McGraw Hill Math

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 10.8 Estimation and Comparison to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 10.8 Estimation and Comparison

Exercises

Use this chart to answer the questions.

Question 1.
Write each distance in the chart in scientific notation.
Answer:

Explanation:
Scientific notation is a way to make these numbers easier to work with.
In scientific notation, you 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, the distance between the sun and planet Mercury is 35,980,000 miles becomes 3.598 x 10⁷
The distance between the sun and planet Venus is 65,240,000 miles becomes 9.296 x 10⁷
The distance between the sun and planet Earth is 92,960,000 miles becomes 3.598 x 10⁷
The distance between the sun and planet Mars is 141,600,000 miles becomes 1.416 x 10⁸
The distance between the sun and planet Jupiter is 483,800,000 miles becomes 4.838 x 10⁸
The distance between the sun and planet Saturn is 888,200,000 miles becomes 8.882 x 10⁹
The distance between the sun and planet Uranus is 1,784,000,000 miles becomes 1.784 x 10⁹
The distance between the sun and planet Neptune is 2,795,000,000 miles becomes 2.795 x 10⁹

Question 2.
How many times larger is Uranus than Saturn?
Answer:
2 times larger
Explanation:
Distance of Uranus – 1784,000,000 = 17.84 x 10⁷
Distance of Saturn – 888,200,000 = 8.882 x 10⁷
8.8 x 2 = 17.6 2 times larger
Uranus is two times  larger than Saturn.

Question 3.
How many times larger is Jupiter than Earth?
Answer:
5 times larger
Explanation:
Distance of Jupiter 483,800,000 = 48.38 x 10⁷
Distance of Earth 92,960,000 = 9.296 x 10⁷
9.296 x 5 = 46.48
Jupiter is 5 times larger times larger than Earth.

Question 4.
Estimate the distance from the Earth to the Sun in scientific notation.
Answer:
9 x 10⁷
Explanation:
Distance of Earth 92,960,000 = 9 x 10⁷ 
9 x 10⁷ the distance from the Earth to the Sun in scientific notation.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 11.1 Order of Operations to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 11.1 Order of Operations

Exercise

CALCULATE

Question 1.
(5 + 2) × (5 – 3) – (3 × 3) + 2^(5-2)
Answer:
13
Explanation:
Use the order of PEMDAS,
P is for parentheses; E is for exponents; M is for multiplication; D is for division; A is for addition and S is for subtraction.
(5 + 2) × (5 – 3) – (3 × 3) + 2^(5-2)
7 x 2 – 9 + 2³
14 – 9 + 2 x 2 x 2
14 – 9 + 8
22 – 9 = 13
Question 2.
(6 – 5) × (6 – 4) – 2³ + 6
Answer:
0
Explanation:
Use the order of PEMDAS,
P is for parentheses; E is for exponents; M is for multiplication; D is for division; A is for addition and S is for subtraction.
(6 – 5) × (6 – 4) – 2³ + 6
1 x 2 – 2 x 2 x 2 + 6
2 – 8 + 6
8 – 8 = 0

Question 3.
(7 – 4)³ + (7 – 2)² + 5 – 2 + 3^(5-3)
Answer:
64
Explanation:
Use the order of PEMDAS,
P is for parentheses; E is for exponents; M is for multiplication; D is for division; A is for addition and S is for subtraction.
(7 – 4)³ + (7 – 2)² + 5 – 2 + 3^(5-3)
(3)³ + (5)² + 5 – 2 + 3⁽²⁾
3 x 3 x 3 + 5 x 5 + 5 – 2 + 3 x 3
27 + 25 + 5 – 2 + 9
66 – 2 = 64
Question 4.
(8 + 2) × (8 – 5) + 42 – (7 – 4)³
Answer:
45
Explanation:
Use the order of PEMDAS,
P is for parentheses; E is for exponents; M is for multiplication; D is for division; A is for addition and S is for subtraction.
(8 + 2) × (8 – 5) + 42 – (7 – 4)³
10 × 3 + 42 – 3³
30 + 42 – 3 x 3 x3
72 – 27 = 45

