McGraw Hill Math Grade 7 Posttest Answer Key

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McGraw-Hill Math Grade 7 Posttest Answer Key

Complete the following test items on pages 156-160.

Question 1.
Restate the number 5,176,802.4539.
Expanded form: ____________________
Written form: ____________________
Answer:
Expanded form:
(5 x 1,000,000) +(1 x 100,000) + (7 x 10,000) + (6 x 1,000) + (5 x 0.01) + (3 x 0.001) + (9 x 0.0001)
Written form :
Five million one hundred seventy-six thousand eight hundred two and four thousand five hundred thirty-nine ten thousandths.
Explanation:
In Expanded form each number is multiplied with their place value, as shown above.
In written form each number is written in word form according to their place values.

Question 2.
Brian’s Bakery is having a sale on cakes. They have 95 cakes and will be baking 23 more before the start of the sale. If at the end of the sale they still have 7 cakes, how many cakes did they sell?
Answer:
111 cakes
Explanation:
Initially they have 95 cakes,
By adding 23 more before the start of the sale ,
the number of cakes are 95 + 23 = 118
They left with 7 cakes at the end of the sale,

Question 3.
Stuart pedals 19 miles a day on his bicycle. How many miles does he pedal in the month of February? (Remember, February has 28 days.)
Answer:
532 miles
Explanation:
pedals 19 miles a day on his bicycle,
He pedal in the month of February which has 28 days.
By multiplying 19 x 28, we get the total number of miles he pedaled in the month of February.

Question 4.

Answer:
-2010
Explanation:

As we are multiplying 134 with -15 which is negative number,
we get the product as -2010 as shown below.

Question 5.

Answer:
5320
Explanation:
As we are multiplying 133 with 40, the product is 5320

Question 6.

Answer:
22032
Explanation:
As we are multiplying -432 with -51, the product is 22032.
Both of the given numbers are negative integers,
So, we get product as positive after multiplication.

Question 7.

Answer:
17617
Explanation:
As we are multiplying 223 with 79, the product is 17,617.

Question 8.

Answer:
28
Explanation:

Question 9.

Answer:
-21
Explanation:
As divisor is negative number, the answer is also with negative sign.

Question 10.

Answer:
19.4166
Explanation:

Question 11.

Answer:
24
Explanation:

Question 12.
Danetta bought 19 \(\frac{3}{8}\) kilograms of gerbil food. On the way home, she spilled 3 \(\frac{4}{5}\) kilograms. How much gerbil food does she still have?
Answer:
15 \(\frac{23}{40}\) kilograms of gerbil food.
Explanation:
19 \(\frac{3}{8}\) – 3\(\frac{4}{5}\)
= \(\frac{155}{8}\) – \(\frac{19}{5}\)
= \(\frac{155 X 5}{8 X 5}\) – \(\frac{19 X 8}{5 X 8}\)
= \(\frac{155 X 5}{8 X 5}\) – \(\frac{19 X 8}{5 X 8}\)
= \(\frac{775 – 152}{40}\)
= \(\frac{623}{40}\)
= 15 \(\frac{23}{40}\)

Question 13.
To make his favorite fruit punch, Ezekiel mixes 1,950 centiliters of juice with 1 \(\frac{4}{9}\) liters of seltzer and \(\frac{3}{8}\) liters of orange juice. How many liters of punch will this make?
Answer:
21 \(\frac{23}{72}\) L
Explanation:
19.50 + 1 \(\frac{4}{9}\) + \(\frac{3}{8}\)
= 19.50 + \(\frac{13}{9}\) + \(\frac{3}{8}\)
= \(\frac{19.50 X 72}{72}\) + \(\frac{13 X 8}{9 X 8}\) + \(\frac{3 X 9}{8 X 9}\)
= \(\frac{1404}{72}\) + \(\frac{104}{72}\) + \(\frac{27}{72}\)
= \(\frac{1404 + 104 + 27}{72}\)
= \(\frac{2714}{72}\)
= \(\frac{1535}{72}\)
= 21 \(\frac{23}{72}\)

