\(\frac{20}{x}\) = \(\frac{40}{100}\)
Answer:
x = 50
Explanation:
\(\frac{20}{x}\) = \(\frac{40}{100}\)
x = \(\frac{20 x 100}{40}\)
x = 50

Question 32.
\(\frac{36}{90}\) = \(\frac{12}{x}\)
Answer:
x = 30
Explanation:
\(\frac{36}{90}\) = \(\frac{12}{x}\)
x = \(\frac{12 x 90}{36}\)
x = 30

Solve.

Question 33.
Walter looked at the list of nutrients in the fruit juice he bought. He noticed that there were a total of 4 grams of carbohydrates and 3 grams of sugar in every bottle of juice. Compare the amount of sugar to carbohydrates in the fruit juice.
Answer:
\(\frac{3}{4}\) grams
Explanation:
Walter noticed that there were a total of 4 grams of carbohydrates and 3 grams of sugar in every bottle of juice. Compare the amount of sugar to carbohydrates in the fruit juice,
= \(\frac{3}{4}\) grams.

Question 34.
Will rides his unicycle at an average speed of 8 miles per hour. How far will he travel in 2\(\frac{1}{2}\) hours?
Answer:
20 miles.
Explanation:
Will rides his unicycle at an average speed of 8 miles per hour.
Total distance he travel in 2\(\frac{1}{2}\) hours,
= 2\(\frac{1}{2}\) x 8
= \(\frac{5}{2}\) x 8
= 2 x 8 + \(\frac{8}{2}\)
= 16 + 4
= 20 miles

Question 35.
Jack makes 22 muffins for every 3 batches he bakes. How many batches of muffins will he need to bake in order to sell 242 muffins?
Answer:
33 batches.
Explanation:
22 muffins for 3 batches
242 muffins  —- x batches
x X 22 = 3 x 242
x = \(\frac{3 x 242}{22}\)
x = 3 x 11
x = 33 batches

Question 36.
Priscilla drinks an average of \(\frac{2}{3}\) quart of water for each mile she walks. How many quarts of water will she drink if she walks \(\frac{2}{3}\) miles?
Answer:
\(\frac{4}{9}\) qts.
Explanation:
Priscilla drinks an average of \(\frac{2}{3}\) quart of water for each mile she walks.
Total quarts of water she drink if she walks \(\frac{2}{3}\) miles,
= \(\frac{2}{3}\) x \(\frac{2}{3}\)
= \(\frac{2 x 2}{3 x 3}\)
= \(\frac{4}{9}\) qts

Question 37.
Jenny changes the oil in her car every 2,250 miles. How many times will she need to change the oil in her car if she takes a trip that is 9,000 miles in length?
Answer:
4 times.
Explanation:
Jenny changes the oil in her car every 2,250 miles.
Number of times she need to change the oil in her car if she takes a trip that is 9,000 miles in length,
= \(\frac{9000}{2250}\)
= 2250 x 4 = 9000
= \(\frac{9000}{2250}\) = 4

Question 38.
30% of 1\(\frac{2}{5}\)
Answer:
\(\frac{21}{50}\)
Explanation:
30% of 1\(\frac{2}{5}\)
= \(\frac{30}{100}\) x \(\frac{7}{5}\)
= \(\frac{3}{10}\) x \(\frac{7}{5}\)
= \(\frac{3 x 7}{10 x 5}\)
= \(\frac{21}{50}\)

Question 39.
40% of 440
Answer:
176
Explanation:
40% of 440
= \(\frac{40}{100}\) x 440
= \(\frac{4}{10}\) x \(\frac{440}{1}\)
= \(\frac{4 x 440}{10}\)
= 4 x 44
= 176

Question 40.
\(\frac{1}{4}\) of 48%
Answer:
12%
Explanation:
\(\frac{1}{4}\) of 48%
= \(\frac{1}{4}\) x \(\frac{48}{100}\)
= \(\frac{1 x 48}{4 x 100}\)
= \(\frac{12}{100}\)
= 12%

Question 41.
\(\frac{2}{5}\) of 70%
Answer:
28%
Explanation:
\(\frac{2}{5}\) of 70%
= \(\frac{2}{5}\) x \(\frac{70}{100}\)
= \(\frac{2 x 70}{100}\)
= \(\frac{2 x 14 }{100}\)
= 28%

Question 42.
\(\frac{3}{8}\) of 340%
Answer:
127.5%
Explanation:
\(\frac{3}{8}\) of 340%
= \(\frac{3}{8}\) x \(\frac{340}{100}\)
= \(\frac{3 x 340}{8 x 100}\)
= \(\frac{127.5 }{4 x 100}\)
= 127.5%

Question 43.
43% of .705
Answer:
0.3032
Explanation:
43% of .705
\(\frac{43}{100}\) x 0.705
= 0.43 x 0.705
= 0.3032

Question 44.
84% of 1.906
Answer:
1.601
Explanation:
84% of 1.906
\(\frac{84}{100}\)
= 0.84 x 1.906
= 1.601

Question 45.
\(\frac{3}{4}\) of 160%
Answer:
120%
Explanation:
\(\frac{3}{4}\) of 160%
= \(\frac{3}{4}\) x \(\frac{160}{100}\)
= \(\frac{3 x 160}{4 x 100}\)
= \(\frac{3 x 40}{100}\)
= 120%

Question 46.
Pete’s Pet Emporium is having a sale on birdcages. Pete is selling his $50 cages at a 20% discount, his $75 cages at \(\frac{1}{3}\) off, and his $100 cages at 60% off the original price. What are the new sale prices for the 3 cages?
$50 cage ________ $75 cage _________ $100 cage
Answer:
$40, $50, $40
Explanation:
Pete is selling his $50 cages at a 20% discount,
$50 cages at a 20% discount,
50 x 20 / 100 = 10
$50 – $10 = $40
his $75 cages at \(\frac{1}{3}\) off,
his $75 cages at \(\frac{1}{3}\) off,
$75 x \(\frac{1}{3}\) = $25
$75 – $25 = $50
and his $100 cages at 60% off the original price,
$100 x 60/100 = 60
$100 – $60 = $40
the new sale prices for the 3 cages,
$50 cage __$40
$75 cage __$50
$100 cage __$40

Question 47.
Tom is selling wristbands for $4.50. He has to charge sales tax of 6% on each wristband. What is the cost to the customer, including sales tax, for one wristband?
Answer:
$4.77
Explanation:
Tom is selling wristbands for $4.50.
He has to charge sales tax of 6% on each wristband.
$4.50x 6%
4.50 x 0.06 = 0.27
the cost to the customer, including sales tax, for one wristband,
4.50 + 0.27 = $4.77

Question 48.
Ursula put $200 into a money market account that pays 3% simple interest. How much will she have in her account at the end of 1 year if she does not deposit any more money in the account? How much will she have at the end of 2 years?
Answer:
$206.00, $212.00

Question 49.
Pam put $400 into a savings account that pays 2.5% in compound interest. How much will she have in the account at the end of 2 years, if she does not deposit any more money in the account? How much will she have at the end of 5 years?
Answer:
$420.25; $452.56

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

Complete the following test items.

Question 1.
Kathy runs 16 miles a week. If she continues to run at this rate, how many miles will she run in a year?
Answer:
832 miles.
Explanation:
Kathy runs 16 miles a week.
If she continues to run at this rate,
There are 52 weeks in a year,
16 x 52 = 832 miles

Question 2.
The women’s clothing department at Ms. Smith’s store had a sale on jeans. There were 945 jeans in stock at the beginning of the sale and another 254 jeans were ordered. At the end of the sale the store still had 245 jeans in stock. How many jeans were sold during the sale?
Answer:
954 jeans.
Explanation:
945 jeans in stock at the beginning of the sale and another 254 jeans were ordered.
At the end of the sale the store still had 245 jeans in stock.
Total 945 + 254 = 1199 jeans
1199 – 245 = 954
954 jeans sold during the sale

Question 3.
Jack has 16 lengths of rope. Each is 6\(\frac{3}{4}\) meters long. How much rope does Jack have to divide among 20 people?
___________________
How much rope will each person receive?
___________________
Answer:
108m;
Each person will receive 5\(\frac{2}{5}\) meters.
Explanation:
Jack has 16 lengths of rope.
Each is 6\(\frac{3}{4}\) meters long.
= 16 x 6\(\frac{3}{4}\)
= 16 x \(\frac{4 x 6 + 3}{4}\)
= 16 x \(\frac{27}{4}\)
= \(\frac{16 x 27}{4}\)
= 4 x 27
= 108 m
Total length of the rope / number of people
\(\frac{108}{20}\)
5\(\frac{2}{5}\)
Each person will receive 5\(\frac{2}{5}\) meters.

Question 4.
David has 176 ounces of hot sauce to divide among the 32 contestants in a chicken-wing eating contest.
How many cups is that per contestant?
Answer:
5.5 oz or 6\(\frac{11}{16}\) cups.
Explanation:
David has 176 ounces of hot sauce to divide among the 32 contestants in a chicken-wing eating contest.
Number of cups for each contestants,

Question 5.
4\(\frac{3}{10}\) + 3\(\frac{2}{5}\) + \(\frac{1}{3}\) + \(\frac{1}{2}\) =
Answer:
8\(\frac{8}{15}\)
Explanation:
4\(\frac{3}{10}\) + 3\(\frac{2}{5}\) + \(\frac{1}{3}\) + \(\frac{1}{2}\)
converting mixed fractions into improper fraction
= \(\frac{40 +3}{10}\) + 3\(\frac{15 + 2}{5}\) + \(\frac{1}{3}\) + \(\frac{1}{2}\)
= \(\frac{43}{10}\) + \(\frac{17}{5}\) + \(\frac{1}{3}\) + \(\frac{1}{2}\)
As denominator are different, take LCM,
LCM of 10, 5, 3, 2 to be found as below shown.

= \(\frac{43}{10}\) + \(\frac{17}{5}\) + \(\frac{1}{3}\) + \(\frac{1}{2}\)
= \(\frac{43 X 3}{30}\) + \(\frac{17 X 6}{30}\) + \(\frac{1 X 10}{30}\) + \(\frac{1 X 15}{30}\)
=\(\frac{129}{30}\) + \(\frac{102}{30}\) + \(\frac{10}{30}\) + \(\frac{15}{30}\)
= \(\frac{129 + 102 + 10 + 15}{30}\)
= \(\frac{256}{30}\)
= 8\(\frac{16}{30}\)
= 8\(\frac{8}{15}\)

Question 6.
-8 + 11 – (-9) + 4(-3) + \(\frac{12}{-4}\) =
Answer:
-3
Explanation:
Given, -8 + 11 – (-9) + 4(-3) + \(\frac{12}{-4}\)
= -8 + 11 + 9 -12 -3
= -8 + 20 -15
= -3

Question 7.
Solve for x: x — 7 = 14
Answer:
x = 21
Explanation:
x — 7 = 14
x — 7 = 14 + 7
x = 21

Question 8.
Solve for x: 2x + 6 = 18
Answer:
x = 6
Explanation:
2x + 6 = 18
2x  = 18 – 6
2x = 12
x = 12/2
x = 6

Question 9.
Solve: 10 + (8 — 6)² — (12 ÷ 4) + 5(6 × 2) + 3(7 — 4) = _______
Answer:
80
Explanation:
10 + (8 — 6)² — (12 ÷ 4) + 5(6 × 2) + 3(7 — 4)
= 10 + (2)² — (3) + 5(12) + 3(3)
= 10 + 4 — 3 + 60 + 9
= 80

Question 10.
Restate in exponent form, then solve: 5 × 5 + 2 × 2 × 2 + 3 × 3 =
___________________
Answer:
5² + 2³+ 3² = 42
Explanation:
5 × 5 + 2 × 2 × 2 + 3 × 3
a x a = a² 
a x a x a = a³ 
5² + 2³+ 3²
= 42

Question 11.
5 meters _________ inches
(Use 2.54 cm = 1 inch)
Answer:
196.85 inches.
Explanation:
5 meters = 500 cms
(by Using 2.54 cm = 1 inch)
1 meter = 39.5
\(\frac{500}{2.54}\)
196.85 inches

Question 12.
10 yards = _________ centimeters
Answer:
914.4 cm
Explanation:
1 yard = 91.44 cm
10 yards = 91.44 x 10
= 914.4 centimeters

Question 13.
What is the area of the rectangle? _______

What is the perimeter?
________________
What is the perimeter, in inches, using the conversion factor of 2.54 cm to the inch?
Answer:
Area = 96 sq cm;
Perimeter = 40 cm or 15.748 in.
Explanation:
Area of a rectangle = Length x width
A = 8 x 12
A = 96 sq cm
Perimeter of a Rectangle = 2(Length + Width)
P = 2( 8 + 12)
P = 2 x 20
P = 40 cm
P = 40/2.54
= 15.748 in

Question 14.