Question 5.
(8 – 6)³ – (7 – 5)³ + 9 – (5 – 2)
Answer:
6
Explanation:
Use the order of PEMDAS,
P is for parentheses; E is for exponents; M is for multiplication; D is for division; A is for addition and S is for subtraction.
(8 – 6)³ – (7 – 5)³ + 9 – (5 – 2)
(2)³ – (2)³ + 9 – 3
2 x 2 – 2 x 2 + 9 – 3
4 – 4 + 9 – 3
4 + 9 – 4 – 3
13 – 4 – 3
9 – 3 = 6

Question 6.
(4)² – (2³ – 5) + (2² + 2) – 2³
Answer:
11
Explanation:
Use the order of PEMDAS,
P is for parentheses; E is for exponents; M is for multiplication; D is for division; A is for addition and S is for subtraction.
(4)² – (2³ – 5) + (2² + 2) – 2³
4 x 4 – (8 – 5) + (2 x 2+ 2) – 2 x 2 x 2
16 – 3 + 6 – 8 = 11
Question 7.
(7 – 2) + (8 – 5) – (4 – 1) – 2
Answer:
3
Explanation:
Use the order of PEMDAS,
P is for parentheses; E is for exponents; M is for multiplication; D is for division; A is for addition and S is for subtraction.
(7 – 2) + (8 – 5) – (4 – 1) – 2
5 + 3 – 3 – 2
8 – 3 – 2
5 – 2 = 3

Question 8.
(4 + 3) × (5 – 2) × (2 – 1)²
Answer:
21
Explanation:
Use the order of PEMDAS,
P is for parentheses; E is for exponents; M is for multiplication; D is for division; A is for addition and S is for subtraction.
(4 + 3) × (5 – 2) × (2 – 1)²
7 x 3 x 1 = 21

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 11.2 Commutative and Associative Properties to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 11.2 Commutative and Associative Properties

Exercises

IDENTIFY

Identify which property is represented in the example (Commutative or Associative).

Question 1.
8 × 4 × 3 = 3 × 4 × 8
Answer:
Commutative property of multiplication
Explanation:
When we multiply the factors by changing the order also,
there is no change in the product.
8 × 4 × 3 = 3 × 4 × 8 => 96

Question 2.
(2 + 9) + 22 = 2 + (9 + 22)
Answer:
Associative property of addition
Explanation:
Grouping the addends by changing the order there is no change in the sum.
(2 + 9) + 22 = 2 + (9 + 22) => 33

Question 3.
3 × 4 + 4 × 2 = 4 × 3 + 2 × 4
Answer:
Commutative property of multiplication
Explanation:
When we multiply the factors by changing the order also there is no change in the product.
3 × 4 + 4 × 2 = 4 × 3 + 2 × 4 => 20

Question 4.
4 × 2 + 3 × 4 = 3 × 4 + 4 × 2
Answer:
Commutative property of addition
Explanation:
When we add the addends by changing the order also there is no change in the sum.
4 × 2 + 3 × 4 = 3 × 4 + 4 × 2 =>20

Question 5.
3 + 2 + 4 = 4 + 2 + 3
Answer:
Commutative property of addition
Explanation:
When we add the addends by changing the order also there is no change in the sum.
3 + 2 + 4 = 4 + 2 + 3 => 9

Question 6.
12 + (7 + 1) = (12 + 7) + 1
Answer:
Associative property of addition
Explanation:
Grouping the addends in any order also there is no change in the sum.
12 + (7 + 1) = (12 + 7) + 1 =>20

Question 7.
(2 + (8 + 6) + 4) = (2 + 8) + (6 + 4)
Answer:
Associative property of addition
Explanation:
Grouping the addends in any order also there is no change in the sum.
(2 + (8 + 6) + 4) = (2 + 8) + (6 + 4) => 20

Question 8.
6 × 4 × 2 = 2 × 4 × 6
Answer:
Commutative property of multiplication
Explanation:
When we multiply the factors by changing the order also there is no change in the product.
6 × 4 × 2 = 2 × 4 × 6 =>48

Question 9.
(8 + 2) + 9 + 14 = 8 + (2 + 9) + 14
Answer:
Associative property of Addition
Explanation:
Grouping the addends in any order also there is no change in the sum.
(8 + 2) + 9 + 14 = 8 + (2 + 9) + 14 =>33

Question 10.
9 × 4 + 27 + 4 × 9 = 4 × 9 + 27 + 9 × 4
Answer:
Commutative property of multiplication
Explanation:
When we multiply the factors by changing the order also there is no change in the product.
9 × 4 + 27 + 4 × 9 = 4 × 9 + 27 + 9 × 4 => 96

