Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 2 Lesson 2.4 Operations with Integers to finish your assignments.

## Math in Focus Grade 7 Course 2 A Chapter 2 Lesson 2.4 Answer Key Operations with Integers

### Math in Focus Grade 7 Chapter 2 Lesson 2.4 Guided Practice Answer Key

**Evaluate each expression.**

Question 1.

14 + 8 – 96

14 + 8 – 9 • 6 = 14 + 8 – Multiply.

= 14 + 8 + Rewrite subtraction as adding the opposite.

= 14 + () + 8 Use the commutative property of addition.

= + 8 Add.

= Add.

Answer:

14 + 8 – 9 • 6

= 14 + 8 – 54

= 14 + (-54) + 8

= -40 + 8

= **-32
**Explanation:

The given expression is 14 + 8 – 9 • 6. Use BODMAS rule.

First we have to perform multiplication operation. Multiply 9 with 6 the product is 54.

We have to use – symbol before 54. Now the expression is 14 + 8 – 54.

Now, use the commutative property of addition the expression is 14 + (-54) + 8.

Add 14 with -54 the sum is -40. The expression is -40 + 8.

Add -40 with 8 the sum is -32.

Question 2.

(-25 – 5) ÷ 6 – 21

(-25 – 5) ÷ 6 – 21 = ÷ 6 – 21 Subtract within the parentheses.

= – 21 Divide.

= Subtract.

Answer:

(-25 – 5) ÷ 6 – 21

= (-30) ÷ 6 – 21

= -5 – 21

= **-26
**Explanation:

The given expression is (-25 – 5) ÷ 6 – 21. Use BODMAS rule.

First we have to perform operation within the parentheses. Subtract -25 with -5 the difference is -30. Now the expression is (-30) ÷ 6 – 21.

Secondly we have to perform division operation. Divide -30 by 6 the quotient is -5.

The expression is -5 -21. Subtract -5 with – 21 the result is -26.

Question 3.

-14 – (3 + 3) • 2

Answer:

-14 – (3 + 3) • 2

= -14 – (6) • 2

= -14 – 12

= **– 26
**Explanation:

The given expression is -14 – (3 + 3) • 2. Use BODMAS rule.

First we have to perform operation within the parentheses. Add 3 with 3 the sum is 6. Now the expression is -14 -(6) • 2

Second we have to perform multiplication operation. Multiply 6 with 2 the product is 12. Now the expression is -14 -12.

Third we have to perform subtraction operation. Subtract -14 with -12 the result is -26.

**Solve.**

Question 4.

Joseph drew a hexagon on a 3-inch square piece of paper. He cut four identical right triangles from the four corners of the paper. The height of each triangle is \(\frac{1}{2}\) the length of the paper. The base of each triangle is \(\frac{1}{3}\) the length of the paper. What is the area of the paper that remained after these triangles are cut off?

Height of a triangle:

Base of a triangle:

Area of remaining paper:

Area of original paper – Area of four cut-off triangles

= 3 • 3 – 4 • (\(\frac{1}{2}\) • • ) Write an expression.

= – Multiply.

= in^{2} Subtract.

The area of the remaining paper is square inches.

Answer:

Length of the paper = 3 inches

Height of a triangle: 1/2 • length of the paper = 1/2 • 3 = **3/2**

Base of a triangle: 1/3 • length of the paper = 1/3 • 3 = **1
**Area of four cut-off triangles = 4 • (1/2 • base • height)

Area of remaining paper = Area of original paper – Area of four cut-off triangles

= 3 • 3 – 4 • (1/2 • 1 • 3/2)

= 9 – 4 •(3/4)

= 9 – 3

= 6 in

^{2}

The area of the remaining paper is

**6**square inches.

### Math in Focus Course 2A Practice 2.4 Answer Key

**Evaluate each expression.**

Question 1.