What is the area of the circle? (Use 3.14 for π.)
What is the circumference of the circle?
________________
Answer:
Area = 78.5 sq in;
Circumference = 31.4 inches.
Explanation:
The area of the circle (Use 3.14 for π)
A = π r²
r = 5 cm
A = 3.14 x 5 x 5
A = 78.5 sq in.
The circumference of the circle,
C = 2πr
C = 2 x 3.14 x 5
C = 31.4 inches.

Question 15.
Identify each angle as obtuse, acute, or right.

Answer:

Explanation:
Any angle that is greater than 90° but less than 180° is known as obtuse angle.
If two rays intersect at a vertex, forming an angle that is less than 90° is known as acute.
If the angle formed between two rays is exactly 90° then it is called a right angle.

Question 16.
Identify each triangle as scalene, isosceles, or equilateral.

Answer:

Explanation:
All angles of a scalene triangle are unequal, all are of different size.
An equilateral triangle is a triangle with all three sides of equal length.
An isosceles triangle is a triangle with two equal sides.

Calculate and reduce the fractions.

Question 17.
4\(\frac{3}{5}\) × 5\(\frac{1}{5}\) =
Answer:
23\(\frac{23}{25}\)
Explanation:
4\(\frac{3}{5}\) × 5\(\frac{1}{5}\)
= \(\frac{23}{5}\) × \(\frac{26}{5}\)
= \(\frac{23 X 26}{5 X 5}\)
= \(\frac{598}{25}\)
= 23\(\frac{23}{25}\)

Question 18.
(\(\frac{3}{4}\) × \(\frac{4}{11}\)) × \(\frac{11}{3}\) = _______
Answer:
1
Explanation:
(\(\frac{3}{4}\) × \(\frac{4}{11}\)) × \(\frac{11}{3}\)
= (\(\frac{3 X 4}{4 X 11}\)) × \(\frac{11}{3}\)
= \(\frac{12}{44}\) × \(\frac{11}{3}\)
= \(\frac{12 X 11}{44 X 3}\)
= \(\frac{132}{132}\) = 1

Question 19.
\(\frac{12}{25}\) ÷ \(\frac{4}{5}\) = _____
Answer:
\(\frac{3}{5}\)
Explanation:
\(\frac{12}{25}\) ÷ \(\frac{4}{5}\)
In division the fraction of one is reciprocal to the other.
= \(\frac{12}{25}\) x \(\frac{5}{4}\)
= \(\frac{12 X 5}{25 X 4}\)
= \(\frac{60}{100}\)
= \(\frac{3}{5}\)

Question 20.
Give the coordinates for points on the grid.
A ___ B __
C ___ D ___

What is the slope of a line drawn between points A and B?
Answer:
A(1,3); B(-3,6); C(2, -5); D(-2, -2)
The slope of a line drawn between points A and B –\(\frac{3}{4}\)

Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
So, co-ordinates on grid are A(1,3); B(-3,6); C(2, -5); D(-2, -2).
Slope:
The slope formula is m=(y2-y1)/(x2-x1),
or the change in the y values over the change in the x values.
The coordinates of the first point represent x1 and y1.
The coordinates of the second points are x2, y2
The slope of a line drawn between points A and B –\(\frac{3}{4}\).
A(1,3); B(-3,6)
m = \(\frac{y2 – y1}{x2 – x1}\)
m = \(\frac{6 – 3}{-3 – 1}\)
m = \(\frac{3}{-4}\)
m = –\(\frac{3}{4}\)

Question 21.
What is the measure of angle DBC?

_______
Answer:
50 degrees

Explanation:
The sum of the two angles in right angle is 90°.
40° + x = 90°
x = 90° – 40°
x = 50°

Question 22.

Answer:
1.566667
Explanation:
0.15 x 1000 = 150
0.235 x 1000 = 235

Question 23.

Answer:
0.1562
Explanation:
0.4686 x 10000 = 4686
3 x 10000 = 30000

Question 24.
what is 40% of .775? _____
Answer:
0.31
Explanation:
40% of .775
\(\frac{40}{100}\) x 0.775
= \(\frac{40 X 0.775}{100}\)
= \(\frac{31}{100}\)
= 0.31

Question 25.
What is \(\frac{5}{8}\) of 72% ?_____
Answer:
45%
Explanation:
\(\frac{5}{8}\) of 72%
= \(\frac{5}{8}\) x \(\frac{72}{100}\)
= \(\frac{5 X 72}{8 X 100}\)
= \(\frac{360}{800}\)
= 0.45
Convert 0.45 to %
= 0.45 x 100 = 45%

Question 26.
Restate 4.25 as an improper fraction and a mixed number.
Improper Fraction _____ Mixed Number ______
Answer:
Improper fraction: \(\frac{17}{4}\)
Mixed fraction: 4\(\frac{1}{4}\)
Explanation:
Restate 4.25 as an improper fraction and a mixed number.
Convert decimal to fraction.
4.25 x \(\frac{100}{100}\)
= \(\frac{425}{100}\)
= \(\frac{85}{20}\)
= \(\frac{17}{4}\)
Convert improper fraction to mixed fraction.
\(\frac{17}{4}\) = 4\(\frac{1}{4}\)

Question 27.
Put the following numbers in order from least to greatest.
1.162, 1.161, 2.16302, 2.163, 2.8022, 1.90688, 1.9122, 1.099
___________________
Answer:
1.099, 1.161, 1.162, 1.90688, 1.9122, 2.163, 2.16302, 2.8022
Explanation:
Arrange all the given numbers in ascending order by placing whole numbers first,
then decimals number with the least digit according to their place values.

Question 28.
Solve for x. \(\frac{15}{32}\) = \(\frac{x}{160}\)
Answer:
75
Explanation:
\(\frac{15}{32}\) = \(\frac{x}{160}\)
x = \(\frac{15 X 160}{32}\)
x = \(\frac{2400}{32}\)
x = 75

Question 29.
Restate 2\(\frac{7}{16}\) as a decimal. _____
Answer:
2.4375
Explanation:
Convert the given mixed fraction to improper fraction,
2\(\frac{7}{16}\)
= \(\frac{39}{16}\)
Convert improper fraction into decimal,
= 2.4375

Question 30.
Sarah manufactured surfboards at a cost of $45.00 each. She wants to sell the surfboards at a 50% markup. What will be the selling price for each?
Answer:
$67.50
Explanation:
Sarah manufactured surfboards at a cost of $45.00 each.
She wants to sell the surfboards at a 50% markup.
50% of $45.00
\(\frac{50}{100}\) x 45
= \(\frac{50 X 45}{100}\)
= \(\frac{2250}{100}\)
= 22.5
The selling price for each, 22.5 + 45 = $67.50

Question 31.
Dexter deposits $200 in a bank account that earns 3% simple interest. How much money will he have
in the account after 1 year? _______
After 2 years? _________
Answer:
After 1 year = $206.00;
After 2 years = $212.18.
Explanation:
Simple Interest SI = PTR/100
Principal = $200
Time T = 1 year
Rate of interest R = 3%
SI = (200 x 1 x 3)/100
SI = 6
Amount after one year = $200 + $6
= $206
now
Principal = $206
Time T = 1 year
Rate of interest R = 3%
SI = (206 x 1 x 3)/100
SI = $6.16
Amount after one year = $206 + $6.18
= $212.18

Question 32.
Identify each quadrilateral.

Answer:

Explanation:
A square is closed, two-dimensional shape with 4 equal sides.
Rhombus is a quadrilateral with all equal sides.
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
The two sides at each corner or vertex meet at the right angles.
The opposite sides of the rectangle are equal in length which makes it different from a square.
Since opposite sides of a parallelogram are equal.
So, Rhombus is a special type of a parallelogram whose all sides are equal.
A kite is a flat shape with 4 straight sides that has two pairs of sides,
which are two adjacent sides that are equal in length.
A trapezoid is a flat closed shape having 4 straight sides,
with one pair of parallel sides.

Question 33.
Restate 5\(\frac{6}{13}\) as an improper fraction.
Answer:
\(\frac{71}{13}\)
Explanation:
Convert the given fraction to improper fraction,
5\(\frac{6}{13}\)
= \(\frac{71}{13}\)

Question 34.
Restate \(\frac{43}{16}\) as a mixed number. _____
Answer:
2\(\frac{11}{6}\)
Explanation:
Convert improper fraction to mixed fraction, \(\frac{43}{16}\)
write the quotient as whole number and remainder as numerator..
quotient = 2
Remainder = 11
2\(\frac{11}{6}\)

Question 35.
\(\frac{4}{7}\) – \(\frac{5}{7}\) + \(\frac{3}{7}\) + \(\frac{4}{7}\) – \(\frac{3}{7}\) = _____
Answer:
\(\frac{3}{7}\)
Explanation:
\(\frac{4}{7}\) – \(\frac{5}{7}\) + \(\frac{3}{7}\) + \(\frac{4}{7}\) – \(\frac{3}{7}\)
As, there is a common denominator in all the fractions add the numerators,
= \(\frac{4 – 5 + 3 + 4 – 3}{7}\)
= \(\frac{3}{7}\)

Question 36.
\(\frac{5}{8}\) × 3\(\frac{13}{25}\) = _____
Answer:
2\(\frac{1}{5}\)
Explanation:
\(\frac{5}{8}\) × 3\(\frac{13}{25}\)
convert mixed fraction improper fraction
= \(\frac{5}{8}\) × \(\frac{75 + 13}{25}\)
= \(\frac{5}{8}\) × \(\frac{88}{25}\)
= \(\frac{5 X 88}{8 X 25}\)
= \(\frac{440}{200}\)
= \(\frac{11}{5}\)
= 2\(\frac{1}{5}\)

Question 37.
10⁴ × 10⁵ = ____
Answer:
10⁹
Explanation:
a^m x aⁿ = a^{m + n}
10⁴ x 10⁵ = 10⁴⁺⁵
= 10⁹

Question 38.
9⁸ ÷ 9⁴ = ____
Answer:
9⁴ or 6561
Explanation:
a^m ÷ aⁿ = a^{m – n}
9⁸ ÷ 9⁴ = 9^{9 – 4} = 9⁴
a⁴ = a x a x a x a
9⁴ = 9 x 9 x 9 x 9
= 81 x 81
= 6561

Question 39.
What is 12²? ________
Answer:
144
Explanation:
a² = a x a =
12² = 12 x 12 = 144

Question 40.
What is the square root of 225? ____
Answer:
15
Explanation:
The square root of 225 is expressed as √225 in the radical form,
and as (225)^½ or (225)^0.5 in the exponent form.
The square root of 225 is 15.
It is the positive solution of the equation x² = 225.
The number 225 is a perfect square.

Question 41.

What is the mode of the data distribution?
____________
What is the median?
_____________
Answer:
Mode = 47
Median = 50
Explanation:
Mode : mode is the number that appears most frequently in the collection of data.