Question 11.
7 + 9 + 6 + 4 = 4 + 6 + 9 + 7
Answer:
Commutative property of Addition
Explanation:
When we add the addends by changing the order also there is no change in the sum.
7 + 9 + 6 + 4 = 4 + 6 + 9 + 7 => 26

Question 12.
(9 + 9) + 6 + 9 = 9 + (9 + 6) + 9
Answer:
Associative property of Addition
Explanation:
Grouping the addends in any order also there is no change in the sum.
(9 + 9) + 6 + 9 = 9 + (9 + 6) + 9 => 34

Question 13.
29 + 2 + 1 + 29 = 2 + 1 + 29 + 29
Answer:
Commutative property of Addition:
Explanation:
When we add the addends by changing the order also there is no change in the sum.
29 + 2 + 1 + 29 = 2 + 1 + 29 + 29 => 61

Question 14.
28 + 20 + 28 + 20 = 20 + 20 + 28 + 28
Answer:
Commutative property of Addition
Explanation:
When we add the addends by changing the order also there is no change in the sum.
28 + 20 + 28 + 20 = 20 + 20 + 28 + 28 => 96

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 11.3 Distributive and Identity Properties to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 11.3 Distributive and Identity Properties

Exercises

IDENTIFY THE PROPERTY

Question 1.
0 + 6 = 6
Answer:
Zero Identity of Addition
Explanation:
Adding 0 to any number, results in the number itself.
This is due to the fact that when we add 0 to any number, it does not change the sum.
0 + 6 = 6

Question 2.
4(4 + 1) = 4 × 4 + 4 × 1
Answer:
Distributive property
Explanation:
To multiply a sum of two or numbers and then add the products the answer will be the same.
4(4 + 1) = 4 × 4 + 4 × 1
4 x 5 = 16 + 5
20 = 20

Question 3.
7 + 0 = 7
Answer:
Zero Identity of Addition
Explanation:
Adding 0 to any number, results in the number itself.
This is due to the fact that when we add 0 to any number, it does not change the sum.
7 + 0 = 7

Question 4.
9 × 12 + 9 × 9 = 9(12 + 9)
Answer:
Distributive property
Explanation:
To multiply a sum of two or numbers and then add the products the answer will be the same.
9 × 12 + 9 × 9 = 9(12 + 9)
108 + 81 = 9 x 21
189 = 189

Question 5.
4(1 + 1) = 4(1) + 4(1)
Answer:
Distributive property
Explanation:
To multiply a sum of two or numbers and then add the products the answer will be the same.
4(1 + 1) = 4(1) + 4(1)
4 x 2 = 4 + 4
8 = 8

Question 6.
15 + (4 + 0) = 15 + 4
Answer:
Zero Identity of Addition
Explanation:
Adding 0 to any number, results in the number itself.
This is due to the fact that when we add 0 to any number, it does not change the sum.
15 + (4 + 0) = 15 + 4
15 + 4 = 19
19 = 19

Question 7.
4(11 + 9) = 4 × 11 + 9 × 4
Answer:
Distributive property
Explanation:
To multiply a sum of two or numbers and then add the products the answer will be the same.
4(11 + 9) = 4 × 11 + 9 × 4
4 x 20 = 44 + 36
40 = 80

Question 8.
6 × 5 + 0 = 6 × 5
Answer:
Zero Identity of Addition
Explanation:
Adding 0 to any number, results in the number itself.
This is due to the fact that when we add 0 to any number, it does not change the sum.
6 × 5 + 0 = 6 × 5
30 = 30

Question 9.
(34 × 0) + (7 × 0) = 0(34 + 7)
Answer:
Distributive property
Explanation:
To multiply a sum of two or numbers and then add the products the answer will be the same.
Multiplying any number with zero or zero with any number the product is zero.
(34 × 0) + (7 × 0) = 0(34 + 7)
0 = 0

Question 10.
(35 – 1) + (3 – 3 + 0) = (35 – 1) + (3 – 3)
Answer:
Zero Identity of Addition
Explanation:
Adding 0 to any number, results in the number itself.
This is due to the fact that when we add 0 to any number, it does not change the sum.
(35 – 1) + (3 – 3 + 0) = (35 – 1) + (3 – 3)
34 = 34

Rewrite the equation using the Distributive Property.