Question 14.
3 \(\frac{7}{12}\) + 5 \(\frac{1}{5}\) + \(\frac{1}{4}\) = _____________
Answer:
9 \(\frac{1}{30}\)
Explanation:
3 \(\frac{7}{12}\) + 5 \(\frac{1}{5}\) + \(\frac{1}{4}\)
= \(\frac{43}{12}\) + \(\frac{26}{5}\) + \(\frac{1}{4}\)
= \(\frac{43 x 5}{12 X 5}\) + \(\frac{26 X 12}{5 X 12}\) + \(\frac{1 X 15}{4 X 15}\)
= \(\frac{215}{60}\) + \(\frac{312}{60}\) + \(\frac{15}{60}\)
= \(\frac{216 + 312 + 15}{60}\)
= \(\frac{542}{60}\)
=9 \(\frac{2}{60}\)
=9 \(\frac{1}{30}\)

Question 15.
-5 + |-17| – (-6) + 7(-5) – \(\frac{9}{3}\) = _____________
Answer:
-20
Explanation:
-5 + |-17| – (-6) + 7(-5) – \(\frac{9}{3}\)
= -5 + 17 + 6 + 7(-5) – \(\frac{9}{3}\)
= -5 + 17 + 6 – 35 – \(\frac{9}{3}\)
= 23 – 40 –\(\frac{9}{3}\)
= -17 –\(\frac{9}{3}\)
= -17 x 3 –\(\frac{9}{3}\)
= –\(\frac{51}{3}\) – \(\frac{9}{3}\)
=- \(\frac{51 + 9}{3}\)
= –\(\frac{60}{3}\)
= -20

Question 16.
Solve for x: x – 91 ≥ 13 ___________
Answer:
x ≥ 104
Explanation:
x – 91 ≥ 13
x  ≥ 13 + 91
x  ≥ 104

Question 17.
Solve for x: 4x + 11 = 15 _____________
Answer:
x = 1
Explanation:
4x + 11 = 15
4x = 15 – 11
4x = 4
x = 4/4
x = 1

Question 18.
What property is represented by the following equation?
2(6 + 9) = 2 × 6 + 2 × 9
Answer:
Distributive property of Multiplication over Addition.
Explanation:
a x (b + c) = a x b + a x c
let a = 2, b =6 and c = 9
2(6 + 9) = 2 × 6 + 2 × 9

Question 19.
What property is represented by the following equation?
(4 + 8) + 8 = 4 + (8 + 8)
Answer:
Associative property of Addition
Explanation:
a+ (b + c) = (a + b) + c
let a=4, b=8 c = 8
(4 + 8) + 8 = 4 + (8 + 8)

Question 20.
|-7| + (1 + 3)² – (9 ÷ 3) + 5(8 × 3) + 2(10 – 7) = ______________
Answer:
146
Explanation:
|-7| + (1 + 3)² – (9 ÷ 3) + 5(8 × 3) + 2(10 – 7)
7 + 16 – 3 + 5(24) + 2(3)
= 7 + 13 + 120 + 6
= 20 + 120 + 6
= 146

Question 21.
Give the coordinates for the points.

A _________________
B _________________
C _________________
D _________________
Answer:
A(3,6);
B(-5,2);
C(2,-4);
D(-1,1)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines also called axes.
A single unit of length for both axes, x axis as horizontal and y axis as vertical lines.

Question 22.
Restate in exponent form, then solve:
5 × 5 × 5 + 3 × 3 = _______________
Answer:
134
Explanation:
5 × 5 × 5 + 3 × 3
= 5³ + 3²
= 5³ + 3²
= 125 + 9
= 134

Question 23.
What is the area of the rectangle?

What is the perimeter of the rectangle?
Answer:
Area = 306 sq cm;
Perimeter = 70 cm
Explanation:
The area of the rectangle,
A = length x width
A = 18 x 17 = 306 cm²
the perimeter of the rectangle
P = 2(Length + Width)
P = 2(17 + 18)
= 2 x 35
= 70 cm

Question 24.
What is the area of the circle? (Use 3.14 for π)

What is the circumference of the circle?
Answer:
Area = 63.585 sq cm;
Circumference = 28.26 cm
Explanation:
The area of the circle (Use 3.14 for π)
A = π r²
r = 4.5 cm
A = 3.14 x 4.5 x 4.5
A = 63.585 sq cm
the circumference of the circle,
C = 2πr
C = 2 x 3.14 x 4.5
C = 28.26 cm

Question 25.
Identify the following angles as obtuse, acute, or right.

