McGraw Hill Math Grade 7 Pretest Answer Key

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Complete the following test items on pages 4-8.

Question 1.
Restate the number 4,587,902.453.
Expanded form: ________________
Written form: _________________
Answer:
Expanded form: (4 x 1,000,000) + (5 x 100,000) + (8 x 10,000) + (7 x 1,000) + (9 x 100) + (2 x 1) + (4 x 0.1) +
(5 x 0.01) + (3 x 0.001)
Written form: For million five hundred eighty seven thousand nine hundred two and four hundred and fifty three thousandths.
Explanation:
Numbers can be written in 3 ways like,
Standard form; Expanded form and Written form.
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.
Numbers can be written according to their place values as shown above.

Question 2.
Cheryl’s Department Store is having a sale. They have 145 coats in stock and are adding 55 more. If at the end of the sale they still have 25 coats in stock, how many coats did they sell?
Answer:
175 coats
Explanation:
Cheryl’s Department Store have 145 coats in stock and are adding 55 more.
145 + 55 = 200
If at the end of the sale they still have 25 coats in stock,
Number of coats sold = 200 – 25 = 175 coats.

Question 3.
Tracey pedals 16 miles a day on a stationary bicycle. How many miles does she pedal in the month of March? (Remember, March has 31 days.) _______
How many yards does she pedal? ___________
Answer:
496 miles;
872,960 yards.
Explanation:
Tracey pedals 16 miles a day on a stationary bicycle.
How many miles does she pedal in the month of March,
March has 31 days = 31 x 16 = 496 miles,
Number of yards she pedal,
1 mile = 1760
496 miles = 1760 x 496
= 872,960 yards.

Calculate.

Question 4.

Answer:
792
Explanation:
Multiply the entire number by ones place and then by tens place.

Question 5.

Answer:
-649
Explanation:
As we are multiplying -11 with 59,
we get the product as -649 as shown below.

Question 6.

Answer:
2812
Explanation:
Multiply the entire number by ones place and then by tens place.

Question 7.

Answer:
1917
Explanation:
Multiply the entire number by ones place and then by tens place.

Question 8.

Answer:
83
Explanation:

Question 9.

Answer:
21
Explanation:

Question 10.

Answer:
107.118
Explanation:

Question 11.

Answer:
6.2
Explanation:

Question 12.
Bailey bought 11\(\frac{1}{4}\) kilograms of bird feed. On the way home, he spilled 3\(\frac{5}{8}\) kilograms. How much bird feed does he still have left? _____________________________
Answer:
7\(\frac{5}{8}\) kilograms
Explanation:
11\(\frac{1}{4}\)– 3\(\frac{5}{8}\)
= \(\frac{(11 X 4) +1}{4}\)– \(\frac{(3 X 8)+5}{8}\)
= \(\frac{45}{4}\)– \(\frac{29}{8}\)
= \(\frac{90}{8}\)– \(\frac{29}{8}\)
= \(\frac{90 – 29}{8}\)
= \(\frac{61}{8}\)
=7\(\frac{5}{8}\) kilograms

Question 13.
Margaret mixes 1,400 centiliters of grape juice with 5\(\frac{2}{3}\) liters of seltzer and \(\frac{2}{5}\) liters of orange juice: How many liters of punch will this make?
Answer:
7\(\frac{7}{15}\) L
Explanation:
Margaret mixes 1,400 centiliters of grape juice with 5\(\frac{2}{3}\) liters of seltzer and,
\(\frac{2}{5}\) liters of orange juice,
Total liters of punch will this make,
1.4 + 5\(\frac{2}{3}\) + \(\frac{2}{5}\)
= 1.4 +\(\frac{15 + 2}{3}\)+\(\frac{2}{5}\)
= 1.4 + \(\frac{17}{3}\) + \(\frac{2}{5}\)
= \(\frac{1.4 X 15}{15}\) + \(\frac{17 X 5}{15}\)+ \(\frac{2 X 3}{15}\)
= \(\frac{21 + 85 + 6}{15}\)
= \(\frac{112}{15}\)
= 7\(\frac{7}{15}\)