Question 11.
4(5 + 7)
Answer:
4(5) + 4(7)
Explanation:
To multiply a sum of two or numbers and then add the products the answer will be the same.
4(5 + 7)
By distributing the number 4 on both sides, we get
4(5) + 4(7)

Question 12.
6 × 2 + 8 × 2
Answer:
2(6 + 8)
Explanation:
To multiply a sum of two or numbers and then add the products the answer will be the same.
6 × 2 + 8 × 2
By taking 2 as common on both sides, we get
2(6 + 8)

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 11.4 Properties of Equality and Zero to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 11.4 Properties of Equality and Zero

Exercises

SOLVE

Question 1.
5 × 0
Answer:
0
Explanation:
Any number multiplied by zero is zero.
5 × 0 = 0

Question 2.
(2 + 4) 0
Answer:
0
Explanation:
Any number multiplied by zero is zero.
(2 + 4) 0
= 6 x 0 = 0

Question 3.
0 × 3.56
Answer:
0
Explanation:
If we multiply zero with any number, the product is zero.
0 × 3.56 = 0

Question 4.
2(5 – 5)
Answer:
0
Explanation:
Any number multiplied by zero is zero.
2(5 – 5)
2 x 0 = 0

Identity which Equality Property is being displayed.

Question 5.
If 8 + 1 = 6 + 3, then does 4(8 + 1) = 4(6 + 3)?
Answer:
Equality property of Multiplication
Explanation:
Multiplying the same number on both sides to keep the equation equal is known as,
Equality property of Multiplication.
8 + 1 = 6 + 3, then does 4(8 + 1) = 4(6 + 3)
9 = 9 then does 4 x 9 = 4 x 9
9 = 9 then does 36 = 36

Question 6.
If 3 × 15 = 9 × 5, then does 6 + 3 × 15 = 6 + 9 × 5?
Answer:
Equality property of Addition
Explanation:
Adding the same number on both sides to keep the equation equal is known as,
Equality property of Addition.
3 × 15 = 9 × 5, then does 6 + 3 × 15 = 6 + 9 × 5
45 = 45 then does 6 + 45 =6 + 45
45 = 45 then 51 = 51

Question 7.
If \(\frac{1}{5}\) = \(\frac{3}{15}\), then does \(\frac{1}{5}\) – 5 = \(\frac{3}{15}\) – 5?
Answer:
Equality property of Subtraction
Explanation:
Subtracting the same number on both sides to keep the equation equal is known as,
Equality property of Subtraction.
\(\frac{1}{5}\) = \(\frac{3}{15}\), then does \(\frac{1}{5}\) – 5 = \(\frac{3}{15}\) – 5
\(\frac{1}{5}\) = \(\frac{1}{5}\), then does \(\frac{1}{5}\)-5 = \(\frac{1}{5}\) – 5

Question 8.
If 6 × 7 = 21 × 2, then does \(\frac{(6 \times 7)}{4}\) = \(\frac{(21 \times 2)}{4}\) ?
Answer:
Equality property of Division
Explanation:
Dividing with the same number on both sides to keep the equation equal is known as,
Equality property of Division.
6 × 7 = 21 × 2, then does \(\frac{(6 \times 7)}{4}\) = \(\frac{(21 \times 2)}{4}\)
42 = 42 then does \(\frac{(42)}{4}\) = \(\frac{(42)}{4}\)

Question 9.
If 3 × .75 = 2 × 1.125, then does \(\frac{(3 \times .75)}{200}\) = \(\frac{(2 \times 1.125)}{200}\)?
Answer:
Equality property of Division
Explanation:
Dividing with the same number on both sides to keep the equation equal is known as,
Equality property of Division.
3 × .75 = 2 × 1.125, then does \(\frac{(3 \times .75)}{200}\) = \(\frac{(2 \times 1.125)}{200}\)
2.25 = 2.25 then does \(\frac{2.25}{200}\) = \(\frac{2.25}{200}\)

Question 10.
If 20 – 3 = 12 + 5, then does 2o – 3 + 11.5 = 12 + 5 + 11.5?
Answer:
Equality property of Addition
Explanation:
Adding the same number on both sides to keep the equation equal is known as,
Equality property of Addition.
20 – 3 = 12 + 5, then does 20 – 3 + 11.5 = 12 + 5 + 11.5
17 = 17 then does 17 + 11.5 = 17 + 11.5
17 = 17 then does 28.5 = 28.5

