﻿ Multiplying and Dividing Rational Numbers Worksheet | Problems & Solutions

# Multiplying and Dividing Rational Numbers Worksheet

Multiplying and Dividing Rational Numbers Worksheet
• Page 1
1.
Find the number that makes the number sentence true.
7.0 × 1.7 = ?
 a. 11.9 b. 1.19 c. 7.7 d. 0.77

#### Solution:

7.0 × 1.7

= 71 × 1710

= 11910

= 11.9

2.
Find the number that makes the number sentence true.
4$\frac{2}{3}$ ÷ 11 = ?
 a. $\frac{33}{14}$ b. $\frac{8}{33}$ c. $\frac{14}{33}$ d. $\frac{154}{3}$

#### Solution:

42 / 3 ÷ 11

= 143 ÷11

= 143 × 111

= 1433

3.
A train runs at a speed of 600 kilometer in 4 hours. Which operation would you use to find its average speed in kilometer per hour?
 a. addition b. division c. multiplication d. subtraction

#### Solution:

Time taken by the train to cover 600 kilometer distance = 4 hours.

To find the average speed of the train, we need to divide the total distance covered by the train by the total time taken.

Therefore, the operation that can be used to find the average speed of train in kilometer per hour is 'division'.

4.
Ethan wants to buy 30 copies of a book. The cost of each book is $175.50. Which operation would you use to find the total amount he needs to spend on the books?  a. subtraction b. addition c. division d. multiplication #### Solution: Cost of each book is$175.50.

To find the total amount Ethan spent on books, we need to multiply the total number of copies of the book with the cost of each book.

Therefore, the operation that can be used to find the total amount Ethan spent on the books is 'multiplication'.

5.
The area of a triangle is 420 m2. If the area of rectangle is $\frac{1}{7}$ of the area of the triangle, then which operation would you use to find the area of the rectangle?
 a. addition b. multiply and then subtract c. multiplication d. subtraction

#### Solution:

The area of the triangle is 420 m2.

Area of rectangle is 17 of the area of the triangle.

To find the area of the rectangle, we need to multiply the fraction with the area of the triangle.

The operation that can be used to find the area of the rectangle is 'multiplication'.

6.
100 grams of spaghetti and meatballs contain 38 grams of proteins, 16 grams of fat, and 42 grams of carbohydrates. Find the fat content in 800 grams of spaghetti and meatballs.
 a. 326 grams b. 128 grams c. 120 grams d. 256 grams

#### Solution:

100 grams of spaghetti and meatballs contain 16 grams of fat.

800 grams of spaghetti and meatballs contain 800100 × 16 = 128 grams of fat.

The total fat content in 800 grams of spaghetti and meatballs is 128 grams.

7.
Students of a school decided to donate money for a charity. 1000 students contributed $30 each. What was the total amount donated?  a.$20,000 b. $875 c.$30,000 d. $82500 #### Solution: Number of students who donated money for charity = 1000. Amount of money each of them contributed =$30.

Total amount of money donated = Number of students × Amount of money contributed by each student

= 1000 × 30 = 30000

Total amount of money donated is \$30,000.

8.
Find the multiplicative inverse of (5 + $\frac{4}{5}$).
 a. $\frac{5}{29}$ b. $\frac{5}{34}$ c. $\frac{5}{31}$ d. $\frac{5}{27}$

#### Solution:

5 + 4 / 5
[Original expression.]

= 25 / 5 + 4 / 5
[Write equivalent fractions with a denominator 5.]

= 25 + 45
[Write the sum of the numerators over the common denominator.]

= 29 / 5
[Simplify.]

The multiplicative inverse of a number is its reciprocal.
[Reciprocal of a number is obtained by interchanging the numerator and the denominator.]

The reciprocal of 29 / 5 is 5 / 29 .
[Interchange numerator and denominator.]

So, the multiplicative inverse of (5 + 4 / 5 ) is 5 / 29.

9.
A square occupies $\frac{2}{3}$ of a rectangle. The area of rectangle is 15 in.2. What is the area of the square?
 a. 10 in.2 b. 22 in.2 c. 25 in.2 d. 15 in.2

#### Solution:

The area of the square = Fraction of the rectangle occupied by the square × Area of the rectangle

= 23 × 15

= (2 × 5)
[Dividing numerator and denominator by their GCF.]

= 10 in.2
[Simplify.]

10.
Simplify the expression. ($\frac{2}{3}$ - $\frac{1}{2}$) × ($\frac{2}{3}$ - $\frac{1}{2}$)
 a. $\frac{-1}{6}$ b. 1 c. $\frac{-7}{18}$ d. $\frac{1}{36}$

#### Solution:

(23 - 12) x (23 - 12)
[Original expression.]

(46 - 36) x (46 - 36)
[Write equivalent fractions with the same denominator inside each grouping symbols.]

= (4-3)6 x (4-3)6
[Write the differences over a common denominators.]

= 16 x 16
[Simplify inside the grouping symbols.]

= 1(6)(6)
[a / b x c / d= ac / bd.]

= 136
[Simplify.]

The simplified expression of (2 / 3 - 1 / 2) x (2 / 3 - 1 / 2) is 1 / 36.