Answer:
Obtuse Angle; Right Angle; Acute Angle.

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

Question 26.
Identify the triangles as scalene, isosceles, or equilateral.

Answer:
Equilateral; Scalene; Isosceles Triangles.

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

Question 27.
Jackie spends $37.95 a month on art supplies. She is working on a project that will take 19 months to finish. How much should she plan to spend on art supplies for the project?
Answer:
$721.05
Explanation:
Jackie spends $37.95 a month on art supplies.
She is working on a project that will take 19 months to finish.
Total amount she plan to spend on art supplies for the project,
$37.95 x 19 = $721.05

Question 28.
Restate 7.6 as an improper fraction and a mixed number.
Answer:
\(\frac{38}{5}\) or 7 \(\frac{3}{5}\)
Explanation:
\(\frac{76}{10}\)
=\(\frac{38}{5}\)
=7\(\frac{3}{5}\)

Question 29.
\(\sqrt{21}\) is between ___________ and _____________.
Answer:
4 and 5
Explanation:
as we know values of
square of 4 is 16 :: sqrt 16 = 4
square of 5 is 25 :: sqrt 25 = 5
sqrt 21 lies between 4 and 5
sqrt 16 < sqrt 21 < sqrt 25

Question 30.
Is the following true or false? \(\frac{4}{11}\) = \(\frac{68}{187}\) _________________
Answer:
True
Explanation:
\(\frac{4}{11}\) = \(\frac{68}{187}\)
\(\frac{4 X 17}{11 X 17}\) = \(\frac{68}{187}\)

Question 31.
Put the following numbers in order from least to greatest:
1.141, 1.014, 1.044, 1.004, 1.9, 1.996, 1.89, .9 ______________
Answer:
0.9; 1.004, 1.014; 1.044; 1.141; 1.89; 1.9; 1.996
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 32.
Juliette deposits $295 in a bank account that earns 6% simple interest. How much money will she have in the account after 1 year?
______________ After 2 years? ________________
Answer:
$312.70; $330.40
Explanation:
Juliette deposits $295 in a bank account that earns 6% simple interest
SI = PRT/100
SI = (295 x 6 x 1)/100
SI = $17.7
Amount = $ 295 +$ 17.7 = $ 312.70 after one year
Amount = $ 312.70 + $ 17.7 = $ 330.40 after two years

Question 33.
What is the mode of the data distribution?

What is the median?
Answer:
Mode = 36
Median = 36
Explanation:
The mode is the number or numbers that occur the most frequently.
Given numbers [14, 16, 22, 25, 27, 31, 36, 36, 36, 43, 43, 45, 47, 47, 52, 55, 56]
Put the numbers in numerical order from smallest to largest.
Mode = 36
 First, arrange the given data in ascending order.
Median = Given data [14, 16, 22, 25, 27, 31, 36, 36, 36, 43, 43, 45, 47, 47, 52, 55, 56]
Next, we need to pick the middlemost data.
For the odd number of data points, there is only one middle data point,
we can take it as the median of the data as 36

Question 34.
\(\frac{2}{7}\) × 2 \(\frac{5}{22}\) = _____________
Answer:
\(\frac{7}{11}\)
Explanation:
Multiply the numerators to get the numerator of the product,
then multiply the denominators to get the denominators of the product.
\(\frac{2}{7}\) × 2\(\frac{5}{22}\)
= \(\frac{2}{7}\) × \(\frac{220}{22}\)
= \(\frac{2 X 220}{7 X 22}\)
= \(\frac{440}{154}\)
= \(\frac{2}{11}\)
= 4\(\frac{2}{3}\)

Question 35.
What is \(\frac{5}{8}\) of 75%? _____________
Answer:
46.875%
Explanation:
\(\frac{5}{8}\) of 75%
\(\frac{5 X 75}{8}\) %
46.875 %

Question 36.
What is 25% of .525?
Answer:
0.13125
Explanation:
25% of .525
\(\frac{25}{100}\) x 0.525
= \(\frac{25 X 0.525}{100}\)
= \(\frac{13.125}{100}\)
= 0.13125

Question 37.