Question 11.
If 3 + 4 + 1 = 11 – 3, then does 3 + 4 + 1 + 8 = 11 – 3 + 8?
Answer:
Equality property of Addition
Explanation:
Adding the same number on both sides to keep the equation equal is known as,
Equality property of Addition.
3 + 4 + 1 = 11 – 3, then does 3 + 4 + 1 + 8 = 11 – 3 + 8
8 = 8 then does 16 = 16

Question 12.
If 5 – 1 = 20 × .2 then does \(\frac{(5-1)}{22}\) = \(\frac{(20 \times .2)}{22}\)?
Answer:
Equality property of Division
Explanation:
Dividing with the same number on both sides to keep the equation equal is known as,
Equality property of Division.
5 – 1 = 20 × .2 then does \(\frac{(5-1)}{22}\) = \(\frac{(20 \times .2)}{22}\)
4 = 4 then does \(\frac{4}{22}\) = \(\frac{4}{22}\)

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 12.1 Negative Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 12.1 Negative Numbers

Exercises

CALCULATE

Question 1.
On the number line, place and label the number values as points on the number line.
A (-1), B (1), C (-2.5), D (1.5), E (-8), F (-8.5), G (-4.5)
Then order values from least to greatest.
Answer:

Order is F(-8.5),E(-8),G(-4.5),C(-2.5),A(-1),B(1),D(1.5),

Explanation:
Placed on the number line, placed and labelled the number values as points on the number line. A (-1), B (1), C (-2.5), D (1.5), E (-8), F (-8.5), G (-4.5)
The order values from least to greatest are as F(-8.5) < E(-8) < G(-4.5) < C(-2.5) < A(-1) < B(1) < D(1.5), therefore order is F(-8.5),E(-8),G(-4.5),C(-2.5),A(-1),B(1),D(1.5).

Question 2.
Order the number values from greatest to least.
4.6, -6.6, -6, -6.7, -4.3, 3, 3.3, -3.3, 8, -8.1
Answer:
Greatest to least:
8, 4.6, 3.3, 3, -3.3, -4.3, -6, -6.6, -6.7, -8.1,

Explanation:
Given to find the order of number values 4.6, -6.6, -6, -6.7, -4.3, 3, 3.3, -3.3, 8, -8.1 from greatest to least as 8 > 4.6 > 3.3 > 3 > -3.3 > -4.3 > -6 > -6.6 > -6.7 > -8.1, therefore greatest to least numbers are
8, 4.6, 3.3, 3, -3.3, -4.3, -6, -6.6, -6.7, -8.1.

Use >(is greater than), < (is less than), or = (is equal to) in comparing the number value pairs.

Question 3.
-4.5 ____4.5
Answer:
< (is less than),

Explanation:
Given to compare -4.5 and 4.5 as the number value pairs -4.5 < 4.5,
so it is <(less than).

Question 4.
-3.3 ____________ -3.0
Answer:
< (is less than),

Explanation:
Given to compare -3.3 and  -3.0 as the number value pairs -3.3 < -3.0,
so it is < (is less than).

Question 5.
7.5 __________ -7.5
Answer:
> (is greater than),

Explanation:
Given to compare 7.5 and -7.5 as the number value pairs 7.5 > -7.5,
so it is > (is greater than).

Question 6.

–7.5 _______ 1.5
Answer:
< (is less than),

Explanation:
Given to compare -7.5 and 1.5 as the number value pairs -7.5 < 1.5,
so it is < (is less than).

Question 7.
-6.1 __________ -6.25
Answer:
> (is greater than),

Explanation:
Given to compare -6.1 and -6.25 as the number value pairs -6.1 > -6.25,
so it is > (is greater than).

Question 8.
-5 ___________ -4.95
Answer:
< (is less than),

Explanation:
Given to compare -5 and -4.95 as the number value pairs -5 < -4.95,
so it is < (is less than).

Question 9.
13.9 __________ 13.9
Answer:
= (equal to),

Explanation:
Given to compare 13.9 and 13.9 as the number value pairs 13.9 = 13.9,
so it is = (equal to).

Question 10.
-9 ___________ 9
Answer:
< (is less than),

Explanation:
Given to compare -9 and 9 as the number value pairs -9 < 9,
so it is < (is less than).

Question 11.
-8 __________ -.888
Answer:
< (is less than),

Explanation:
Given to compare -8 and -.888 as the number value pairs -8 < -.888,
so it is < (is less than).