The median is the number in the middle,
if the collection of data has an even numbers of addends,
then the median is the average of the two middle numbers.
22, 23, 31, 36, 38, 42, 47, 47, 47, 53, 54, 54, 56, 56, 61, 64, 64, 65

Median is the average of (47 + 53 )/2 = 100/2 = 50

Question 42.
According to this graph, what frozen yogurt is the most preferred? ____________________
The least preferred? ___________

Answer:
The most preferred frozen yogurt is Mango;
The least preferred frozen yogurt is Strawberry.
Explanation:
A pie chart is a pictorial representation of data in circular statistical graphic,
which is divided into slices to illustrate numerical proportion.

In a pie chart, the arc length of each slice is proportional to the quantity it represents.
The most preferred frozen yogurt is Mango,
due to maximum portion of the pie chart shows Mango;
The least preferred frozen yogurt is Strawberry,
due to minimum portion of the pie chart shows Strawberry.

Question 43.
Brandon collected about 20 cans more than what person? ______
Who collected the second fewest cans? ______________

Answer:
Brandon collected about 20 cans more than Molly.
Megan collected the second fewest cans.
Explanation:
Above chart shows the Recycling contest results.
Brandon collected about 20 cans more than Molly,
he collected 70 cans.
Megan collected the second fewest cans.

Question 44.
How many possible combinations are there?
___________________

Answer:
12
Explanation:
If an event can occur in ‘m’ different ways following,
which another event can occur in ‘n’ different ways,
following which a third event can occur in ‘p’ different ways.
The total number of occurrence to the events in the given order is m x n x p.
2 Shirts,
3 Pants,
2 Shoes,
2 x 3 x 2 = 12

Question 45.
What is the range of the data in the box-and-whisker plot?
______________

Answer:
18
Explanation:

The range difference between the upper extreme to lower extreme
Range = 22 – 4 = 18

Question 46.
Use the Pythagorean Theorem to find the value of x.

Answer:
x = 12
Explanation:
In Pythagorean Theorem the square of the length of the hypotenuse of a right triangle,
equals the sum of the squares of the lengths of the other two sides.

AC² = AB² + BC²
13² = AB² + 5²
169 – 25 = AB²
AB² = 144
AB = 12
x = 12

Question 47.

Name two pairs of alternate interior angles.
________ and ________ ________ and _________

Name two pairs of alternate exterior angles.
________ and ________ ________ and _________
Name a pair of vertical angles.
_______ and _______
Name two pairs of supplementary angles.
_____ and _____ _____ and _____
Answer:
Alternate interior angles:
\(\angle{4}\) and \(\angle{5}\);
\(\angle{3}\) and \(\angle{6}\).
Alternate exterior angles:
\(\angle{2}\) and \(\angle{7}\);
\(\angle{1}\) and \(\angle{8}\).
Vertical angles:
\(\angle{2}\) and \(\angle{3}\);
\(\angle{1}\) and \(\angle{4}\);
\(\angle{6}\) and \(\angle{7}\);
\(\angle{5}\) and \(\angle{8}\).
Supplementary angles:
\(\angle{1}\) and \(\angle{3}\);
\(\angle{2}\) and \(\angle{4}\);
\(\angle{5}\) and \(\angle{7}\);
\(\angle{6}\) and \(\angle{8}\).
Explanation:
Alternate interior angles:
The two angles, formed when a line crosses two other lines,
that lie on opposite sides of the transversal line and on opposite relative sides of the other lines.
If the two lines crossed are parallel, the alternate angles are equal
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.
They lie on the inner side of the parallel lines but on the opposite sides of the transversal.
The transversal crosses through the two lines which are Coplanar at separate points.
\(\angle{4}\) and \(\angle{5}\);
\(\angle{3}\) and \(\angle{6}\).
Alternate exterior angles:
The term alternate exterior angles is often used when two lines are cut by a third line, a transversal .
The Alternate Exterior Angles Theorem states that if k and l are parallel ,
then the pairs of alternate exterior angles are congruent .
\(\angle{2}\) and \(\angle{7}\);
\(\angle{1}\) and \(\angle{8}\).
Vertical angles:
Vertical angles are angles opposite each other where two lines cross.
\(\angle{2}\) and \(\angle{3}\);
\(\angle{1}\) and \(\angle{4}\);
\(\angle{6}\) and \(\angle{7}\);
\(\angle{5}\) and \(\angle{8}\).
Supplementary angles:
The two angles or arcs whose sum is 180 degrees.
\(\angle{1}\) and \(\angle{3}\);
\(\angle{2}\) and \(\angle{4}\);
\(\angle{5}\) and \(\angle{7}\);
\(\angle{6}\) and \(\angle{8}\).

Question 48.
Name two line segments.
Name four rays. __________
Name a line. ____________________________

Answer:
Line segments:
\(\overline{AB}\), \(\overline{AC}\), \(\overline{AF}\), \(\overline{DB}\),\(\overline{BE}\), \(\overline{HG}\);
Rays:
\(\overline{AF}\), \(\overline{AC}\), \(\overline{BE}\), \(\overline{BD}\),
\(\overline{AB}\), \(\overline{BA}\);
Line:
\(\overline{AB}\)
Explanation:
A line segment is part of a line that has two endpoints and is finite in length.
A ray is a line segment that extends indefinitely in one direction.
A line has no end points.

Calculate the volume and surface area of the figures shown.

Question 49.

Volume ___
Surface Area ____
Answer:
Volume = 72 cu in;
Surface Area = 108 sq in.
Explanation:
Volume = length x width x height
V = 4 x 3 x 6
V  = 72 cu in;
Surface Area = 2(lxw + wxh + hxl)
SA= 2(4×3 + 3×6 + 6×4)
SA = 2(12 + 18 + 24)
SA = 108 sq in.

Question 50.

Volume ___
Surface Area ____
Answer:
Volume = 128π cu in;
Surface Area = 96π sq in.
Explanation:
Volume V = π r² h
V = πr²h
V = π x 4² x 8
V = 128π cu in;
Surface Area SA = 2π rh + 2π r²
SA = 2π rh + 2π r²
= 2 π 4 x 8 + 2 π 4 x 4
= 64π +32π
= 96π sq in.

Question 51.

Volume ______
Answer:
Volume = 96π cu units;
Explanation:
Volume of cone V= π r²h(1/3)
V = π 3²x 8 (1/3)
V = π 9 x 8 x 1/3
V = 72 π cu units;

Question 52.
Estimate the value of \(\sqrt{30}\) _____________________ Of \(\sqrt{97}\). _________
Answer:
Estimate: 5.5;
9.8
Explanation:
\(\sqrt{25}\) = 5
\(\sqrt{36}\) = 6
\(\sqrt{30}\) lies between 5 and 6
\(\sqrt{30}\) =5.5
\(\sqrt{100}\) = 10
\(\sqrt{97}\) is nearer to 100
\(\sqrt{97}\) = 9.8

Question 53.
Convert \(2 . \overline{14}\) to an improper fraction. _______
Answer:
\(\frac{212}{99}\)
Explanation:
\(2 . \overline{14}\)
2.14141414…….
Let
x = 2.14141414 ………….. Eq(1)
by multiplying 100 on both sides
100 x = 214.141414 ……………….Eq (2)
by subtracting Eq(1) from Eq(2) as shown below

99 x = 212
x = \(\frac{212}{99}\)

Question 54.
Solve 4x² + 14 — 4x² = 7. ____________________
Answer:
No solution.
Explanation:
4x² + 14 — 4x² = 7
4x² — 4x² = 14 – 7
0 = 7
So, No solution.

Question 55.
Solve 4x² + 7 — 4x² = 7. _________________________________
Answer:
Infinite Solutions.
Explanation:
4x² + 7 — 4x² = 7
4x² — 4x² = 7 – 7
0 = 0
So, Infinite Solutions.

Question 56.
Complete and graph the function table for y = 2x – 1.

Answer:
Explanation:
y = 2x – 1.
Given the values of x.
y = 2 x -2 – 1
y = -4 – 1
y = -5
Create function table for each equation as shown above.
Substitute a number of values of x in the equation,
then complete the equation to determine the value of y as shown above.
Slope refers to the amount by which a line rises or falls,
as you read a co ordinate grid from left to right.
Positive Slope or Negative Slope
Slope = rise/run
Slope =  2/1 = 2

Question 57.
Look at the graph. Is this a linear or nonlinear function?
______________

The function is increasing between points
__________________
The function is decreasing between points
__________________
The function is positive between points
__________________
The function is negative between points
__________________
Answer:
The function is increasing between non-linear points A and B.
The function is decreasing between C and D points.
The function is positive between B or B and C points.
The function is negative between C and D points.
Explanation:
A non-linear equation is such which does not form a straight line.
It looks like a curve in a graph and has a variable slope value.
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin

Question 58.
How many times greater is 6 × 10⁷ than 3 × 10⁵?
Answer:
200 times.
Explanation:
\(\frac{6 x 10⁷}{3 x 10⁵}\)
= 2 x 10²
= 2 x 100
= 200

Question 59.
In the graph below, is triangle ABC congruent to triangle ADC?
__________________
What type of transformation created triangle ADC? __________

Answer:
Yes; Reflection.
Explanation:
Reflection occurs when we create a mirror image of the original.
To do this, pretend you are flipping the figure over an imaginary line called a line of reflection.
Each point of the new image is the same distance from the line as the original image was,
just on the opposite side of the line.

Question 60.
What type of transformation is shown below? _____

Answer:
Dilation.
Explanation:
Dilation occurs when you change the size of the original figure by enlarging or shrinking it.
The process produce an image that is the exact same shape as the original figure,
but is larger or smaller then the original.

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

McGraw-Hill Math Grade 8 Posttest Answer Key

Complete the following test items.

Question 1.
Robin runs 24 kilometers a week. If she continues to run at this rate, how many kilometers will she run in a year?
Answer:
1248 km
Explanation:
Robin runs 24 kilometers a week.
If she continues to run at this rate,
Number of kilometers she run in a year,
1 year = 52 weeks
= 52 x 24
= 1,248 km.

Question 2.
The fashion department at an outlet store had a sale on t-shirts. There were 1,124 t-shirts in stock at the beginning of the sale and another 426 more were ordered. At the end of the sale the store still had 335 t-shirts in stock. How many t-shirts were sold during the sale?
Answer:
1215 T-shirts.
Explanation:
There were 1,124 t-shirts in stock at the beginning of the sale,
another 426 more were ordered.
1124 + 426 = 1550
At the end of the sale the store still had 335 t-shirts in stock.
Total t-shirts sold during the sale,
1550 – 335 = 1215 T- shirts.

