Go through the Math in Focus Grade 7 Workbook Answer Key Chapter 2 Rational Number Operations to finish your assignments.

## Math in Focus Grade 7 Course 2 A Chapter 2 Answer Key Rational Number Operations

### Math in Focus Grade 7 Chapter 2 Quick Check Answer Key

**Complete each ? with > or <.**

Question 1.

-3 ? 5

Answer:

**-3 < 5**

Explanation:

Compare the above two numbers. The number -3 is less than 5.

Question 2.

-7 ? -12

Answer:

**-7 > -12**

Explanation:

Compare the above two numbers. The number -7 is greater than -12.

Question 3.

10 ? -16

Answer:

**10 > -16**

Explanation:

Compare the above two numbers. The number 10 is greater than -16.

Question 4.

-28 ? 0

Answer:

**-28 < 0**

Explanation:

Compare the above two numbers. The number -28 is less than 0.

Question 5.

\(\frac{1}{2}\) ? \(\frac{3}{4}\)

Answer:

**1/2 < 3/4**

Explanation:

Compare above two fractions. The fraction 1/2 is less than 3/4.

Question 6.

-1\(\frac{1}{4}\) ? 2\(\frac{2}{3}\)

Answer:

The mixed fraction -1(1/4) in fraction form as -5/4.

The mixed fraction 2(2/3) in fraction form as 8/3.

**-1(1/4) < 2(2/3)**

Explanation:

Compare above two mixed fractions. The mixed fraction -1(1/4) is less than 2(2/3).

Question 7.

0.15 ? 0.13

Answer:

**0.15 > 0.13**

Explanation:

Compare the above decimal numbers. The decimal number 0.15 is greater than 0.13.

Question 8.

-1.23 ? -1.25

Answer:

**-1.23 > -1.25**

Explanation:

Compare the above decimal numbers. The decimal number -1.23 is greater than -1.25.

**Evaluate each expression.**

Question 9.

75 – (18 + 2) ∙ 3

Answer:

75 – (18 + 2) ∙ 3 Given

= 75 – 20 ∙ 3 Perform operation in parentheses

= 75 – 60 Multiply

= 15 subtract

Question 10.

15 ∙ (40 ÷ 8) + 72

Answer:

15 ∙ (40 ÷ 8) + 72 Given

= 15 ∙ 5 + 72 Perform operation in parentheses

= 75 + 72 Multiply

= 147 Add

= 147

**Express each improper fraction as a mixed number.**

Question 11.

\(\frac{12}{17}\)

Answer:

Question 12.

\(\frac{19}{3}\)

Answer:

**19/3 = 6(1/3)**

Explanation:

The mixed number for the improper fraction 19/3 is 6(1/3).

**Express each mixed number as an improper fraction.**

Question 13.

4\(\frac{3}{5}\)

Answer:

**4(3/5) =(20 + 3)/5 = 23/5**

Explanation:

The improper fraction for the mixed number 4(3/5) is 23/5.

Question 14.

6\(\frac{7}{9}\)

Answer:

**6(7/9) = (54 + 7)/9 = 61/9**

Explanation:

The improper fraction for the mixed number 6(7/9) is 61/9.

**Add or subtract. Express your answer in simplest form.**

Question 15.

\(\frac{2}{3}\) + \(\frac{5}{4}\)

Answer:

2/3 + 5/4

= (8 + 15)/12

= **23/12**

The simplest form of 2/3 + 5/4 is 23/12.

Explanation:

Perform addition operation on above two fractions. Add 2/3 with 5/4 the sum is 23/12.

Question 16.

\(\frac{7}{8}\) – \(\frac{2}{3}\)

Answer:

7/8 – 2/3

= (21 – 16)/24

**= 5/24**

The simplest form of 7/8 – 2/3 is 5/24.

Explanation:

Perform subtraction operation on above two fractions. Subtract 2/3 from 7/8 the difference is 5/24.