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 13.2 Solving Equations with Addition and Subtraction to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 13.2 Solving Equations with Addition and Subtraction

Exercises

SOLVE

Question 1.
x + 9 = 17
Answer:
x = 8,

Explanation:
Asking to solve x + 9 = 17,
So x = 17 – 9 = 8.

Question 2.
17 = s + 8
Answer:
s = 9,

Explanation:
Asking to solve 17 = s + 8,
So s = 17 – 8 = 9.

Question 3.
14 + z = 49
Answer:
z = 35,

Explanation:
Asking to solve 14 + z = 49,
So z = 49 – 14 = 35.

Question 4.
17 – f = 14
Answer:
f = 3,

Explanation:
Asking to solve 17 – f = 14,
So f = 17 – 14 = 3.

Question 5.
m – 30 = 35
Answer:
m = 5,

Explanation:
Asking to solve m – 30 = 35,
So m = 35 – 30 = 5.

Question 6.
c – 22 = 22
Answer:
c = 44,

Explanation:
Asking to solve c – 22  = 22,
So c = 22 + 22 = 44.

Question 7.
y + 11 = 42
Answer:
31,

Explanation:
Asking to solve y + 11 = 42,
So y = 42 – 11 = 31.

Question 8.
107 = 17 + l
Answer:
I = 90,

Explanation:
Asking to solve 107 = 17 + I,
So I = 107 – 17 = 90.

Question 9.
k + 28 = 64
Answer:
k = 36,

Explanation:
Asking to solve k + 28 = 64,
So k = 64 – 28 = 36.

Question 10.
28 + u = 43
Answer:
u = 15,

Explanation:
Asking to solve 28 + u = 43,
So u = 43 – 28 = 15.

Question 11.
59 – t = 42
Answer:
t = 17,

Explanation:
Asking to solve 59 – t = 42,
So t = 59 – 42 = 17.

Question 12.
13 – a = 4
Answer:
a = 9,

Explanation:
Asking to solve 13 – a = 4,
So a = 13 – 4 = 9.

Question 13.
24 + b = 54
Answer:
b = 30,

Explanation:
Asking to solve 24 + b = 30,
So b = 54 – 24 = 30.

Question 14.
54 – e = 22
Answer:
e = 32,

Explanation:
Asking to solve 54 – e = 22,
So e = 54 – 22 = 32.

Question 15.
15 + d = 39
Answer:
d = 24,

Explanation:
Asking to solve 15 + 9 = 39,
So d = 39 – 15 = 24.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 13.1 Understanding Variable Expressions to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 13.1 Understanding Variable Expressions

Exercises

EXPLAIN

Write in words what each expression is describing.

Question 1.
\(\frac{a}{2}\) + 22
Answer:
Dividing a by 2 add 22,

Explanation:
Asked to write the expression \(\frac{a}{2}\) + 22
in words, it is dividing a by 2 then adding 22.

Question 2.
y + 4
Answer:
Adding 4 to y,

Explanation:
Asked to write the expression y + 4 in words,
it is adding 4 to y.

Question 3.
4b + 3
Answer:
Multiplying 4 to b and adding 3,

Explanation:
Asked to write the expression 4b + 3 in words,
it is multiplying 4 to b and adding 3.

Question 4.
.9q – 9
Answer:
Multiplying .9 to q and subtracting 9,

Explanation:
Asked to write the expression .9q – 9 in words,
it is multiplying .9 to q and subtracting 9.

Question 5.
(x – 4) ÷ 20
Answer:
Subtracting 4 from x and dividing by 20,

Explanation:
Asked to write the expression (x – 4) ÷ 20 in words,
it is subtracting 4 from x and dividing by 20.

Question 6.
(3g + 7) – 8 + 33
Answer:
Multiplying 3 to g, adding 7, subtracting 8,
adding 33,

Explanation:
Asked to write the expression (3g + 7) – 8 + 33
in words, it is multiplying 3 to g then
adding 7 then subtracting 8 and adding 33.

Question 7.
3n – 9
Answer:
Multiplying 3 to n and subtracting 9,

Explanation:
Asked to write the expression 3n – 9 in words,
it is multiplying 3 to n and subtracting 9.