Question 3.
Ronnie has 12 lengths of garden hose. Each is 6\(\frac{3}{4}\) meters long. How many meters of garden hose does Ronnie have to divide among 6 people working in the community garden? _____________
How much hose will each person receive? _____________
Answer:
81 meters;
Each person will receive 13\(\frac{1}{2}\).
Explanation:
Ronnie has 12 lengths of garden hose.
Each is 6\(\frac{3}{4}\) meters long.
Ronnie have to divide among 6 people working in the community garden as,
6\(\frac{3}{4}\) x 12
= \(\frac{27}{4}\) x 12
= \(\frac{27 X 12}{4}\)
= \(\frac{324}{4}\)
= 81 meters
Each person receive \(\frac{81}{6}\)
= 13\(\frac{1}{2}\)

Question 4.
Don has 112 quarts of tomato sauce to divide among the 12 contestants in a pasta cooking contest. How many cups is that per contestant?
Answer:
37\(\frac{1}{3}\) cups
Explanation:
Don has 112 quarts of tomato sauce to divide among the 12 contestants in a pasta cooking contest.
1 quart = 4 cups
112 x 4 = 448 cups
Number of cups per contestant,
= \(\frac{448}{12}\) cups
= 37\(\frac{1}{3}\) cups

Question 5.
6\(\frac{5}{8}\) + 3\(\frac{1}{4}\) + \(\frac{1}{6}\) + 1\(\frac{1}{3}\) = _____________
Answer:
11\(\frac{3}{8}\)
Explanation:
6\(\frac{5}{8}\) + 3\(\frac{1}{4}\) + \(\frac{1}{6}\) + 1\(\frac{1}{3}\)
= \(\frac{53}{8}\) + \(\frac{13}{4}\) + \(\frac{1}{6}\) + \(\frac{4}{3}\)
= \(\frac{(53 X 3) + (13 X 6) + (1 X 4) + (4 X 8)}{24}\)
= \(\frac{159 + 78 + 4 + 32}{24}\)
= \(\frac{273}{24}\)
= \(\frac{91}{8}\)
= 11\(\frac{3}{8}\)

Question 6.
-10 + 15 – (-6) + 5(-4) + \(\frac{16}{-8}\) = ______________
Answer:
-11
Explanation:
-10 + 15 – (-6) + 5(-4) + \(\frac{16}{-8}\)
= 5 + 6 – 20 – 2
= 11 – 22
= – 11

Question 7.
Solve for x: x – 8 = 16
Answer:
x = 24
Explanation:
Given, x – 8 = 16
x = 16 + 8
x = 24

Question 8.
Solve for x: 3x + 6 = 30
Answer:
x = 8
Explanation:
Given, 3x + 6 = 30
3x = 30 – 6
3x = 24
x = \(\frac{24}{3}\)
x = 8

Question 9.
Solve: 12 + (11 – 7)² – (16 ÷ 2) + 4(8 × 2) – 3(8 – 2) = ____________
Answer:
66
Explanation:
12 + (11 – 7)² – (16 ÷ 2) + 4(8 × 2) – 3(8 – 2)
= 12 + (4)² – (8) + 4(16) – 3(6)
= 12 + 16 – 8 + 64 – 18
= 28 – 8 + 64 – 18
= 20 + 64 – 18
= 84 – 18
= 66

Question 10.
Restate in exponent form, then solve: 4 × 4 × 4 × 3 × 3 + 5 × 5 = ______________
Answer:
4³ x 3² + 5² = 601
Explanation:
Given, 4 × 4 × 4 × 3 × 3 + 5 × 5
= 4³ x 3² + 5²
= 64 x 9 + 25
576 + 25
= 601

Question 11.
4.65 meters = _____________ inches (Use 2.54 cm = 1 inch)
Answer:
183.1 inches
Explanation:
Given, 4.65 meters
1m = 100 cm
4.65 x 100 = 465 cm
Given, 2.54 cm = 1 inch
465 ÷ 2.54 = 183.1 inches

Question 12.
16 yards = _____________ centimeters
Answer:
1463 yards
Explanation:
1 yard = 91.44
16 yards = 1463 yards

Question 13.
What is the area of the rectangle?

What is the perimeter of the rectangle?
Answer:
Area of the rectangle = 75 sq cm;
Perimeter of the rectangle = 40 cm.
Explanation:
Area of rectangle = length x breadth
length = 15 cm; breadth = 5 cm
A = 15 x 5 = 75 cm
Perimeter of Rectangle = 2 (l + b)
= 2(15 + 5)
= 40 cm

Question 14.
What is the area of the circle? (Use 3.14 for π)

What is the circumference of the circle?
Answer:
Area = 50.24 sq in;
Circumference = 25.12 in.
Explanation:
Area of the circle = π r²
r = 4 cm
A = 3.14 x 4 x 4
A = 50.24 sq in
The circumference of the circle (Use 3.14 for π)
C = 2πr
r = d/2 = 8/2 = 4
C = 2 x 3.14 x 4
C = 25.12 in.

Question 15.
Identify each angle as obtuse, acute, or right.

Answer:

Explanation:
Any angle that is greater than 90° but less than 180° is known as obtuse angle.
If two rays intersect at a vertex, forming an angle that is less than 90° is known as Acute Angle.
Any angle that is greater than 90° but less than 180° is known as obtuse angle.

Question 16.
Identify each triangle as scalene, isosceles, or equilateral.

Answer:

Explanation:
A scalene triangle is a triangle in which all three sides are in different lengths,
and all three angles are of different measures.
The sum of all the interior angles is always equal to 180 degrees.
An equilateral triangle is a triangle with all three sides of equal length.
An Isosceles triangle is a triangle with two equal sides.

Calculate and reduce the fractions.

Question 17.
\(\frac{5}{12}\) × 168 = _____________
Answer:
70
Explanation:
\(\frac{5}{12}\)
= \(\frac{5 X 168}{12}\)
= \(\frac{840}{12}\)
= 70

Question 18.
(\(\frac{1}{3}\) × \(\frac{9}{14}\)) × \(\frac{14}{3}\) = ____________
Answer:
1
Explanation:
(\(\frac{1}{3}\) × \(\frac{9}{14}\)) × \(\frac{14}{3}\)
= \(\frac{9}{42}\) × \(\frac{14}{3}\)
= \(\frac{9 X 14}{42 X 3}\)
= \(\frac{126}{126}\)
= 1

Question 19.
\(\frac{56}{65}\) ÷ 14 = ______________
Answer:
\(\frac{4}{65}\)
Explanation:
\(\frac{56}{65}\) ÷ 14
= \(\frac{56 ÷ 14}{65}\)
= \(\frac{4}{65}\)

Question 20.
Give the coordinates for points on the grid.
A __________
B __________
C __________
D __________
What is the slope of a line drawn between points D and A?

Answer:
A(1,3); B(-3,6); C(2, -5); D(-2,-2); \(\frac{5}{3}\)

Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
the co-ordinates are A(1,3); B(-3,6); C(2, -5); D(-2,-2);
Slope:
The slope formula is m=(y2-y1)/(x2-x1),
or the change in the y values over the change in the x values.
The coordinates of the first point represent x1 and y1.
The coordinates of the second points are x2, y2.
The slope of a line drawn between points D and A \(\frac{5}{3}\).
D(-2, -2); A(1, 3)
m = \(\frac{y2 – y1}{x2 – x1}\)
m = \(\frac{3 – (-2)}{1 – (-2)}\)
m = \(\frac{3+2}{1+2}\)
m = \(\frac{5}{3}\)

Question 21.
What is the measure of angle DBC?

Answer:
27 °.

Explanation:
The sum of the two angles in right angle is 90°.
63° + x = 90°
x = 90° – 63°
x = 27°

Question 22.

Answer:
1.7
Explanation:
0.35 x 1000 = 350
0.595 x 1000 = 595

Question 23.

Answer:
0.18653
Explanation:
0.5596 x 10000 = 5596
3 x 10000 = 30000

Question 24.
What is 30% of .802?
Answer:
0.2406
Explanation:
30% of 0.802
\(\frac{30}{100}\) x 0.802
= \(\frac{30 X 0.802}{100}\)
= \(\frac{24.06}{100}\)
= 0.2406

Question 25.
What is \(\frac{3}{8}\) of 96%
Answer:
36%
Explanation:
\(\frac{3}{8}\) of 96%
= \(\frac{3 x 96}{8}\)%
= 3 x 12 %
= 36%

Question 26.
Restate 5.625 as an improper fraction and a mixed number.
Improper Fraction ______________
Mixed Number ______________
Answer:
Improper Fraction = \(\frac{45}{8}\)
Mixed Number = 5\(\frac{5}{8}\)
Explanation:
5.625 by multiplying 1000 and divided by 1000 as shown below to get in to p/q form
\(\frac{5.625 x 1000}{1000}\)
= \(\frac{5625}{1000}\)
= \(\frac{45}{8}\)
convert into mixed fraction,
= 5\(\frac{5}{8}\)

Question 27.
Put the following numbers in order from least to greatest.
2.356, 1.3561, 3.56302, 2.5631, 2.35692, 1.35688, 2.5622, 1.599
Answer:
1.3561, 1.35688, 1.599, 2.356, 2.35692, 2.5622, 2.5631, 3.56302
Explanation:
Arrange all the given numbers in ascending order by placing whole numbers first,
then decimals number with the least digit according to their place values.

Question 28.
Solve for x: \(\frac{45}{64}\) = \(\frac{x}{192}\)
Answer:
135
Explanation:
\(\frac{45}{64}\) = \(\frac{x}{192}\)
x = \(\frac{45 X 192}{64}\)
x = \(\frac{8640}{64}\)
x = 135

Question 29.
Restate 2\(\frac{7}{25}\) as a decimal.
Answer:
2.28
Explanation:
Convert the given mixed fraction to improper fraction,
2\(\frac{7}{25}\)
= \(\frac{57}{25}\)
Convert improper fraction into decimal,
= 2.28

Question 30.
An item costs you $13.50 to produce. What price would you charge if you wanted to mark up the item by 20%?
Answer:
$16.20
Explanation:
An item costs you $13.50 to produce.
if wanted to mark up the item by 20%,
20% of $13.50
\(\frac{20}{100}\) x 13.50
= \(\frac{20 X 13.50}{100}\)
= \(\frac{270}{100}\)
= 2.7
total price he should charge = 13.50 + 2.7
= $16.20

Question 31.
Darma deposits $500 in a bank account that earns 2.5% simple interest. How much money will she have in the account after 1 year? ____________
After 2 years? ____________
Answer:
After 1 year $512.50;
After 2 years $525.00.
Explanation:
Simple Interest SI = PTR/100
Principal = $500
Time T = 1 year
Rate of interest R = 2.5%
SI = (500 x 1 x 2.5)/100
SI = 1250/100
SI = 12.5
Amount after one year = $500 + $12.5
= $512.5
now
Principal = $512.5
Time T = 1 year
Rate of interest R = 2.5%
SI = (512.5 x 1 x 3)/100
SI = $12.8125
Amount after one year = $512.5 + $12.8125
= $525.3125 = $525

Question 32.
Identify each quadrilateral.

Answer:

Explanation:
A Square is a simple polygon with 4 equal sides and 4 right angles.
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
The two sides at each corner or vertex meet at the right angles.
The opposite sides of the rectangle are equal in length which makes it different from a square.
Rhombus is a quadrilateral with all equal sides.
Since opposite sides of a parallelogram are equal.
So, Rhombus is a special type of a parallelogram whose all sides are equal.
A kite is a flat shape with 4 straight sides that has two pairs of sides,
which are two adjacent sides that are equal in length.
A trapezoid is a flat closed shape having 4 straight sides,
with one pair of parallel sides.

Question 33.
Restate 4\(\frac{11}{13}\) as an improper fraction.
Answer:
\(\frac{63}{13}\)
Explanation:
To convert mixed fraction to improper fraction,
multiply the denominator with whole number and,
then add the numerator.
4\(\frac{11}{13}\)
= \(\frac{63}{13}\)

Question 34.
Restate \(\frac{73}{13}\) as a mixed number.
Answer:
5\(\frac{8}{13}\)
Explanation:
Convert improper fraction to mixed fraction, \(\frac{73}{13}\)
write the quotient as whole number and remainder as numerator..
quotient = 5
Remainder = 8
5\(\frac{8}{13}\)

Question 35.
\(\frac{6}{7}\) – \(\frac{2}{7}\) + \(\frac{5}{7}\) + \(\frac{3}{7}\) – \(\frac{1}{7}\) = ____________
Answer:
\(\frac{11}{7}\) or 1\(\frac{4}{7}\)
Explanation:
\(\frac{6}{7}\) – \(\frac{2}{7}\) + \(\frac{5}{7}\) + \(\frac{3}{7}\) – \(\frac{1}{7}\)
When all the denominators are same add or subtract the numerators.
\(\frac{(6 – 2 + 5 + 3 – 1)}{7}\)
= \(\frac{11}{7}\) or 1\(\frac{4}{7}\)

Question 36.
\(\frac{15}{16}\) × 3\(\frac{1}{5}\) = _____________
Answer:
3
Explanation:
\(\frac{15}{16}\) × 3\(\frac{1}{5}\)
convert mixed fraction to improper fraction
= \(\frac{15}{16}\) × \(\frac{16}{5}\)
= \(\frac{15 X 5}{16 X 16}\)
= \(\frac{75}{256}\)
= 0.29 = 3

Question 37.
10⁷ × 10² = ______________
Answer:
10⁹
Explanation:
a^m x aⁿ = a^{m + n}
10⁷ x 10² = 10⁷⁺²
= 10⁹

Question 38.
4⁶ ÷ 4² = ______________
Answer:
4⁴
Explanation:
a^m ÷ aⁿ = a^{m – n}
4⁶ ÷ 4² = 4^{6 – 2} = 4⁴
a⁴ = a x a x a x a
4⁴ = 4 x 4 x 4 x 4
= 16 x 16
= 256

Question 39.
What is 15²?
Answer:
225
Explanation:
a² = a x a
15² = 15 x 15
= 225

Question 40.
What is the square root of 169?
Answer:
13
Explanation:
The square root of 169 is expressed as √169 in the radical form
and as (169)^½ or (169)^0.5 in the exponent form.
The square root of 169 is 13.
It is the positive solution of the equation x² = 169.
The number 169 is a perfect square.

