We included **HMH Into Math Grade 6 Answer Key PDF** **Module 9 Solve Problems Using Equations and Inequalities **to make students experts in learning maths.

## HMH Into Math Grade 6 Module 9 Answer Key Solve Problems Using Equations and Inequalities

**Expression Data**

Write expressions to match the scenario given.

The dartboard has sections numbered 1 to 20. You can “hit” a number on the dartboard by writing an expression equal to the number. Each expression must include each of the numbers 1, 2, 3, and 4 exactly once, but no other numbers. Try to get as many hits as you can. An example is shown.

Answer:

1. (4 + 2) ÷ 3 – 1 = 1

2. (4 – 2) ÷ 1 + 3 = 5

3. (4 + 2) ÷ 1 + 3 = 9

4. (4 + 2) ÷ 3 + 1 = 3

5. (4 + 3) ÷ 1 + 2 = 9

6. (4 – 3) ÷ 1 + 2 = 3

7. (4 – 1) ÷ 3 + 2 = 3

8. (3 × 2) ÷ 1 + 4 = 10

9. (4 × 2) ÷ 1 + 3 = 11

10. (4 × 3) ÷ 2 + 1 = 7

11. (4 × 3) ÷ 3 – 1 = 4

12. (3 × 2) ÷ 1 – 4 = 2

13. (4 ÷ 1) + 2 × 3 = 18

14. (4 × 3) ÷ 1 + 2 = 14

15. (4 × 3) + 2 + 1 = 15

16. (4 × 1) ÷ 2 + 3 = 5

17. (3 × 2) + 1 + 4 = 13

18. (2 × 1) + 4 ÷ 3 = 2

19. (4 × 3) × 1 ÷ 2 = 6

20. (1 × 4) + 3 + 2 = 9

**Turn and Talk**

Question 1.

Describe a strategy you used to hit different numbers

Answer: By using the numbers 1, 2, 3, 4 and by including the different arithmetic operations we can hit different numbers.

Question 2.

How did grouping symbols help you hit different numbers?

Answer: We can group the symbols to hit different numbers we use parentheses () and then find the numbers.

**Are You Ready?**

Complete these problems to review prior concepts and skills you will need for this module.

**Expressions with Variables**

**For Problems 1-10, find the value of the expression. Show your work.**

Question 1.

25 – m if m = 9

Answer:

Given expression,

25 – m

m = 9

25 – 9 = 16

So, the value of 25 – m when m = 9 is 16.

Question 2.

50 + t if t = 18

Answer:

Given expression,

50 + t

t = 18

50 + 18 = 68

So, the value of 50 + t when t = 18 is 68.

Question 3.

105 – a if a = 75

Answer:

Given expression,

105 – a

a = 75

105 – 75 = 30

So, the value of 105 – a when a = 75 is 30.

Question 4.

112 + c if c = 35

Answer:

Given expression,

112 + c

c = 35

112 + 35 = 147

So, the value of 112 + c when c = 35 is 147.

Question 5.

15 × x if x = 5

Answer:

Given expression,

15 × x

x = 5

15 × 5 = 75

So, the value of 15 × x when x = 5 is 75.

Question 6.

36 ÷ y if y = 3

Answer:

Given expression,

36 ÷ y

y = 3

36 ÷ 3 = 12

So, the value of 36 ÷ y when y = 3 is 12.

Question 7.

64 ÷ d if d = 4

Answer:

Given expression,

64 ÷ d

d = 4

64 ÷ 4 = 16

So, the value of 64 ÷ d when d = 4 is 16.

Question 8.

24 × n if n = 8

Answer:

Given expression,

24 × n

n = 8

24 × 8 = 192

So, the value of 24 × n when n = 8 is 192.

Question 9.

125 ÷ k if k = 25

Answer:

Given expression,

125 ÷ k

k = 25

125 ÷ 25 = 5

So, the value of 125 ÷ k when k = 25 is 5.

Question 10.

120 × b if b = 10

Answer:

Given expression,

120 × b

b = 10

120 × 10 = 1200

So, the value of 120 × b when b = 10 is 1200.

**Plot Points on a Number Line**

**For Problems 11-16, plot and label each integer on the number line.**

Question 11.

-2

Answer:

A number line is simply a representation of real numbers. Generally, we mark 0 in the middle, the negative integers on the left, and the positive integers on the right.

To mark -2 on the number line move 2 parts on the left of zero.

Question 12.

1

Answer:

A number line is simply a representation of real numbers. Generally, we mark 0 in the middle, the negative integers on the left, and the positive integers on the right.

To mark 1 on the number line move 1 part on the right side of zero.

Question 13.

4

Answer:

A number line is simply a representation of real numbers. Generally, we mark 0 in the middle, the negative integers on the left, and the positive integers on the right.

To mark 4 on the number line move 4 parts on the right side of zero.

Question 14.

-9

Answer:

A number line is simply a representation of real numbers. Generally, we mark 0 in the middle, the negative integers on the left, and the positive integers on the right.

To mark -9 on the number line move 9 parts on the left of zero.

Question 15.

10

Answer:

A number line is simply a representation of real numbers. Generally, we mark 0 in the middle, the negative integers on the left, and the positive integers on the right.

To mark 10 on the number line move 10 parts on the right side of zero.

Question 16.

-5

Answer:

A number line is simply a representation of real numbers. Generally, we mark 0 in the middle, the negative integers on the left, and the positive integers on the right.

To mark -5 on the number line move 5 parts on the left of zero.