Question 8.
\(\frac{5}{h}\)
Answer:
Dividing 5 by h,

Explanation:
Asked to write the expression \(\frac{5}{h}\) in words,
it is dividing 5 by h.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 10.6 Irrational Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 10.6 Irrational Numbers

Exercises

CALCULATE

Estimate the square root of a number.

Question 1.
\(\sqrt{89}\) is between ___________ and ____________ but closer to ______________.
Answer:
\(\sqrt{89}\) 9 and 10; but closer to 9
Explanation:
\(\sqrt{89}\) 9 and 10; but closer to 9
9 x 9 = 81
10 x 10 = 100
89 is closer to 81 rather then 100
\(\sqrt{89}\) 9 and 10; but closer to 9

Question 2.
\(\sqrt{44}\) is between ___________ and ____________ but closer to ______________.
Answer:
\(\sqrt{44}\) 6 and 7; but closer to 7
Explanation:
\(\sqrt{44}\) 6 and 7; but closer to 7
6 x 6 = 36
and
7 x 7 = 49
44 is closer to 49, rather then 36
\(\sqrt{44}\) 6 and 7; but closer to 7

Question 3.
\(\sqrt{5}\) is between ___________ and ____________ but closer to ______________.
Answer:
\(\sqrt{5}\) 2 and 3; but closer to 2
Explanation:
\(\sqrt{5}\) 2 and 3; but closer to 2
2 x 2 = 4
and
3 x 3 = 9
4 is closer to 5, rather then 9
\(\sqrt{5}\) 2 and 3; but closer to 2

Question 4.
\(\sqrt{50}\) is between ___________ and ____________ but closer to ______________.
Answer:
\(\sqrt{50}\) 7 and 8; but closer to 7
Explanation:
\(\sqrt{50}\) 7 and 8; but closer to 7
7 x 7 = 49
and
8 x 8 = 64
49 is closer to 50, rather then 64
\(\sqrt{50}\) 7 and 8; but closer to 7

Question 5.
\(\sqrt{97}\) is between ___________ and ____________ but closer to ______________.
Answer:
\(\sqrt{97}\) 9 and 10; but closer to 10
Explanation:
\(\sqrt{97}\) 9 and 10; but closer to 10
9 x 9 = 81
and
10 x 10 = 100
97 if closer to 10, rather then 81
\(\sqrt{97}\) 9 and 10; but closer to 10

Question 6.
\(\sqrt{23}\) is between ___________ and ____________ but closer to ______________.
Answer:
\(\sqrt{23}\) 4 and 5; but closer to 5
Explanation:
\(\sqrt{23}\) 4 and 5; but closer to 5
4 x 4 = 16
and
5 x 5 = 25
25 is closer to 23, rather then 16
\(\sqrt{23}\) 4 and 5; but closer to 5

Question 7.
Noah’s garden is a square with an area of 73 square feet. The length of each side is between which two whole numbers? _______________
Answer:
8 and 9
Explanation:
Noah’s garden is a square with an area of 73 square feet.
8 x 9 = 72 square feet
The length of each side is between which two whole numbers are 8 and 9

Question 8.
Isabella wants to add a wallpaper border along one wall of her room. If her room is a square with an area of 154 square feet, and the wallpaper border is sold only in whole numbers of feet, how many feet of border should she purchase?
Answer:
13
Explanation:
a square with an area of 154 square feet
13 x 13 = 169
She should purchase 13 feet of border.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 10.5 Rational Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 10.5 Rational Numbers

Exercises

CALCULATE

Circle each group the number belongs to (there can be more than one).

Question 1.
-16
whole
integer
rational
Answer:
integer, rational
Explanation:
Any number expressed in fraction are called rational numbers.
An integer is a whole number with a positive or negative numbers.
So, -16 is an integer and rational number.

Question 2.
0.006
whole
integer
rational
Answer:
rational
Explanation:
Any number expressed in fraction are called rational numbers.
So, 0.006 is a rational number.

Question 3.
7
whole
integer
rational
Answer:
whole, integer, rational
Explanation:
Whole numbers are a set of numbers including all natural numbers and 0.
They are a part of real numbers that do not include fractions, decimals, or negative.
Any number expressed in fraction are called rational numbers.
An integer is a whole number with a positive or negative numbers.
So, 7 is an integer, whole and rational number.

Question 4.
-1.953
whole
integer
rational
Answer:
rational
Explanation:
Any number expressed in fraction are called rational numbers.
So, -1.953 is a rational number.