Question 41.
What is the mode of the data distribution?

What is the median?
Answer:
Mode = 57
Median = 57
Explanation:
32, 33, 42, 43, 46, 48, 54, 57, 57, 57, 61, 62, 64, 64, 66, 71, 74
Mode : mode is the number that appears most frequently in the collection of data.
In the above stem and leaf data 57 is observer 3 number of times,
mode is 57

Median : the median is the number in the middle. if the collection of data has an even numbers of addends, then the median is the average of the two middle numbers.

Question 42.
What is the range of the data in the box and-whisker plot?

Answer:
Range = 20
Explanation:

The range difference between the upper extreme to lower extreme
Range = 25 – 5 = 15

Question 43.
What fruit is the least preferred by the students? ____________
What is the second most preferred fruit? _______________

Answer:
The least fruit preferred by the students is Pineapple.
The second most preferred fruit by the students is Banana.
Explanation:
A pie chart is a pictorial representation of data in circular statistical graphic, which is divided into slices to illustrate numerical proportion.

In a pie chart, the arc length of each slice is proportional to the quantity it represents
The least fruit preferred by the students is Pineapple.
The second most preferred fruit by the students is Banana.

Question 44.
Clarence collected about 5 more stamps than what person? Who collected the second fewest stamps?

Answer:
Frank;
Barton.
Explanation:
Above Stamp collecting chart,
Clarence collected 55 stamps,
Clarence collected about 5 more stamps than Frank.
Barton collected 45 stamps and stood in the second fewest pace.

Question 45.
How many possible combinations are there?

Answer:
18
Explanation:
If an event can occur in ‘m’ different ways following,
which another event can occur in ‘n’ different ways,
following which a third event can occur in ‘p’ different ways.
The total number of occurrence to the events in the given order is m x n x p.
3 Breads,
3 Cold cuts,
3 Cheese
2 x 3 x 3 = 18
18 different combinations are possible from the choices.

Question 46.

Name two pairs of alternate interior angles.
___________ and ___________
___________ and ___________
Name two pairs of alternate exterior angles.
___________ and ___________
___________ and ___________
Name a pair of vertical angles.
___________ and ___________
Name two pairs of supplementary angles.
___________ and ___________
___________ and ___________
Answer:
Alternate interior angles:
\(\angle{D}\) and \(\angle{F}\);
\(\angle{E}\) and \(\angle{C}\).
Alternate exterior angles:
\(\angle{A}\) and \(\angle{G}\);
\(\angle{B}\) and \(\angle{H}\).
Vertical angles:
\(\angle{A}\) and \(\angle{C}\);
\(\angle{B}\) and \(\angle{D}\);
\(\angle{E}\) and \(\angle{G}\);
\(\angle{F}\) and \(\angle{H}\).
Supplementary angles:
\(\angle{A}\) and \(\angle{B}\);
\(\angle{B}\) and \(\angle{C}\);
\(\angle{A}\) and \(\angle{D}\);
\(\angle{F}\) and \(\angle{G}\);
\(\angle{D}\) and \(\angle{F}\);
\(\angle{G}\) and \(\angle{H}\);
\(\angle{H}\) and \(\angle{E}\);
\(\angle{H}\) and \(\angle{A}\).
\(\angle{G}\) and \(\angle{B}\);
\(\angle{E}\) and \(\angle{B}\).
\(\angle{F}\) and \(\angle{A}\).
Explanation:
Alternate interior angles:
The two angles, formed when a line crosses two other lines,
that lie on opposite sides of the transversal line and on opposite relative sides of the other lines.
If the two lines crossed are parallel, the alternate angles are equal
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.
They lie on the inner side of the parallel lines but on the opposite sides of the transversal.
The transversal crosses through the two lines which are Coplanar at separate points.
Alternate exterior angles:
The term alternate exterior angles is often used when two lines are cut by a third line, a transversal .
The Alternate Exterior Angles Theorem states that if k and l are parallel ,
then the pairs of alternate exterior angles are congruent .
Vertical angles:
Vertical angles are angles opposite each other where two lines cross.
Supplementary angles:
The two angles or arcs whose sum is 180 degrees.

Question 47.
Use the Pythagorean Theorem to find the value of x.

Answer:
8
Explanation:

AC² = AB² + BC²
10² = x² + 6²
100 – 36 = AB²
AB² = 64
AB = 8
x = 8

Question 48.
Name 2 line segments.

Name 4 rays. ______________
Name a line. ______________
Answer:
Line segments:
\(\overline{AB}\), \(\overline{AF}\), \(\overline{AC}\), \(\overline{DB}\),\(\overline{BE}\), \(\overline{HG}\);
Rays:
\(\overline{AF}\), \(\overline{AC}\), \(\overline{BE}\), \(\overline{BD}\),
\(\overline{AB}\), \(\overline{BA}\);
Line:
\(\overline{AB}\)
Explanation:
A line segment is part of a line that has two endpoints and is finite in length.
A ray is a line segment that extends indefinitely in one direction.
A line has no end points.

Calculate the volume and surface area of the figures

Question 49.

Volume _____________
Surface Area ____________
Answer:
Volume = 24 cu in;
Surface Area = 52 sq in.
Explanation:
Volume = length x width x height
V = 2 x 4 x 3
V  = 24 cu in;
Surface Area = 2(lxw + wxh + hxl)
SA= 2(2×4 + 4×3 + 3×2)
SA = 2(8 + 12 + 6)
SA = 52 sq in.

Question 50.

Volume _____________
Surface Area ____________
Answer:
Volume = 288π cu units;
Surface Area = 168π sq units.
Explanation:
Volume = πr² h cu in
V = π 6² 8
V = π x 36 x 8
V = 288π cu in
Surface Area (SA)= 2πrh + 2πr²  sq in
SA = 2π x 6 x 8 + 2π 6²  sq yd
SA = 168π sq in

Question 51.

Volume ______________
Answer:
Volume = \(\frac{40}{3}\)π cubic units.
Explanation:
Volume of cone V= π r²h(1/3)
V = π 2²x 10 (1/3)
V = π 4 x 10 x 1/3
V = \(\frac{40}{3}\)π cu units;

Question 52.
Estimate the value of \(\sqrt{140}\) __________. Of \(\sqrt{48}\) ____________
Answer:
Estimate: 11.8;
6.9
Explanation:
\(\sqrt{140}\)
11 x 11 = 121
12 x 12 = 144
\(\sqrt{140}\) can estimate as nearer to 12
\(\sqrt{140}\) = 11.8
\(\sqrt{48}\)
6 x 6 = 36
7 x 7 = 49
\(\sqrt{48}\) can estimate as nearer to 7
\(\sqrt{48}\) = 6.9

Question 53.
Convert \(0 . \overline{573}\) to a fraction.
Answer:
\(\frac{573}{999}\) = \(\frac{191}{333}\)
Explanation:
\(0 . \overline{573}\)
Let
x = 0.573573573573 …….  Eq(1)
by multiplying 1000 on both sides
1000 x = 573.573573573…….Eq(2)
by subtracting Eq(1) from Eq(2) as shown below

999 x = 573
= \(\frac{573}{999}\)
Dividing both the numerator and denominator by 3
= \(\frac{573÷3}{999÷3}\)
= \(\frac{191}{333}\)

Question 54.
Solve 3(2x + 4) = 6(x + 2).
Answer:
Infinite solutions.
Explanation:
3(2x + 4) = 6(x + 2).
a(b+c) = a x b + a x c Distributive property
3(2x + 4) = 6(x + 2).
6x + 12 = 6x + 12
6x – 6x = 12 – 12
Infinite solutions.

Question 55.
Solve 26x + 4 = 6 + 26x – 3.
Answer:
No solutions.
Explanation:
26x + 4 = 6 + 26x – 3.
26x – 26x = 6 – 3 – 4
26x – 26x = 6 – 7
0 = – 1   No solutions.

Question 56.
Complete and graph the function table for y = x². Is it a linear or nonlinear function?

Answer:
Non Linear
Explanation:
A non-linear equation is such which does not form a straight line.
It looks like a curve in a graph and has a variable slope value.

Question 57.
Look at the graph below.

The function is increasing between points _______________
The function is decreasing between points _______________
Answer:
The function is increasing between points A and B;
The function is decreasing between points B and C.
Explanation:
The function is increasing between points A and B
y value is  increasing from negative to positive
i.e from third quadrant to second quadrant.
The function is decreasing between points B and C.
y value is  decreasing from positive to negative
i.e from  second quadrant to third quadrant

Question 58.
How many times greater is 12 × 10³ than 4 × 10²?
Answer:
30
Explanation:
\(\frac{12 × 10³}{4 x 10²}\)
= 3 x 10^3-2
= 3 x 10
= 30

Question 59.
Are these polygons similar? _____________ If so, what is the scale factor? _____________

Answer:
Yes,
Explanation:
Larger is 6 times bigger than the smaller.
Explanation:

So, when two polygons are similar,
then the ratio of the lengths of any two corresponding sides is called the scale factor.
This means that the ratio of all parts of a polygon is the same as the ratio of the sides.
using the figure above, the simplified ratios of the lengths of the corresponding sides of the similar trapezoids is the scale factor.
\(\frac{PQ}{AB}\) = \(\frac{90}{15}\) = 6
\(\frac{PR}{AC}\) = \(\frac{42}{7}\) = 6
Larger is 6 times bigger than the smaller.

Question 60.
What type of transformation is shown below?

Answer:
Translation:
Explanation:
A translation occurs when we take a figure and make an identical duplicate figure of it.
We can move the figure from left to right or bottom to top or up down.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Unit Test Lessons 10–12 to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Unit Test Lessons 10–12 Answer Key

Restate in exponential form, then calculate.

Question 1.
4 × 4 × 4 + 3 × 3 × 3
Answer:
91
Explanation:
a x a x a … a(m times) = a^m
4 × 4 × 4 + 3 × 3 × 3
= 4³ + 3³
= 64 + 27
= 91

Question 2.
3 × 3 × 2 × 2 – 3 × 3 × 3
Answer:
91
Explanation:
a x a x a … a(m times) = a^m
3 × 3 × 2 × 2 – 3 × 3 × 3
= 3² x 2² – 3³ 
= 9 x 4 – 27
= 36 – 27
= 9

Question 3.
4 × 4 × 4 × 2 × 2 + 4 × 4 + 6 × 6 – 3 × 3
Answer:299
Explanation:
a x a x a … a(m times) = a^m
4 × 4 × 4 x 2 × 2 + 4 x 4 + 6 x 6 – 3 × 3
= 4³x 2² + 4² + 6² – 3² 
= 64 x 4 + 16 + 36 – 9
= 256 + 16 + 36 – 9
= 308 – 9
= 299

Restate using scientific notation.