Question 14.
1\(\frac{4}{15}\) + 7\(\frac{2}{5}\) + \(\frac{1}{3}\) = ___________
Answer:
9
Explanation:
1\(\frac{4}{15}\) + 7\(\frac{2}{5}\) + \(\frac{1}{3}\)
= \(\frac{(15 X 1) + 4}{15}\) + \(\frac{(7 X 5) + 2}{5}\) + \(\frac{1}{3}\)
= \(\frac{19}{15}\) + \(\frac{37}{5}\) + \(\frac{1}{3}\)
= \(\frac{19}{15}\) + \(\frac{37 X 3}{5 X 3}\) + \(\frac{1 X 5}{3 X 5}\)
= \(\frac{19}{15}\) + \(\frac{111}{15}\) + \(\frac{5}{15}\)
= \(\frac{19 + 111 + 5}{15}\)
= \(\frac{135}{15}\)
= 9

Question 15.
-9 + 10 – (-8) + 6(-2) + \(\frac{6}{-2}\) =
Answer:
-6
Explanation:
-9 + 10 – (-8) + 6(-2) + \(\frac{6}{-2}\)
= 1 + 8 – 12 + \(\frac{6}{-2}\)
= – 3 – 3
= -6

Question 16.
Solve for x: x — 9 = 18 ______________
Answer:
x = 27
Explanation:
x — 9 = 18
x = 18 + 9
x = 27

Question 17.
Solve for x: 2x + 5 < 15 _____
Answer:
x < 5
Explanation:
2x + 5 < 15
= 2x  < 15 – 5
2x <10
x < 5

Question 18.
What property is represented by the following equation?
4(5 + 6) = 4 × 5 + 4 × 6
______________
Answer:
Distributive Property of Multiplication over Addition.
Explanation:
Distributive Property of Multiplication over Addition.
a x (b x c) = a x b + a x c
4(5 + 6)
= 4 × 5 + 4 × 6
= 20 + 24
= 44

Question 19.
What property is represented by the following equation?
(3 + 6) + 6 = 3 + (6 + 6)
Answer:
Associative Property of Addition.
Explanation:
Associative Property of Addition.
(x + y) + z = x + (y + z)
(3 + 6) + 6 = 3 + (6 + 6)
15 = 15

Question 20.
|—9| + (2 + 3)² — (6 ÷ 3) + 4(8 × 3) + 4(5 — 3) = ___________
Answer:
136
Explanation:
|—9| + (2 + 3)² — (6 ÷ 3) + 4(8 × 3) + 4(5 — 3)
= 9 + 5² — 2 + 96 + 8
= 9 + 25 — 2 + 96 + 8
= 9 + 23 + 96 + 8
= 136

Question 21.
Give the coordinates for the points.
A ___________
B ___________
C ___________
D __________

Answer:
A(2,3); B(-3,5); C(1,-5); D(-3,-3)
Explanation:
A Cartesian coordinate system in two dimensions is called a rectangular coordinate system,
which is defined by an ordered pair of perpendicular lines 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:
4 × 4 × 4 + 2 × 2 =
_________________
Answer:
= 68
Explanation:
= 4 × 4 × 4 + 2 × 2
= 4³ + 2²  
= 68

Question 23.
What is the area of the rectangle?
__________________

What is the perimeter of the rectangle?
______________
Answer:
Area = 120 sq cm;
Perimeter = 44 cm.
Explanation:
Area of a rectangle = length x width
A = l x w
A = 12 x 10
A = 120 sq cm
Perimeter of  a rectangle P = 2(length + width)
P = 2(L+W)
P = 2(12 + 10)
P = 44 cm

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

What is the circumference of the circle?
_______________
Answer:
Area = 19.625 sq cm;
Circumference = 15.75 cm.
Explanation:
Area of circle A = π.r²
A = 3.14 x 2.5²
A = 19.625 sq cm
Circumference = 2 πr
= 2 x 3.14 x 2.5
= 15.75 cm.

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



Answer:



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:



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.

Question 27.
Ramon spends $28.94 a month having pictures developed. He is working on a project that will take 19 months to finish. How much should he plan to spend on developing pictures for the project?
Answer:
$549.86
Explanation:
Ramon spends $28.94 a month having pictures developed.
He is working on a project that will take 19 months to finish.
Total amount he plan to spend on developing pictures for the project,
$28.94 a month x 19 months
28.94 x 19 = 549.86

Question 28.
Restate 3.6 as an improper fraction and a mixed number. ____________
Answer:
3\(\frac{3}{5}\) or \(\frac{18}{5}\)
Explanation:
3\(\frac{3}{5}\) or \(\frac{18}{5}\)
= \(\frac{15 + 3}{5}\)
= \(\frac{18}{5}\)

Question 29.
Restate 4\(\frac{5}{8}\) as a decimal. __________________ ________________
Answer:
4.625
Explanation:
4\(\frac{5}{8}\)
= \(\frac{(4 X 8) +5}{8}\)
= \(\frac{37}{8}\)
= 4.625

Question 30.
Is the following true or false? \(\frac{5}{16}\) = \(\frac{60}{192}\) _______ _______________
Answer:
True
Explanation:
\(\frac{5}{16}\) = \(\frac{60}{192}\)
\(\frac{5 X 12}{16 X 12}\) = \(\frac{60}{192}\)
Thus, equation is TRUE.