Question 5.
–\(\frac{8}{17}\)
whole
integer
rational
Answer:
rational
Explanation:
Any number expressed in fraction are called rational numbers.
So, –\(\frac{8}{17}\) is a rational number.

Question 6.
3\(\frac{4}{5}\)
whole
integer
rational
Answer:
rational
Explanation:
Any number expressed in fraction are called rational numbers.
So, –\(\frac{8}{17}\) is a rational number.

Question 7.
-1\(\frac{3}{4}\)
whole
integer
rational
Answer:
rational
Explanation:
Any number expressed in fraction are called rational numbers.
So, -1\(\frac{3}{4}\) is a rational number.

Question 8.
\(\frac{78}{79}\)
whole
integer
rational
Answer:
rational
Explanation:
Any number expressed in fraction are called rational numbers.
So, \(\frac{78}{79}\) is a rational number.

Change each number to a fraction.

Question 9.
-23
Answer:
\(\frac{-23}{1}\)
Explanation:
The given number -23 is an integer.
So, just put that integer as the numerator of a fraction with a denominator of 1.
-23 = \(\frac{-23}{1}\)

Question 10.
0.156
Answer:
\(\frac{156}{1000}\)
Explanation:
To convert a decimal to a fraction, place the decimal number over its place value.
0.156, the six is in the thousandths place, to create the equivalent fraction.
so, 0.156 = \(\frac{156}{1000}\)

Question 11.
19
Answer:
\(\frac{19}{1}\)
Explanation:
Given number 19 is whole number,
to convert the whole number place the given number in numerator and 1 in the denominator.
So, 19 = \(\frac{19}{1}\)

Question 12.
8\(\frac{2}{3}\)
Answer:
\(\frac{26}{3}\)
Explanation:
To convert mixed fraction into improper fraction,
Multiply the whole number by the denominator.
Add that number to the numerator.
Write that sum on top of the original denominator.
8\(\frac{2}{3}\) = \(\frac{26}{3}\)

Question 13.
-8
Answer:
\(\frac{-8}{1}\)
Explanation:
The given number -8 is an integer.
So, just put that integer as the numerator of a fraction with a denominator of 1.
-8 = \(\frac{-8}{1}\)

Question 14.
2\(\frac{7}{9}\)
Answer:
\(\frac{25}{9}\)
Explanation:
To convert mixed fraction into improper fraction,
Multiply the whole number by the denominator.
Add that number to the numerator.
Write that sum on top of the original denominator.
2\(\frac{7}{9}\) = \(\frac{25}{9}\)

Question 15.
1.945
Answer:
\(\frac{1945}{1000}\)
Explanation:
To convert a decimal to a fraction, place the decimal number over its place value.
Count the numbers after decimal and place the tenths place, hundredths, thousandths and so on to create the equivalent fraction.
so, 1.945 = \(\frac{1945}{1000}\)

Question 16.
78
Answer:
\(\frac{78}{1}\)
Explanation:
Given number 78 is whole number,
to convert the whole number place the given number in numerator and 1 in the denominator.
So, 78 = \(\frac{78}{1}\)

Question 17.
13\(\frac{1}{2}\)
Answer:
\(\frac{27}{2}\)
Explanation:
To convert mixed fraction into improper fraction,
Multiply the whole number by the denominator.
Add that number to the numerator.
Write that sum on top of the original denominator.
13\(\frac{1}{2}\) = \(\frac{27}{2}\)

Question 18.
76.38
Answer:
\(\frac{7638}{100}\)
Explanation:
To convert a decimal to a fraction, place the decimal number over its place value.
Count the numbers after decimal and place the tenths, hundredths, thousands and son on to create the equivalent fraction.
so, 76.38 = \(\frac{7638}{100}\)

Question 19.
-302
Answer:
\(\frac{-302}{1}\)
Explanation:
The given number -8 is an integer.
So, just put that integer as the numerator of a fraction with a denominator of 1.
-302 = \(\frac{-302}{1}\)

Question 20.
\({9 . \overline{3}}\)
Answer:
\(\frac{28}{3}\)
Explanation:
Let x = 9.333333……   Equation (1)
multiplying Equation (1) by 10 on both sides
10 x = 93.333333….. Equation (2)
subtracting (1) from (2)
10x = 93.3333333……
– x = 9. 33333……
= 9x =93 – 9
9x = 84
x = 84/9
x = 28/3