Question 4.
13,224,714.066
Answer:
1.3224714066 x 10⁷
Explanation:
Scientific notation is a way to make these numbers easier to work with.
In scientific notation, we move the decimal place until you have a number between 1 and 10.
Then you add a power of ten that tells how many places you moved the decimal.
In scientific notation, 13,224,714.066 becomes 1.3224714066 x 10⁷.

Question 5.
25,354.011
Answer:
25354011 x 10⁴
Explanation:
Scientific notation is a way to make these numbers easier to work with.
In scientific notation, we move the decimal place until you have a number between 1 and 10.
Then you add a power of ten that tells how many places you moved the decimal.
In scientific notation, 25,354.011 becomes 25354011 x 10⁴

Question 6.
0.180705
Answer:
1.80705 x 10^-1
Explanation:
Scientific notation is a way to make these numbers easier to work with.
In scientific notation, we move the decimal place until you have a number between 1 and 10.
Then you add a power of ten that tells how many places you moved the decimal.
In scientific notation, 0.180705 becomes 1.80705 x 10^-1
Question 7.
22,294,698,171.7
Answer:
2.22946981717 x 10⁴
Explanation:
Scientific notation is a way to make these numbers easier to work with.
In scientific notation, we move the decimal place until you have a number between 1 and 10.
Then you add a power of ten that tells how many places you moved the decimal.
In scientific notation, 22,294,698,171.7 becomes 2.22946981717 x 10⁴

Question 8.
866.0506
Answer:
8.660506 x 10²
Explanation:
Scientific notation is a way to make these numbers easier to work with.
In scientific notation, we move the decimal place until you have a number between 1 and 10.
Then you add a power of ten that tells how many places you moved the decimal.
In scientific notation, 866.0506 becomes 8.660506 x 10²

Question 9.
Estimate 118.6591
Answer:
1 x 10²
118.6591 x 10⁴
Explanation:
Scientific notation is a way to make these numbers easier to work with.
In scientific notation, we move the decimal place until you have a number between 1 and 10.
Then you add a power of ten that tells how many places you moved the decimal.
In scientific notation, 118.6591 becomes 118.6591 x 10⁴

Calculate using Order of Operations (PEMDAS).

Question 10.
4 × 2(8 – 4) + (12 – 6) × 2 + (6 – 4) × 3 + 22
Answer:
72
Explanation:
4 × 2(8 – 4) + (12 – 6) × 2 + (6 – 4) × 3 + 22
= 4 × 2(4) + 6 × 2 + 2 × 3 + 22
= 32 + 12 + 6 + 22
= 72

Question 11.
12 + 2(7 – 5) + (5 – 2) × 2 + 2(6 – 2)
Answer:
30
Explanation:
12 + 2(7 – 5) + (5 – 2) × 2 + 2(6 – 2)
= 12 + 2(2) + 3 × 2 + 2(4)
= 12 + 4 + 6 + 8
= 30

Question 12.
22 + (2 × 5) × 2 + 2(7 – 3)
Answer:
50
Explanation:
= 22 + (2 × 5) × 2 + 2(7 – 3)
= 22 + 10 × 2 + 2(4)
=  22 + 20 × 2 + 8
= 22 + 40 + 8
= 50

Question 13.
36 – 3(6 – 2) + 7 × 3 + 2(5) – 4
Answer:
51
Explanation:
36 – 3(6 – 2) + 7 × 3 + 2(5) – 4
= 36 – 3(4) + 7 × 3 + 2(5) – 4
= 36 – 12 + 21 + 10 – 4
= 51

Calculate

Question 14.
4³
Answer:
64
Explanation:
a^m = a x a x a … a(m times) =
= 4 x 4 x 4
= 64

Question 15.
6³
Answer:
216
Explanation:
a^m = a x a x a … a(m times) =
= 6 x 6 x 6
= 216

Question 16.
2⁵ × 2^-3
Answer:
4
Explanation:
a^m  x aⁿ  = a^m+n
a^m  x a^-n  = a^m-n
= 2⁵ × 2^-3
= 2^{5 – 3}
= 2²
= 4
Question 17.
10⁹ ÷ 10⁷
Answer:
100
Explanation:
a^m  ÷ aⁿ  = a^{m – n}
= 10⁹ ÷ 10⁷
= 10^{9 – 7}
= 10²
= 100

Question 18.
12¹¹ × 12^-11
Answer:
1
Explanation:
a^m  x a^-n  = a^m-n
= 12¹¹ × 12^-11
= 12^{11 – 11}
= 12⁰      (a⁰  = 1)
= 1

Question 19.
\(\sqrt{64}\)
Answer:
8
Explanation:
8 x 8 = 64
\(\sqrt{64}\) = 8

Question 20.
\(\sqrt{144}\)
Answer:
12
Explanation:
12 x 12 = 144
\(\sqrt{144}\)
= 12

Question 21.
\(\sqrt{625}\)
Answer:
25
Explanation:
25 x 25 = 625
\(\sqrt{625}\) = 25

Question 22.
\(\sqrt{196}\)
Answer:
14
Explanation:
14 x 14 = 196
\(\sqrt{196}\)
= 14

Question 23.
\(\sqrt{2.25}\)
Answer:
1.5
Explanation:
1.5 x 1.5 = 2.25
\(\sqrt{2.25}\)
= 1.5

Question 24.
\(\sqrt{1.69}\)
Answer:
1.3
Explanation:
\(\sqrt{1.69}\)
1.3 x 1.3 = 1.69
\(\sqrt{1.69}\) =1.3

Question 25.
Estimate \(\sqrt{8200}\)
Answer:
90
Explanation:
Estimate \(\sqrt{8200}\)
90 x 90 = 8100
Estimate \(\sqrt{8200}\) = 90

Identity the number property that each expression displays.

Question 26.
44(1) = 44
Answer:
Identity Property of Multiplication.
Explanation:
The identity property of multiplication says that the product of 1 and any number is that number.
44 × 1 = 44 times of 1.

Question 27.
19 + 0 = 19
Answer:
Identity Property of Addition.
Explanation:
When we add zero to any whole number, we get the same whole number.
Zero is an additive identity for whole numbers.
Is it an additive identity again for integers also
a + 0 = a  = 0 + a
19 + 0 = 19 = 0 + 19

Question 28.
6 + (7 + 6) = (6 + 7) + 6
Answer:
Associative Property of Addition.
Explanation:
The addition is commutative for integers.
Changing the grouping of addends does not change the sum.
In general, for any two integers a and b, we can say as,
a + b = b + a
Addition is associative for integers.
In general for any integers a, b and c, we can say as,
a + (b + c) = (a + b) + c

Question 29.
3(7 + 3) = 3(7) + 3(3)
Answer:
Distributive Property.
Explanation:
a( b +c ) = (a x b) + (a x c)
Distributive property is multiplying the sum of two or more addends ,
by a number will give the same result as multiplying each addend individually,
by the number and then adding the products together.
3(7 + 3) = 3 x 10 = 30
3(7) + 3(3)
= 21 + 9
= 30

Question 30.
14 + 16 + 20 = 20 + 16 + 14
Answer:
Commutative Property of Addition.
Explanation:
Commutative property of addition is when we Change the order of addends does not change the sum.
14 + 16 + 20 = 20 + 16 + 14
a + (b + c) = (c + b) + a
= 14 + 16 + 20
= 50

Question 31.
17 = 8 + 9, 17 – 15 = 8 + 9 – 15
Answer:
Equality Property of Subtraction.
Explanation:
The subtraction property of equality states that,
when the same number is subtracted from both sides of an equality,
then the two sides of the equation still remain equal.
17 = 8 + 9,
17 = 17
17 – 15 = 8 + 9 – 15
2 = 17 – 15 = 2

Question 32.
43 × 0 = 0
Answer:
Zero Property of Multiplication.
Explanation:
According to the zero property of multiplication,
the product of any number and zero, is zero.
a x 0 = 0 = 0 x a
43 x 0 = 0 = 0 x 43

Question 33.
35 = 18 + 17, 35 + 9 = 18 + 17 + 9
Answer:
Equality Property of Addition.
Explanation:
The addition property of equality states that,
if the same amount is added to both sides of an equation.
35 = 18 + 17,
35 = 35
35 + 9 = 18 + 17 + 9
44 = 44

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

Question 34.
-5 + 5 – 5
Answer:
-5 – Point A
Explanation:
In Maths, number lines are the horizontal straight lines in which the integers are placed in equal intervals.

– 5 + 5 – 5 = – 5

Question 35.
-10 + 4 – 1
Answer:
-7 – Point B
Explanation:
In Maths, number lines are the horizontal straight lines in which the integers are placed in equal intervals.

-10 + 4 – 1
= -11 + 4
= -7

Question 36.
-7 + (-4) + 3
Answer:
-8 – Point D
Explanation:
In Maths, number lines are the horizontal straight lines in which the integers are placed in equal intervals.

-7 + (-4) + 3
= -7 – 4 + 3
= – 11 + 3
= – 8

Question 37.
9 – 5 + (-7)
Answer:
-3 – Point C
Explanation:
In Maths, number lines are the horizontal straight lines in which the integers are placed in equal intervals.

9 – 5 + (-7)
= 9 – 5 – 7
= 9 – 12
= – 3

Calculate.

Question 38.
-60 × 25
Answer:
-1500
Explanation:
Multiply the given numbers or factors starting from ones, tens and so on..
Once you get the product or answer add minus sign to the answer.

Question 39.
-135 ÷ 15
Answer:
-9
Explanation:
-135 ÷ 15
= -135 ÷ 15    (15 x – 9 = -135)
= -9

Question 40.
12 × (-5 – 7) ÷ (8 – 16)
Answer:
78
Explanation:
12 × (-5 – 7) ÷ (8 – 16)
12 × -12÷ -8
3 x 6 ÷ (8 – 16)

Question 41.
630 ÷ -70
Answer:
-9
Explanation:
630 ÷ -70
= 63 ÷ -7
= -9

Question 42.
14(-6) ÷ -7
Answer:
12
Explanation:
14(-6) ÷ -7
= -14 x 6 ÷ -7
= 14 x 6 ÷ 7
= 2 x 6
= 12

Question 43.
-5 × (-3) × (14 – 18)
Answer:
-60
Explanation:
-5 × (-3) × (14 – 18)
= -5 ×-3  × -4
= -5 ×12
= – 60

Question 44.
-24 × -3 ÷ -2
Answer:
-36
Explanation:
-24 × -3 ÷ -2
= -24 × -3 ÷ -2
= -24 × -3 ÷ -2
= -36

Question 45.
15 × -3 ÷ 9
Answer:
-5
Explanation:
15 × -3 ÷ 9
= 15 × -3 ÷ 9
= -5

Question 46.
(19 – 23) × (5 – 4) × (17 – 15)
Answer:
-8
Explanation:
(19 – 23) × (5 – 4) × (17 – 15)
= (19 – 23) × 1 × 2
= -4 × 2
= -8

Question 47.
How many times larger is the total U.S. federal budget of $4 × 10⁹ than the budget for education of $8 × 10⁷?
Answer:
50
Explanation:
The total U.S. federal budget of $4 × 10⁹ than the budget for education of $8 × 10⁷
$4 × 10⁹ of  $8 × 10⁷
= \(\frac{4 × 10⁹}{8 × 10⁷}\)
= \(\frac{1 × 10²}{2}\)
= 0.5 × 10²
= 50

Convert the following to fractions.

Question 48.
7\(\frac{2}{3}\)
Answer:
\(\frac{23}{3}\)
Explanation:
7\(\frac{2}{3}\)
Convert mixed fraction to improper fraction.
= 7\(\frac{3 x 7 + 2}{3}\)
= \(\frac{23}{3}\)

Question 49.
0.262626…
Answer:
\(\frac{26}{99}\)
Explanation:
0.26262626…
let
x = 0.262626…————-(Eq 1)
multiplying by 100 on both side
100 x = 26.262626….————-(Eq 2)
on subtracting Eq 1 from Eq 2

x = \(\frac{26}{99}\)

Question 50.
1.56
Answer:
\(\frac{156}{100}\) or \(\frac{39}{25}\)
Explanation:
By multiplying both the numerator and denominator by 100.
\(\frac{1.56 x 100}{100}\)
= \(\frac{156}{100}\)
Dividing both the numerator and denominator by 4.
= \(\frac{39}{25}\)

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Unit Test Lessons 13–14 to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Unit Test Lessons 13–14 Answer Key

Describe in words the following expressions.