Question 31.
\(\sqrt{73}\) is between ____________ and _______________
Answer:
8 and 9
Explanation:
Given, \(\sqrt{73}\)
\( sqrt {64} \) = 8
\( sqrt {81} \) = 9
\( sqrt {73} \) lies between 8 and 9

Question 32.
Drayson deposits $125 in a bank account that earns 4% simple interest. How much money will he have in the account after 1 year? ______
After 2 years ? _____
Answer:
$130 after 1year,
$135.20 after 2 years.
Explanation:
SI = (PTR)/100
SI = 125 x 4 x 1 / 100
SI = 5
Amount after 1 year = 125 + 5 = $130
SI = (PTR)/100
SI = 130 x 4 x 1 / 100
SI = 5.2
Amount after 1 year = 130 + 5.2 = $135.2

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

What is the median?
___________
Answer:
Mode = 38
Median = 38
Explanation:
values with respect to the stem leaf data plot is,
{13, 15, 23, 26, 29, 33, 38, 38, 38, 44, 44, 45, 46, 46, 43, 54, 56}
Median is the mid point in the given data.
Mode : frequently occurring or observed value

Question 34.
\(\frac{4}{7}\) × 5\(\frac{4}{9}\) = ______
Answer:
3\(\frac{1}{9}\)
Explanation:
\(\frac{4}{7}\) × 5\(\frac{4}{9}\)
= \(\frac{4}{7}\) × 5\(\frac{9 x 5 + 4}{9}\)
= \(\frac{4}{7}\) × \(\frac{45}{9}\)
= \(\frac{4 X 45}{63}\)
= \(\frac{180}{63}\)
= 3\(\frac{1}{9}\)

Question 35.
What is \(\frac{3}{8}\) of 88%?
Answer:
33%
Explanation:
\(\frac{3}{8}\) of 88%
= \(\frac{3}{8}\) x 88%
= 3 x 11%
= 33%

Question 36.
What is 30% of .675? _______________
Answer:
0.2025
Explanation:
30% x 0.675
(30 x 0.675)/100 = 0.2025

Question 37.

Answer:
1.5667
Explanation:
0.15 x 100 = 15
0.235 x 100 = 23.5

0.235 / 0.15 = 1.5667

Question 38.
latex]\frac{4}{3}[/latex] + latex]\frac{2}{3}[/latex] + latex]\frac{5}{3}[/latex] – latex]\frac{1}{3}[/latex] – latex]\frac{7}{3}[/latex] = _____
Answer:
1
Explanation:
latex]\frac{4}{3}[/latex] + latex]\frac{2}{3}[/latex] + latex]\frac{5}{3}[/latex] – latex]\frac{1}{3}[/latex] – latex]\frac{7}{3}[/latex]
= latex]\frac{4 + 2 + 5 – 1 – 7}{3}[/latex]
= latex]\frac{11 – 8}{3}[/latex]
= latex]\frac{3}{3}[/latex]
=1

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

_____

_____

_____

_____

_____
Answer:





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:



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 5\(\frac{6}{13}\) as an improper fraction.
Answer:
\(\frac{71}{13}\)
Explanation:
5\(\frac{6}{13}\)
= 5\(\frac{(5 X 13) + 6}{13}\)
= \(\frac{65 + 6}{13}\)
= \(\frac{71}{13}\)

Question 42.
Restate \(\frac{43}{16}\) as a mixed number.
Answer:
2\(\frac{11}{16}\)
Explanation:
\(\frac{43}{16}\)

2\(\frac{11}{16}\)

Question 43.
What are the chances of choosing a black marker out of a bag containing 3 red markers, 5 blue markers, 3 yellow markers, and 4 black markers? What is the probability of choosing two black markers if the first marker is put back before the second is drawn?
Answer:
\(\frac{4}{15}\); \(\frac{16}{225}\)
Explanation :
Total number of markers = 3 + 5 + 3 + 4 = 15
Probability of choosing black markers
Number of black markers = 4
Probability = black markers ÷ total no of markers
4 ÷ 15 = \(\frac{4}{15}\)
Probability of choosing a black markers again
Number of black markers = 4
remaining number of marbles after choosing a black markers = 4 – 1 + 1 = 4
[the black marker is put back ]
Probability of choosing black markers= black markers ÷ total markers x remaining markers
= 4 ÷ 15 x 15
= \(\frac{4}{225}\)

Question 44.
According to the graph, how many videos did Jamie watch in July?