Answer:
2350
Explanation:
While dividing the divisor with the decimal dividend,
multiply the divisor and divided with 100.

Question 38.
\(\frac{5}{4}\) + \(\frac{7}{4}\) + \(\frac{15}{4}\) – \(\frac{9}{4}\) – \(\frac{17}{4}\) = ____________
Answer:
\(\frac{1}{4}\)
Explanation:
\(\frac{5}{4}\) + \(\frac{7}{4}\) + \(\frac{15}{4}\) – \(\frac{9}{4}\) – \(\frac{17}{4}\) =
= \(\frac{5 + 7 + 15 – 9 – 17}{4}\)
= \(\frac{27 – 26}{4}\)
= \(\frac{1}{4}\)

Question 39.
Identify each quadrilateral as a square, rectangle, kite, rhombus, or trapezoid.

Answer:
Trapezoid; Square; Rhombus; Rectangle and Kite.

Explanation:
A trapezoid is a flat closed shape having 4 straight sides,
with one pair of parallel sides.
A square is closed, two-dimensional shape with 4 equal sides.
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 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.
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.

Question 40.
Identify the following figures.

Answer:
Hexagon; Pentagon; Heptagon.

Explanation:
Hexa means six and gona means angles.
A hexagon is a closed two-dimensional polygon with six sides.
Hexagon has 6 vertices and 6 angles.
Penta denotes five and gon denotes angle.
A pentagon is a simple polygon, which has five sides and five angles.
Hepta means seven and gon means sides.
A Heptagon is a polygon with seven sides and seven angles.
It has seven straight sides and seven corners or vertices.

Question 41.
Restate 9 \(\frac{11}{13}\) as an improper fraction.
Answer:
\(\frac{128}{13}\)
Explanation:
9 \(\frac{11}{13}\)
= \(\frac{9 x 13 + 11}{13}\)
=  \(\frac{117 + 11}{13}\)
=  \(\frac{128}{13}\)

Question 42.
Restate \(\frac{72}{13}\) as a mixed number.
Answer:
5\(\frac{7}{13}\)
Explanation:
=  \(\frac{72}{13}\)
= \(\frac{5 x 13 + 7}{13}\)
=  \(\frac{72}{13}\)

Question 43.
What are the chances of choosing a blue marble out of a bag containing 7 red marbles, 6 green marbles, 11 yellow marbles, and 4 blue marbles?
What is the probability of choosing a blue marble, not replacing it, and then choosing a green marble?
Answer:
\(\frac{1}{7}\) and \(\frac{6}{189}\)
Explanation:
Total number of marbles = 7 + 6 + 11 + 4 = 28
Probability of choosing blue marbles
Number of blue marbles = 4
Probability = marbles ÷ total no of marbles
4 ÷ 28 = \(\frac{1}{7}\)
Probability of choosing a green marble
Number of green marbles = 6
remaining number of marbles after choosing a blue marble = 28 – 1 = 27
Probability of choosing green marbles = marbles ÷ total marbles x remaining marbles
= 6 ÷ 27 x 28
= \(\frac{6}{189}\)

Question 44.
According to the graph, how many miles did Janice swim in September?

Answer:
10 miles
Explanation:
From the above graph of Janice’s Swimming Chart,
he swims 10 miles in september.

Question 45.
During which week did Brian and Ray run the same distance?

Answer:
week 2
Explanation:
From the given chart of Brain nd Ray’s Running Schedule,
they both run same distance in second week.

Question 46.
Which vegetable is most preferred by the students?

Answer:
Cauliflower
Explanation:
From the above pie chart of Favorite vegetables Of The Students,
Cauliflower is preferred by many of the students.

Question 47.
Dean’s score was about 20 points higher than whose score?

Answer:
Joe’s
Explanation:
From the above Dart Scores,
Dean scored the highest and also 20 points more than Joe.

Question 48.
What is the range of the data in the box-and-whisker plot below?