-3 • 5 + 7

Answer:

-3 • 5 + 7

= – 15 + 7

= **-8**

Explanation:

The given expression is -3 • 5 + 7. Use BODMAS rule.

First multiply -3 with 5 the product is -15. Now the expression is -15 + 7.

Next perform addition operation. Add -15 with 7 the sum is -8.

Question 2.

50 ÷ (-5) + (-4)

Answer:

50 ÷ (-5) + (-4)

= 50 ÷ -5 – 4

= -10 – 4

= -14

Explanation:

The given expression is 50 ÷ (-5) + (-4). Use BODMAS rule.

First perform operations within the parentheses. Now the expression is 50 ÷ – 5 – 4.

Next perform division operation. Divide 50 by -5 the quotient is -10. Now the expression is -10 -4.

Subtract -10 with -4 the result is -14.

Question 3.

4 • (-6) + (-3) • 5

Answer:

4 • (-6) + (-3) • 5

= 4 • -6 – 3 • 5

= -24 – 15

**= -39**

Explanation:

The given expression is 4 • (-6) + (-3) • 5. Use BODMAS rule.

First perform operations within the parentheses. Now the expression is 4 • -6 – 3 • 5.

Next perform multiplication operation. Multiply 4 with -6 the product is -24. Multiply -3 with 5 the product is -15. Now the expression is -24 – 15.

Subtract -24 with -15 the result is -39.

Question 4.

11 – 2 • 8 – (-9)

Answer:

= 11 – 2 • 8 – (-9)

= 11 – 2 • 8 + 9

= 11 – 16 + 9

= 20 – 16

= **4**

Explanation:

The given expression is 11 – 2 • 8 – (-9). Use BODMAS rule.

First perform operations within the parentheses. Now the expression is 11 – 2 • 8 + 9.

Next perform multiplication operation. Multiply 2 with 8 the product is 16. Now the expression is 11 – 16 + 9.

Add 11 with 9 the sum is 20. The expression is 20 -16.

Subtract 16 from 20 the result is 4.

Question 5.

-64 ÷ 4. 5 – 37

Answer:

-64 ÷ 4. 5 – 37

= -16. 5 – 37

= – 80 – 37

= **– 117**

Explanation:

The given expression is-64 ÷ 4. 5 – 37. Use BODMAS rule.

First perform division operation. Divide 64 by 4 the quotient is 16. Now the expression is -16. 5 – 37.

Next perform multiplication operation. Multiply 16 with 5 the product is 80. Now the expression is -80 – 37.

subtract -80 with -37 the result is -117.

Question 6.

-28 – 350 ÷ 7 + 8

Answer:

-28 – 350 ÷ 7 + 8

= -28 – 50 + 8

= -28 -42

= **– 70**

Explanation:

The given expression is -28 – 350 ÷ 7 + 8. Use BODMAS rule.

First perform division operation. Divide 350 by 7 the quotient is 50. Now the expression is -28 – 50 + 8.

Next perform addition operation. Add -50 with 8 the sum is -42. Now the expression is -28 -42.

subtract -28 with -42 the result is -70.

Question 7.

1oo – (8 – 15) • 9

Answer:

1oo – (8 – 15) • 9

= 100 – (-7) • 9

= 100 + 63

= **163**

Explanation:

The given expression is 1oo – (8 – 15) • 9. Use BODMAS rule.

First perform operations within the parentheses. Subtract 15 from 8 the difference is -7. Now the expression is 100 – (-7) • 9.

Next perform multiplication operation. Multiply -7 with 9 the product is -63. Now the expression is 100 + 63.

Add 100 with 63 the sum is 163.

Question 8.

70 ÷ (-4 – 3) + 60

Answer:

70 ÷ (-4 – 3) + 60

= 70 ÷ (-7) + 60

= – 10 + 60

= **50**

Explanation:

The given expression is 70 ÷ (-4 – 3) + 60. Use BODMAS rule.

