McGraw Hill Math

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.

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

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

Solve

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

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

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

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

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

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

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

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

Exercises Add

Question 1.

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

Question 2.

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

Question 3.

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

Question 4.

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

Question 5.

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

Question 6.

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

Question 7.

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

Question 8.

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

Question 9.

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

Question 10.

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

Question 11.

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

Question 12.

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

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

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

Exercises Subtract

Question 1.

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

Question 2.

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

Question 3.

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

Question 4.

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

Question 5.

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

Question 6.

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

Question 7.

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

Question 8.

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

Question 9.

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

Question 10.

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

Question 11.

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

Question 12.

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

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

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

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

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

Round to the nearest tenth.

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

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

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

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

Round to the nearest hundredth.

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

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

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

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

Round to the nearest ten thousandth.

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

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

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

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

Convert decimals to fractions.

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

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

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

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

Convert fractions to decimals.

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

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

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

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

Put the decimals in order from greatest to least.

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

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

Add or Subtract.

Question 23.

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

Question 24.

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

Question 25.

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

Question 26.

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

Question 27.

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

Question 28.

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

Question 29.

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

Question 30.

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

Multiply or Divide.

Question 31.

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

Question 32.

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

Question 33.

Answer:
$0.1068
round off to
$0.11
Explanation:

Question 34.

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

Question 35.

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

Question 36.

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

Question 37.

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

Question 38.

Answer:
1.478625
Explanation:

Question 39.

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

6.38098883 is round off to 6.380989

Question 40.

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

11.6956 is round off to 11.70

Question 41.

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

Question 42.

Answer:
1.4189
Explanation:

Estimate, then multiply or divide.

Question 43.

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

Question 44.

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

0.636191111 is round off to the nearest 0.6362

Question 45.

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

Question 46.

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

Question 47.

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

Question 48.

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

Question 49.

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

Question 50.

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

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

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

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

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

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

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

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

Change to mixed numbers.

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

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

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

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

Change to improper fractions.

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

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

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

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

Add or subtract, and reduce to simplest form.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Estimate, then add or subtract.

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

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

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

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

Multiply or divide, and reduce to simplest form.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Identify each angle as obtuse, acute or right.

Question 1.

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

Question 2.

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

Question 3.

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

Question 4.

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

Question 5.

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

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

Question 6.

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

Question 7.

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

Question 8.

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

Question 9.

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

Question 10.

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

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

Question 11.

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

Question 12.

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

Question 13.

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

Question 14.

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

Question 15.

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

Question 16.

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

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

Question 17.

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

Question 18.

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

Question 19.

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

Question 20.

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

Question 21.

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

Question 22.

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

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

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

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

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

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

Identify the figures and fill in the missing information.

Question 27.

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

Question 28.

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

Question 29.

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

Question 30.

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

Question 31.

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

Question 32.

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

Identify the figures.

Question 33.

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

Question 34.

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

Question 35.

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

Question 36.

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

Question 37.

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

Question 38.

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

Question 39.

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