What is the average (mean) of the data points shown? ____________
What is the mean absolute deviation of the data points shown? ___________
Answer:
15; 12.4; 4.72
Explanation:
Range of the data is the difference between max – min
Range = 20 – 5 = 15
mean = \(\frac{5 + 8 + 13 + 16 + 20}{5}\)
mean =\(\frac{62}{5}\)
mean  =12.4
the mean absolute deviation of the data points
I 12.4 – 5 I = 7.4
I 12.4 – 8 I = 4.4
I 12.4 – 13 I = 0.6
I 12.4 – 16 I = 3.6
I 12.4 – 20 I = 7.6
mean absolute deviation( MAD )= \(\frac{7.4 + 4.4 + 0.6 + 3.6 + 7.6}{5}\)
MAD=\(\frac{23.6}{5}\)
MAD  = 4.72

Question 49.
How much plastic wrap would you need to cover this rectangular solid?

Answer:
318 sq in.
Explanation:
TSA – Total Surface Area to be calculated
the surface area of a cuboid, add the areas of all 6 faces.
We can also label the length (l), width (w), and height (h) of the prism and use the formula,
SA=2lw+2lh+2hw, to find the surface area
TSA = 2(7 x 6 + 6 x 9 + 9 x 7)
TSA = 2(42 + 54 + 63)
TSA = 2 x 159
TSA = 318 sq in

Question 50.
Name two line segments.

Name 4 rays. _______________
Name a line. ___________
Answer:
Line segments:
\(\overline{YS}\), \(\overline{XT}\), \(\overline{XR}\), \(\overline{YZ}\),\(\overline{LM}\), \(\overline{ML}\), \(\overline{XY}\), \(\overline{TX}\),\(\overline{RX}\), \(\overline{SY}\), \(\overline{ZY}\);
Rays:
\(\overline{XR}\), \(\overline{XT}\), \(\overline{YS}\), \(\overline{YZ}\),
\(\overline{XY}\), \(\overline{YX}\);
Line:
\(\overline{XY}\)
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.

Question 51.
Fill in a Venn Diagram that displays the following data:

There are two groups of students, 25 who are in the drama club and 15 who enjoy math. There are 8 students who are in the drama club who also enjoy math.
Answer:

Explanation:
There are two groups of students,
25 who are in the drama club and 15 who enjoy math.
There are 8 students who are in the drama club who also enjoy math.
Number of students in Drama Club = 25 – 8 = 17
Number of students enjoy Math = 15 – 8 = 7

Question 52.
Are the rates in the table below proportional?

Answer:
Yes, Both are $2.50 per pound.
Explanation:
Lets write them in the form of ratio
$5.00 : 2 pounds
$1.25 : 0.5 pounds
according to proportion,
product of means = product of extremes
5 : 2 = 1.25 : 0.5
product of means :
= 2 x 1.25 = 2.5
product of extremes :
= 2 x 0.5 = 2.5
product of means = product of extremes = 2.5
Hence ; both of them are proportioanal

Question 53.
What is the unit rate for the speed of the car shown on the graph below?

Answer:
\(\frac{1}{2}\)
Explanation :
By observing the graph we can see that
it took 6 seconds to travel 4 miles
that means the distance traveled in 1 second = \(\frac{1}{2}\)

Question 54.
Ebony asked four of her female friends if they liked wearing sandals better than wearing boots. All four said yes. Ebony concluded that none of the girls her age like boots. Is her conclusion valid? Did she use a representative sample for her survey?
Answer:
No
Explanation:
The Conclusion is based on too small a sample,
A representative sample is a sample from a larger group,
that accurately represents the characteristics of a larger population.
It’s known as a representative sample because the answers obtained from it,
accurately reflect the results you would achieve by interviewing the entire population.
The sample is not representative since she only asked her friends.

Question 55.
Create a probability table for choosing a marble out of a bag of 14 white, 18 black, and 6 red marbles.

Answer:

Explanation:
Total number of marbles = 14+ 18 + 6 = 38
Probability of choosing white marble,
number of white marbles = 14
probability = no of marbles ÷ total number of marbles
= 14 ÷ 38
= \(\frac{14}{38}\)
= 0.37
Probability of choosing black marble,
number of black marbles = 18
probability = no of marbles ÷ total number of marbles
= 18 ÷ 38
= \(\frac{18}{38}\)
= 0.47
Probability of choosing red marble,
number of red marbles = 6
probability = no of marbles ÷ total number of marbles
= 6 ÷ 38
= \(\frac{6}{38}\)
= 0.16