First perform operations within the parentheses. Subtract -4 with -3 the result is -7. Now the expression is 70 ÷ (-7) + 60.

Next perform division operation. Divide 70 by – 7 the quotient is -10. Now the expression is -10 + 60.

Add -10 with 60 the result is 50.

Question 9.

(4 + 2) • 3 – 8 • (2 + 3)

Answer:

(4 + 2) • 3 – 8 • (2 + 3)

= 6 • 3 – 8 • 5

= 18 – 40

= **-22**

Explanation:

The given expression is (4 + 2) • 3 – 8 • (2 + 3). Use BODMAS rule.

First perform operations within the parentheses. Add 4 with 2 the sum is 6. Add 2 with 3 the sum is 5. Now the expression is 6 • 3 – 8 • 5.

Next perform multiplication operation. Multiply 6 with 3 the product is 18. Multiply 8 with 5 the product is 40. Now the expression is 18 – 40.

Subtract 40 from 18 the difference is -22.

Question 10.

70 ÷ (-4 – 3) + 60

Answer:

= 70 ÷ (-7) + 60

= – 10 + 60

= **50**

Explanation:

The given expression is 70 ÷ (-4 – 3) + 60. Use BODMAS rule.

First perform operations within the parentheses. Subtract -4 with -3 the result is -7. Now the expression is 70 ÷ (-7) + 60.

Next perform division operation. Divide 70 by – 7 the quotient is -10. Now the expression is -10 + 60.

Add -10 with 60 the result is 50.

Question 11.

15 ÷ (4 + 1) – 8.3

Answer:

15 ÷ (4 + 1) – 8 • 3

= 15 ÷ 5 – 8 • 3

= 3 – 8 • 3

= 3 – 24

= **-21**

Explanation:

The given expression is 15 ÷ (4 + 1) – 8 • 3. Use BODMAS rule.

First perform operations within the parentheses. Add 4 with 1 the sum is 5. Now the expression is 15 ÷ 5 – 8 • 3.

Next perform division operation. Divide 15 by 5 the quotient is 3. Now the expression is 3 – 8 • 3.

Perform multiplication operation. Multiply 8 with 3 the product is 24. Now the expression is 3 – 24.

Subtract 24 from 3 the difference is -21.

Question 12.

24 ÷ 4 – (-13 + 3) • 2

Answer:

24 ÷ 4 – (-13 + 3) • 2

= 24 ÷ 4 + 10 • 2

= 6 + 10 • 2

= 6 + 20

= **26**

Explanation:

The given expression is 24 ÷ 4 – (-13 + 3) • 2. Use BODMAS rule.

First perform operations within the parentheses. Add 3 with -13 the sum is -10. Now the expression is 24 ÷ 4 + 10 • 2.

Next perform division operation. Divide 24 by 4 the quotient is 6. Now the expression is 6 + 10 • 2.

Perform multiplication operation. Multiply 10 with 2 the product is 20. Now the expression is 6 + 20.

Add 6 with 20 the sum is 26.

Question 13.

-12 + 50 ÷ (-2 – 3) + 72 ÷ (4 + 2)

Answer:

-12 + 50 ÷ (-2 – 3) + 72 ÷ (4 + 2)

= -12 + 50 ÷ (-5) + 72 ÷ 6

= -12 – 10 + 12

= -12 + 2

=** -10**

Explanation:

The given expression is -12 + 50 ÷ (-2 – 3) + 72 ÷ (4 + 2). Use BODMAS rule.

First perform operations within the parentheses. Add -2 with -3 the sum is -5. Add 4 with 2 the sum is 6. Now the expression is-12 + 50 ÷ (-5) + 72 ÷ 6.

Next perform division operation. Divide 50 by -5 the quotient is -10. Divide 72 by 6 the quotient is 12. Now the expression is -12 – 10 + 12.

Add -10 with 12 the sum is 2. Now the expression is -12 + 2.

Add -12 with 2 the sum is -10.

Question 14.