Question 17.

1\(\frac{1}{4}\) + 3\(\frac{2}{5}\)

Answer:

The mixed fraction 1(1/4) in fraction form as 5/4.

The mixed fraction 3(2/5) in fraction form as 17/5.

1(1/4) + 3(2/5)

= 5/4 + 17/5

= (25 + 68)/20

= **93/20
**The simplest form of 1(1/4) + 3(2/5) is 93/20.

Explanation:

Perform addition operation on above two fractions. Add 1(1/4) with 3(2/5) the sum is 93/20.

Multiply or divide. Express your answer in simplest form.

Question 18.

\(\frac{2}{9}\) • \(\frac{3}{4}\)

Answer:

2/9 • 3/4

= 6/36

= **1/6**

The simplest form of 2/9 • 3/4 is 1/6.

Explanation:

Perform multiplication operation on above two numbers. Multiply 2/9 with 3/4 the product is 1/6.

Question 19.

1\(\frac{2}{9}\) • \(\frac{3}{4}\)

Answer:

1(2/9) • 3/4

= 11/9 • 3/4

= **33/36**

The simplest form of 1(2/9) • 3/4 is 33/36.

Explanation:

Perform multiplication operation on above two numbers. Multiply 1(2/9) with 3/4 the product is 33/36.

Question 20.

\(\frac{5}{8}\) ÷ \(\frac{21}{4}\)

Answer:

5/8 ÷ 21/4

= 5/8 • 4/21

= 5/2 • 1/21

= **5/42**

The simplest form of 5/8 ÷ 21/4 is 5/42.

Explanation:

Perform division operation on above two numbers. Divide 5/8 by 21/4 the result is 5/42.

Question 21.

\(\frac{3}{4}\) ÷ 1\(\frac{1}{2}\)

Answer:

3/4 ÷ 1(1/2)

= 3/4 ÷ 3/2

= 3/4 • 2/3

= **1/2**

The simplest form of 3/4 ÷ 1(1/2) is 1/2.

Explanation:

Perform division operation on above two numbers. Divide 3/4 by 1(1/2) the result is 1/2.

**Multiply or divide.**

Question 22.

15.8 • 2.7

Answer:

15.8 • 2.7

=** 42.66**

Explanation:

Perform multiplication operation on above two numbers. Multiply 15.8 with 2.7 the product is 42.66.

Question 23.

8.82 ÷ 0.6

Answer:

8.82 ÷ 0.6

= **14.7**

Explanation:

Perform division operation on above two numbers. Divide 8.82 by 0.6 the result is 14.7.

Question 24.

25% of $420

Answer:

25% of $420

= 25/100 • $420

= 1/4 • $420

= $420/4

= **$105**

Explanation:

Perform multiplication operation. Multiply 25/100 with $420 the product is $105.

Question 25.

115 is what percent of 345?

Answer:

X% of 345 = 115

x/100 • 345 = 115

x = 115/345 • 100

x = 1/3 • 100

**x = 33.33%**

115 is 33.33% of 345.

Question 26.

24 boys out of 64 classmates is what percent?

Answer:

24/64 • 100

= 3/8 • 100

= 75/2

= **37.5%**

24 boys out of 64 classmates is 37.5%.

**Solve.**

Question 27.

A seedling that Jeffrey planted in 2009 was 50 centimeters tall. In 2010, it was 120 centimeters tall.

a) Find the increase in the height of the seedling Jeffrey planted.

Answer:

A seedling that Jeffrey planted in 2009 was 50 centimeters tall.

In 2010, it was 120 centimeters tall.

**120 – 50 = 70 centimeters**.

The height of the seedling Jeffrey planted is increased by 70 centimeters.

b) Find the percent increase in the height of the seedling.

Answer:

Percent in the increase in height :

\(\frac{70}{50}\) × 100%

= 1.4 × 100%

= 140%

70 centimeters ; 140%