Question 1.
2x + 15
Answer:
Two times a number plus fifteen.
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
2x + 15
Two times a number plus fifteen.

Question 2.
5y – 12
Answer:
A number 5 times less twelve.
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
5y – 12
A number 5 times less twelve.

Solve for x.

Question 3.
x + 4 = 7
Answer:
x = 3
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x + 4 = 7
x = 7 – 4
x = 3

Question 4.
x + 8 = 124
Answer:
x = 116
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x + 8 = 124
x = 124 – 8
x = 116

Question 5.
x + 2 = 7
Answer:
x = 5
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x + 2 = 7
x = 7 – 2
x = 5

Question 6.
x + 9 = 14
Answer:
x = 5
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x + 9 = 14
x = 14 – 9
x = 5

Question 7.
x – 6 = 4
Answer:
x = 10
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x – 6 = 4
x = 4 + 6
x = 10

Question 8.
11x – 2 – 11x = -2
Answer:
Infinite
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
11x – 2 – 11x = -2
11x – 11x = -2 + 2
x = 0

Question 9.
x – 2 = 13
Answer:
x = 15
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x – 2 = 13
x = 13 + 2
x = 15

Question 10.
x – 5 = 9
Answer:
x = 14
Explanation:
An algebraic expression is a letter, a number, or a combination of the two, connected by some,
mathematical operation such as addition, subtraction, multiplication, or division.
x – 5 = 9
x = 9 + 5
x = 14

Solve for y.

Question 11.
3y – 5 = 7
Answer:
y = 4
Explanation:
3y – 5 = 7
3y = 7 + 5
y = 12 ÷ 3
y = 4

Question 12.
2y + 3 = 11
Answer:
y = 4
Explanation:
2y + 3 = 11
2y = 11 – 3
y = 8 ÷ 2
y = 4

Question 13.
4y – 3 = 13
Answer:
y = 4
Explanation:
4y – 3 = 13
4y = 13 + 3
y = 16 ÷ 4
y = 4

Question 14.
2y – 7 = 9 + 2y
Answer:
No solution
Explanation:
2y – 7 = 9 + 2y
2y – 2y = 9 + 7
0 = 16
So, there is no solution.

Question 15.
6y – 6 = 18
Answer:
y = 4
Explanation:
6y – 6 = 18
6y = 18 + 6
y = 24 ÷ 6
y = 4

Question 16.
7y – 14 = 28
Answer:
y = 6
Explanation:
7y – 14 = 28
7y = 28 + 14
y = 42 ÷ 7
y = 6

Question 17.
6y + 26 = 56
Answer:
y = 5
Explanation:
6y + 26 = 56
6y = 56 – 26
y = 30 ÷ 6
y = 5

Question 18.
12y – 24 = 48
Answer:
y = 6
Explanation:
12y – 24 = 48
12y = 48 + 24
12y = 72
y = 72 ÷ 12
y = 6

Give the coordinates for each point.

Question 19.
A _____________
Answer:
A(1,1)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
A(1,1) is marked on the above cartesian plane x-axis and y-axis.

Question 20.
B _____________
Answer:
B(3,1)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
B(3,1) is marked on the above cartesian plane x-axis and y-axis.

Question 21.
C _____________
Answer:
C(-1,-3)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
C(-1, -3) is marked on the above cartesian plane x-axis and y-axis.

Question 22.
D _____________
Answer:
D(-1,2)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
D(-1,2) is marked on the above cartesian plane x-axis and y-axis.

Question 23.
E _____________
Answer:
E(-2,1)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
E(-2,1) is marked on the above cartesian plane x-axis and y-axis.

Question 24.
F _____________
Answer:
F(-3,-3)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
F(-3,-3) is marked on the above cartesian plane x-axis and y-axis.

Question 25.
G _____________
Answer:
G(4, -4)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis. The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
G(4, -4) is marked on the above cartesian plane x-axis and y-axis.

Question 26.
H _____________
Answer:
H(5, 5)
Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
H(5, 5) is marked on the above cartesian plane x-axis and y-axis.

Plot the following points on the grid.

Question 27.
Point A (6, 6)
Point B (-3, -3)
Point C (-1, 2)
Point D (3, -2)
Point E (4, -2)
Point F (-4, 2)
Point G (-6, -6)
Point H (-1, 3)
Answer:

Explanation:
Find the first number along the x-axis.
Put your finger on that spot and move your finger up and down in a vertical line,
then still you will be at the same x number.
To find the exact point you want, look at the second number.
It tells you where to move your finger along the vertical line.
The above diagram shows the following points as,
Point A (6, 6)
Point B (-3, -3)
Point C (-1, 2)
Point D (3, -2)
Point E (4, -2)
Point F (-4, 2)
Point G (-6, -6)
Point H (-1, 3)

Create a function table for 2x + 1 and plot the ordered pairs on the grid.

Question 28.
2x + 1

What is the slope of the line created?
Answer:
The slope is 2.
Explanation:
Create function table for each equation.
y = 2x + 1
x = 0, 1, 2, 3…
y =  2 x 0 + 1
y = 1
Substitute a number of values of x in the equation,
then complete the equation to determine the value of y.

Slope refers to the amount by which a line rises or falls,
as you read a co ordinate grid from left to right.
Positive Slope or Negative Slope.
Slope = rise/run
Slope =  2/1 = 2

Question 29.
If the function table above (for question 28) were changed to 2x + 3, what would happen to the slope of the line?
Answer:
The line shifts, but the slope is still 2.
Explanation:
Slope refers to the amount by which a line rises or falls,
as you read a co ordinate grid from left to right.
Positive Slope or Negative Slope
Slope = rise/run
Slope =  2/1 = 2

Create function tables for 2x – 1 and x + 3.
Plot the ordered pairs and determine the value of x,
where the equation 2x – 1 = x + 3 is true.

Question 30.
2x – 1

x + 3

Answer:

Explanation:
Create function table for each equation as shown above.
Substitute a number of values of x in the equation,
then complete the equation to determine the value of y.
Pot the two lines on a co-ordinate plane.
Visually assess the lines to determine the point of intersection.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Unit Test Lessons 15–17 to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Unit Test Lessons 15–17 Answer Key

Question 1.
Manny is going to replace the trim around the windows in his house. The trim for each window measures 10\(\frac{1}{2}\) feet. If Manny has 15 windows in his house, how many inches of trim does he need to replace?
Answer:
1890 in.
Explanation:
The trim for each window measures 10\(\frac{1}{2}\) feet.
10\(\frac{1}{2}\)
1 feet = 12 inches
Half feet = 6 inches.
= 10 x 12 + 6
= 126 inches
If Manny has 15 windows in his house,
126 x 15 =1890 inches.

Question 2.
Annie’s fish tank holds 39\(\frac{1}{2}\) gallons of water. She is using a 1 quart container to fill the tank. How many full containers will Annie need to fill the tank?
Answer:
158 containers full.
Explanation:
1 gallon = 4 quarts
39\(\frac{1}{2}\) = x
convert mixed fraction in to improper fraction
39\(\frac{1}{2}\) = \(\frac{79}{2}\)
\(\frac{79}{2}\)  x 4
= \(\frac{79 x 4}{2}\)
= 79 x 2
= 158  full containers will Annie need to fill the tank.

Question 3.
Florence weighed boxes for the shipping department. The first box weighed 196 ounces. The second box weighed 13\(\frac{3}{8}\) pounds. Which box weighed more?
Answer:
The second box 13\(\frac{3}{8}\) vs 12.25 lb
Explanation:
The first box weighed 196 ounces.
1 pound = 16 ounces
first box weighed 196 ounces
= \(\frac{196}{16}\)
=12.25 lb
The second box 13\(\frac{3}{8}\) is weighed more

Question 4.
Mandie plans to paint the side of her barn. The side measures 10 meters long arid 5.5 meters high. How much area does Mandie need to cover with paint?
____________ square meters
Answer:
55 square meters.
Explanation:
The side measures 10 meters long arid 5.5 meters high.
Area of the side of her barn to paint A
A = length x width
A = 10 x 5.5
A = 55 square meters

Question 5.

What is the area of the rectangle? ______________
What is the perimeter of the rectangle? ____________
Answer:
Area 132 sq ft,
Perimeter 46.
Explanation:
The area of the rectangle = l x b
1 ft = 12 in
132 in = 132/12 = 11 ft
A =  12 x 11
A = 132 sq ft
Perimeter is P = 2(Length + Width)
P = 2(12 + 11)
P = 2(23)
P =46 sq ft

Question 6.

What is the area of the right triangle?
_____________ square feet
What is the perimeter?
____________ inches
Answer:
Area 54 sq ft,
Perimeter 432 inches.
Explanation:
Area of a triangle A = (1/2) base x height
A = 1/2 x b x h
A = 1/2 x 9 x 12
A = 54 sq ft
Perimeter of a trangle is sum of 3 sides.
P = 9ft + 12 ft + 180in
P = (9 + 12) 12 + 180 in
P = 252 + 180
P = 432 in
Question 7.
What is the area of the base of the rectangular box?

_____________ square feet
Answer:
7.5 sq ft.
Explanation:
Area of a rectangle A = length x width
A = l x w
L = 36/12 = 3 ft
A = 3 x 2 \(\frac{1}{2}\)
A = 3 x \(\frac{5}{2}\)
A = \(\frac{15}{2}\)
A = 7.5 sq ft

Question 8.
A spacecraft must travel 24.1 kilometers per second to leave the Earth’s atmosphere. How far does the spacecraft travel in a minute?
In an hour? _____________________
In a day? _________________
Answer:
1446 km in an minute.
86,760 km in a hour.
2,082240 km in a day.
Explanation:
A spacecraft must travel 24.1 kilometers per second to leave the Earth’s atmosphere.
1 minute = 60 sec
24.1 x 60 = 1,446 km per minute
1 hour = 60 minutes
1,446 x 60 = 86,760 km
1 day = 24hrs
86,760 x 24 = 2,082,240 km

Question 9.
A school banner is 5.5 meters in length and 1,850 millimeters in width. How much fabric was used to make the banner?
_____________ sq cm
Answer:
101750 sq cm
Explanation:
A school banner is 5.5 meters in length and 1,850 millimeters in width.
convert 5.5 meters in cm,
1m = 100 cm
5.5 x 100 = 550 cm
1,850 millimeters in width
1,850/10 = 185 cm
Area = Length x Width
A = 550 x 185
A = 101750 sq cm

Question 10.
Blanche has three cans of paint to mix. One can holds 1,957 milliliters of paint, the second can holds 115.6 centiliters of paint, and the third can holds 3.9 liters of paint. How much paint will Blanche mix?
______________ liters
Answer:
7.013 Lits
Explanation:
One can holds 1,957 milliliters of paint
1957/1000 = 1.957 liters
Second can holds 115.6 centiliters of paint,
115.6/100 = 1.156
The third can holds 3.9 liters of paint.
3.9 liters
Total paint will Blanche mix
3.9 + 1.156 + 1.957
= 7.013 liters

Question 11.
What is the area of a triangle with sides of 12 cm, a base of 6 cm, and a height of 8 cm?