180 ÷ (4 + 16) – 8 • 3 + 7 • (2 + 3)

Answer:

180 ÷ (4 + 16) – 8 • 3 + 7 • (2 + 3)

= 180 ÷ 20 – 8 • 3 + 7 • 5

= 9 – 8 • 3 + 7 • 5

= 9 – 24 + 35

= 9 + 11

=** 20**

Explanation:

The given expression is 180 ÷ (4 + 16) – 8 • 3 + 7 • (2 + 3). Use BODMAS rule.

First perform operations within the parentheses. Add 4 with 16 the sum is 20. Add 2 with 3 the sum is 5. Now the expression is 180 ÷ 20 – 8 • 3 + 7 • 5.

Next perform division operation. Divide 180 by 20 the quotient is 9. Now the expression is9 – 8 • 3 + 7 • 5.

Perform multiplication operation. Multiply 8 with 3 the product is 24. Multiply 7 with 5 the product is 35. Now the expression is 9 – 24 + 35.

Add -24 with 35 the sum is 11.

Add 9 with 11 the sum is 20.

**Solve. Show your work.**

Question 15.

Emily made a sketch of an octagonal window on a 27-inch square piece of paper. First she cut four identical isosceles triangles from the corners of the paper. Then she cut a square from the center of the octagon. Each leg of a cut-off triangle is \(\frac{1}{3}\) the length of the paper. The side length of the cut-out square is also \(\frac{1}{3}\) the length of the paper. What ¡s the area of the sketch after she removed the triangles and the square?

Answer:

Length of the paper =** 27-inch **

Area of square piece of paper = side • side = 27 in • 27 in = **729 square inches**

Each leg of a cut-off triangle = 1/3 • length of the paper = 1/3 • 27 =**9 inches**

Side length of a cut-out square = 1/3 • length of the paper = 1/3 • 27 = **9 inches
**Area of a square = side x side

**Area of four cut-off triangles = 4 • (1/2 • base • height)**

From the above image we can observe both base and height are same.

Area of octagonal window = Area of a square piece of paper – Area of four cut-off triangles – Area of a square

= 729 – 4 • (1/2 • 9 • 9) – 9 • 9

= 729 – 4 • (81/2) – 81

= 729 – 2 • 81 – 81

= 729 – 162 – 81

=

**486 square inches**

The area of the sketch after she removed the triangles and the square is

**486 square inches**.

Question 16.

**Math Journal** Suppose that Lydia shows you some of her homework:

Lydia made a common error when she used the distributive property to evaluate the expression -2(6 – 8). Evaluate the expression using the order of operations. Then explain how Lydia can correctly use the distributive property to evaluate the expression.

Answer:

Distributive property = **A ( B+ C) = AB + AC
**Use distributive property to evaluate the given expression -2 (6 – 8).

-2 (6 – 8) = -2 • 6 + (-2) • (-8)

= -12 + 16

= 4

**– 2 (6 – 8) = 4**

Question 17.

Sylvia took three turns in a video game. She scored -120 points during her first turn, 320 points during her second turn, and -80 points during her third turn. What was her average score for the three turns?

Answer:

Sylvia scored -120 points during her first turn.

Sylvia scored 320 points during her second turn.

Sylvia scored -80 points during her third turn.

Average = (-120 + 320 -80)/ 3 = 120/3 = **40 **

Average score for the three turns is 40 points.

Question 18.

**Math Journal** Benjamin wrote: -20 + 4 • 2 + 7 – 35 = -19. Where can he place the parentheses so that the equation will be a true statement?

Answer:

-20 + 4 • 2 + 7 – 35 = -19

= -20 + 4 • (2 + 7) – 35

= -20 + 4 • 9 – 35

= -20 + 36 – 35

= -20 + 1

= -19

The equation will be a true statement by keeping parentheses to 2 + 7. The equation is – 20 + 4 • (2 + 7) – 35 = -19