Answer:
15
Explanation:
According to the graph of Jamie’s Summer Video List
he watched 15 videos July.

Question 45.
During which week did Kelly and Heather swim the same distance?

Answer:
Week 2
Explanation:
According to the graph of Kelly and Heather’s Workout Schedule,
second week they swim the same distance.

Question 46.
What fruit is most preferred by the students?

Answer:
Apples
Explanation:
From the above pie chart of Favorite Fruits,
most preferred fruit by the students are Apples.

Question 47.
Peggy’s score was about 30 pins higher than whose score?

Answer:
Kathy
Explanation:
From the above chart of Bowling Scores,
Peggy’s score was about 30 pins higher than Kathy score.

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?
________________

Answer:
15; 11.9; 4.12
Explanation:
The range of the data in the box-and-whisker plot is,
R = max – min
R = 20 – 5 = 15
mean average = sum of event / total number of events.
mean average = 5 + 8.5 + 12 + 14 + 20 / 5
mean average = 59.5/5 = 11.9
11.9 – 5 = 6.9
11.9 – 8.5 = 3.4
12 – 11.9 = 0.1
14 – 11.9 = 2.1
20. – 11.9 = 8.1
6.9 + 3.4 + 0.1 + 2.1 + 8.1 = 20.6
average mean = 20.6/5 = 4.12

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

Answer:
94 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(4 x 5 + 5 x 3 + 3 x 4)
TSA = 2(20 + 15 + 12)
TSA = 2 x 47
TSA = 94 sq in

Question 50.
Name two line segments. _____________
Name four rays. ________
Name a line. _________________

Answer:
Line segments:\(\overline{BD}\), \(\overline{DB}\), \(\overline{CA}\), \(\overline{AC}\),\(\overline{HG}\), \(\overline{GH}\), \(\overline{BE}\), \(\overline{EB}\),\(\overline{AB}\), \(\overline{AF}\), \(\overline{FA}\);
Rays: \(\overline{AC}\), \(\overline{BD}\), \(\overline{BE}\),
\(\overline{AF}\), \(\overline{BA}\), \(\overline{AB}\);
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.

Question 51.
Fill in a Venn Diagram that displays the following data: There are two groups of students, 30 who take the bus to school and 25 who have a younger sibling in the school. There are 10 students who take the bus and who also have a younger sibling in the school.

Answer:

Explanation:
There are two groups of students,
30 who take the bus to school and,
25 who have a younger sibling in the school.
There are 10 students who take the bus and who also have a younger sibling in the school.
who take bus to school 30 – 10 = 20,
who have younger siblings 25 – 10 = 15.

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

Answer:
No,
Explanation:
Car A is going 45 miles per hour and Car b is going 48 miles per hour.
So, they are not proportional to each other.

Question 53.
What is the unit rate for the price of grapes as shown on the graph below?

Answer:
1.50
Explanation :
By observing the graph we can conclude that,
for 6 dollars we get 9 pounds of grapes.
for 1 dollar we get,
9 ÷ 6 = 1.50 pounds of grapes
Hence, 1.5 is the unit rate for the price of grapes.

Question 54.
What is the best way to get a representative sample of the people at a baseball game for a survey about parking at the stadium?
(a) Choose one of the luxury boxes at random and survey all the people in that box.
(b) Survey the first 50 people to walk into the stadium.
(c) Choose 50 seat numbers at random and survey the people in those seats.
Answer:
Option(C)
Explanation :
A representative survey must be done at random.
If we choose to survey the people in luxury boxes,
we can not get a perfect result as they might get a better parking space.
If we choose to survey the first 50 people that walk in,
we can’t get a perfect result,
as the first 50 people are likely to find more empty spots that the people that come in later.

Question No 55.
Complete the probability table below.

Answer:

Explanation:
By looking at the A probability we can say that
Number of wins = 23
Total matches = 90
Line-wise By looking at the C probability we can say that,
probability of a match being a draw = \(\frac{53}{90}\) = 0.59
Number of draws = 53
Therefore number of loses = 90 – 23 + 53
= 13
Probability of losing a match = 13 ÷ 90
= \(\frac{13}{90}\)
= 0.16