______________ sq cm
What is the perimeter of the triangle?
Answer:
Area = 24 sq cm.
Perimeter = 30 cm.
Explanation:
Area of Triangle A = (1/2) x 3 x 8
A = 12 x 2
Area of triangle = 24 sq cm

Question 12.
Frank walked around the entire rectangular school playground, which measures 126 meters by 6,500 centimeters. How far did Frank walk?
____________ meters
What is the area of the school playground?
_____________ square meters
Answer:
Distance = 382 meter;
Area = 8190 sq m.
Explanation:
A rectangular school playground,
which measures 126 meters by 6,500 centimeters
6500/100 = 65 meters
Frank walk is the perimeter of the rectangle P.
P = 2(length + width)
P = 2( 126 + 65)
Distance = 382 meter Frank walked.
Area of a rectangular school playground,
A = length x width
A = 126 x 65
Area = 8190 sq m.

Question 13.
What is the area of a rectangle that measures 4.6 meters in width, and 5.5 meters in length?
_______________ square meters
Answer:
25.3 sq m.
Explanation:
The area of a rectangle that measures 4.6 meters in width, and 5.5 meters in length.
Area of a rectangle = length x width
A = 4.6 x 5.5
A = 25.3 sq m

Question 14.
The average player on the soccer team weighs 165 pounds. About how much is that in kilograms?
Answer:
75 kg
Explanation:
The average player on the soccer team weighs 165 pounds.
1 kg = 2.2 pounds
x kg = 165 pounds
x = 165/2.2 =75 kg

Question 15.
The average pickup truck has a gas tank that holds 95 liters of gasoline. How much is that in quarts and in gallons?
_____________ quarts
_____________ gallons
Answer:
About 100 quarts;
25 gallons.
Explanation:
A gas tank that holds 95 liters of gasoline.
1 gallon = 3.8 liters
95 / 3.8 = 25 gallons
1 liter = 1.06 quarts
95 liter = 95 x 1.06
= 100 quarts

Question 16.
Pauline was looking for lawn-mowing jobs for the summer. She surveyed the neighborhood and found out that the average lawn measured 60 feet by 45 feet. What is the area in square feet?
_____________ sq ft
About how much is the total area in square meters?
______________ sq meters
Answer:
2700 sq ft;
About 250 sq m.
Explanation:
The average lawn measured 60 feet by 45 feet.
Area = Length x width
A = 60 x 45
A = 2700 sq ft
as we know..
1 meter = 3.28 ft
60 ft = 18.28 m
45 ft = 13.7 m
The area in square meters,
Area = Length x width
A = 18.28 x 13.7
A = 250 sq m

Question 17.
The distance of a flight from Cleveland to New Orleans is about 1,250 miles. The average speed of a commercial airliner is about 830 kilometers per hour. About how long will it take to fly from Cleveland to New Orleans?
______________ hours
Answer:
About 2\(\frac{1}{2}\) hours.
Explanation:
The distance of a flight from Cleveland to New Orleans is about 1,250 miles.
The average speed of a commercial airliner is about 830 kilometers per hour.
1 mile = 1.6 km
1250 miles = 1250 x 1.6 = 2000 km
time = distance / speed
time = 2000/ 830
2\(\frac{1}{2}\)

Question 18.
The air-conditioning company suggests that people keep the temperature in their homes between 22 and 28 degrees Celsius during the summer. What is the temperature range in degrees Fahrenheit?
Answer:
71.6° to 82.4°F
Explanation:
To convert temperatures in degrees Fahrenheit to Celsius,
multiply by 1.8 (or 9/5) and add 32
The formula for converting Celsius to Fahrenheit  is
F = 1.8 x C + 32
F = 1.8 x 22 + 32
F = 39.6 + 32
F = 71.6°F
F = 1.8 x C + 32
F = 1.8 x 28 + 32
F = 50.4 + 32
F = 82.4°F

Question 19.

What is the area of the base of the rectangular solid shown?
Answer:
32 sq m.
Explanation:
Area of the base of a rectangle = Length x Width
A = l x w
A = 8 x 4
A = 32 sq cm

Question 20.

What is the area of the triangular face on the figure shown?
Answer:
48 sq in.
Explanation:
Area of the triangular face = (1/2) x base x height
A = (1/2) x 12 x 8
A= 48 sq in.

Question 21.
In track and field, the standard middle distance event is the 5,000 meter race. About how many feet, is 5,000 meters?
______________ feet
Answer:
16,500 ft
Explanation:
Standard middle distance event is the 5,000 meter race.
About how many feet, is 5,000 meters,
1 meter = 3.3 ft
5000 meters =
5000 x 3.3 = 16,500 ft

Question 22.
A body temperature of 103.6° F is considered an extremely high fever. What temperature is that in Celsius?
Answer:
39.8°C
Explanation:
To convert temperatures in degrees Fahrenheit to Celsius,
subtract 32 and multiply by 0.5556 (or 5/9).
Fahrenheit and Celsius are the same at -40°.
The formula for converting Fahrenheit to Celsius is
C = 5/9(F-32).
C = 5/9(103.6 – 32)
C = 39.8°C

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Unit Test Lessons 23–24 to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Unit Test Lessons 23–24 Answer Key

Question 1.
What is the probability of:

Spinning an odd number? ________________
Spinning a 2? ________________
Spinning either a 2 or 4? ________________
Spinning a 1? ________________
Answer:
Spinning an odd number is \(\frac{6}{12}\);
Spinning a 2 is \(\frac{1}{6}\);
Spinning either a 2 or 4 \(\frac{5}{12}\);
Spinning a 1 \(\frac{1}{6}\).
Explanation:
Total event on the spinning wheel,
[1, 2, 4, 5, 2, 3,7, 6, 4, 4, 1, 3]
and the total possible events on the spinning wheel is 12.
all positive events = [2, 2, 4, 4, 4, 6]
all negative events = [1, 1, 3, 3, 5, 7]
Spinning an odd number is \(\frac{6}{12}\)
Spinning an odd number is \(\frac{1}{2}\)
Total event on the spinning wheel,
[1, 2, 4, 5, 2, 3,7, 6, 4, 4, 1, 3]
Spinning a 2 is \(\frac{2}{12}\)
\(\frac{1}{6}\)
Spinning either a 2 or 4,
[2, 2 and 4, 4, 4] total 5 events.
\(\frac{2+3}{12}\)
\(\frac{5}{12}\)
Spinning a 1 = \(\frac{2}{12}\)
= \(\frac{1}{6}\)

Question 2.

What is the range of the data? ________________
What is the median of the data? ________________
What is the mean of the data? ________________
Answer:
The range of the data is 49;
The median of the data 67;
The mean of the data 67.5.
Explanation:
In the above given stem and leaf diagram,
the starting point is 45 and the ending point or number is 94.
The difference between the ending number – starting number is range.
Range = 94 – 45 = 49
The range of the data is 49.
[45, 46, 56, 58, 61, 67, 72, 77, 78, 89, 94]
The median of the data 67.
The median is the middle number in a sorted,
ascending or descending list of numbers can be more descriptive of the data set than the average.

Mean is the average number by adding all data points and dividing by the number of data points.
Mean = [45 + 46 + 56 + 58 + 61 + 67 + 72 + 77 + 78 + 89 + 94]/11
Mean = 743/11 = 67.5
The mean of the data 67.5

Question 3.

How many different combinations of outfits can be created from the choices? ________________
How many possibilities are there that include green-striped shirts? ________________
How many possibilities are there that include a yellow tie and gray pants? ________________
Answer:
27 different combinations of outfits can be created from the choices.
9 possibilities are there that include green-striped shirts.
3 possibilities are there that include a yellow tie and gray pants.
Explanation:
If an event can occur in ‘m’ different ways following,
which another event can occur in ‘n’ different ways,
following which a third event can occur in ‘p’ different ways.
The total number of occurrence to the events in the given order is m x n x p.
3 Ties,
3 Pants,
3 Shirts,
3 x 3 x 3 = 27
27 different combinations of outfits can be created from the choices.
9 possibilities are there that include green-striped shirts.
3 x 3 = 9
3 possibilities are there that include a yellow tie and gray pants.
1 x 3 = 3

Question 4.

What is the median of this data plot? ________________
What is the range of the data? ________________
Answer:
The median of this data plot is 6.
The range of the data 1.5,
Explanation:
Range of the data = Max – Min
Range = 6.5 – 5 = 1.5
Median on the box plot is the middle point =6.0

Question 5.
Students in James’s health class were polled on their favorite health food snack. The results are displayed on the graph.

What is the least favorite health food snack? ________________
What is the favorite health food snack? ________________
How many more people preferred carrots to cauliflower? ________________
Answer:
The least favorite health food snack is Broccoli;
The favorite health food snack is Hummus;
7 more people preferred carrots to cauliflower.
Explanation:
Students in James’s health class were polled on their favorite health food snack.
The results displayed on the above graph tells that,
only 4 of the students preferred Broccoli,
14 students that is majority of them like Hummus,
and 7 more people preferred carrots to cauliflower.

Question 6.
Janice was making a schedule to determine how many volunteers she needed for the nature center guided tours. She charted the number of visitors to the nature center during the prior summer.

What month had the most visitors? ________________
What month had the fewest visitors? ________________
During what months should Janice increase her staffing to meet the demand for guided tours? ________________
Answer:
July month had the most visitors.
September month had the fewest visitors.
During July to august months Janice increase her staffing to meet the demand for guided tours.
Explanation:
Janice  charted the number of visitors to the nature center during the prior summer.
As she was making a schedule to determine number of volunteers needed for the nature center guided tours.
According to the given chart in July month number of visitors are more and,
in September month number of visitors are less.
During July to August months Janice need to increase her staffing to meet the demand for guided tours.

Question 7.
Peggy charted bike rentals for the previous month. What was the most popular kind of bike rented?

Which kind of bike speed was the least popular?
Answer:
The most popular kind of bike rented is 12 speed.
3 speed bike was the least popular.
Explanation:
Peggy charted bike rentals for the previous month.
From the above pie chart,
12 speed bike is the most popular kind of bike rented and,
3 speed bike was the least popular.

Question 8.
Coach Taylor made a chart of the performance of his two best hitters. In which month did Langely hit more extra base hits than Stanton?

How many more extra base hits did Stanton have than Langely in the month of September?
Answer:
In June month Langely hit more extra base hits than Stanton.
5 more extra base hits Stanton than Langely in the month of September.
Explanation:
Coach Taylor made a chart of the performance of his two best hitters.
From the above chart given,
June is the month where Langely hit more extra base hits than Stanton.
In the month of September 5 more extra base hits Stanton than Langely.

Question 9.
Use the Venn Diagram to display the following data: 25 students take Algebra I, 22 students take US History, and 8 students take both courses.

Answer:

Explanation:
25 students take Algebra I,
22 students take US History,
8 students take both courses.
Number students in Algebra I = 25 – 8 = 17
Number students in U.S. History = 22 – 8 = 14.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 18.1 Points and Lines to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 18.1 Points and Lines

Exercises

SOLVE

Question 1.
Draw the line denoted by \(\overleftrightarrow{\mathrm{CD}}\).
Answer:

Explanation:
Drawn the line denoted by \(\overleftrightarrow{\mathrm{CD}}\) as shown above.

Question 2.
Draw \(\overleftrightarrow{\mathrm{QR}}\).
Answer:

Explanation:
Drawn the line denoted by \(\overleftrightarrow{\mathrm{QR}}\) as shown above.

Question 3.
What would the single letter D indicate?
Answer:
Line Segement,

Explanation:
The single letter D indicates Line segment.

Question 4.
What two lines are shown in the figure?

Answer:
\(\overleftrightarrow{\mathrm{AB}}\),
\(\overleftrightarrow{\mathrm{GH}}\),

Explanation:
The lines shown are \(\overleftrightarrow{\mathrm{AB}}\),
The lines shown are \(\overleftrightarrow{\mathrm{GH}}\).

Question 5.
Describe in words what \(\overleftrightarrow{\mathrm{JK}}\) denotes.
Answer:
Line JK,

Explanation:
In words the given \(\overleftrightarrow{\mathrm{JK}}\) denotes
line JK.

Question 6.
Which of the following is not a line?

Answer:
Bit C,

Explanation:
Bit C is not a line as both sides it has ends.