# Worksheet on Properties of Multiplication of Rational Numbers

Practice the questions given in the worksheet on properties of multiplication of rational numbers. The questions are based on different properties of multiplication of rational numbers i.e. closure property, associative property, commutative property, existence of multiplicative inverse property, existence of multiplicative identity property, distributive property of multiplication over addition and multiplicative property of 0.

1. Multiply the rationals:

(i) -5/17 by 51/(-60)

(ii) -6/11 by -55/36

(iii) -8/25 by -5/16

(iv) 6/7 by -49/36

2. Verify each of the following:

(i) 4/17 × (-7)/9 = (-7)/9 × 4/17

(ii) (-8)/11 × 1/5 = 1/5 × (-8)/11

(iii) (-12)/5 × 7/(-36) = 7/-36 × (-12)/5

(iv) -8 × (-13)/12 = (-13)/12 × (-8)

3. Verify each of the following:

(i) (3/5 × 12/13) × 7/18 = 3/5 ×(12/13 × 7/8)

(ii) (-13)/24 × {(-12)/5 × 35/36} = {(-13)/24 × (-12)/5} × 35/36

(iii) {(-9)/5 × (-10)/3} × 21/-4 = (-9)/5 × {(-10)/3 × 21/-4}

4. Fill in the blanks:

(i) (-23)/17 × 18/35 = 18/35 × (_____)

(ii) -38 × (-7)/19 = (-7)/19 × (_____)

(iii) {15/7 × -21/10} × (-5)/6 = (_____) × {(-21)/10 × (-5)/6}

(iv) (-12)/5 × {4/15 × 25/-16} = {(-12)/5 × (4/15) × (_____)

5. Find the multiplicative inverse of:

(i) -11/-15

(ii) -5

(iii) 0/7

(iv) 2/-5

(v) (-1)/8

6. Verify the following rational numbers using the multiplication properties:

(i) 3/7 × {5/6 + 12/13} = (3/7 × 5/6) + (3/7 × 12/13)

(ii) -15/4 × (3/7 + (-12)/5) = (-15/4 × 3/7) + (-15/4 × (-12)/5)

(iii) (-8/3 + -13/12) × 5/6 = (-8/3 × 5/6) + (-13/12 × 5/6)

(iv) -16/7 × {-8/9 + (-7)/6} = (-16/7 × (-8)/9) + ((-16)/7 × -7/6)

7. Name the property of multiplication illustrated by the following statements:

(i) -11/13 × -17/5 = -17/5 × -11/13

(ii) {(-2)/3 × 7/9} × (-9)/5 = (-2)/3 × {7/9 × (-9)/5}

(iii) (-3)/4 × {(-5)/6 + 7/8 = {(-3)/4 × (-5)/6} + {(-3)/4 × 7/8}

(iv) (-16)/9 × 1 = 1 × (-16)/9 = (-16)/9

(v) (-11)/15 × 15/-11 = 15/-11 × (-11)/15 = 1

(vi) -7/5 × 0 = 0

Answers for the worksheet on properties of multiplication of rational numbers are given below to check the exact answers of the above questions.

1. (i) 1/4

(ii) 5/6

(iii) 1/10

(iv) -7/6

4. (i) -23/17

(ii) -38

(iii) 15/7

(iv) 25/-16

5. (i) -15/-11

(ii) 1/-5

(iii) Does not exist

(iv) -5/2

(v) 8/-1

7. (i) Commutative property

(ii) Associative property

(iii) Distributive property

(iv) Property of multiplicative identity

(v) Property of multiplicative inverse

(vi) Multiplicative property of 0

Rational Numbers - Worksheets

Worksheet on Rational Numbers

Worksheet on Lowest form of a Rational Number

Worksheet on Standard form of a Rational Number

Worksheet on Equality of Rational Numbers

Worksheet on Comparison of Rational Numbers

Worksheet on Representation of Rational Number on a Number Line

Worksheet on Properties of Addition of Rational Numbers

Worksheet on Rational Expressions Involving Sum and Difference

Worksheet on Multiplication of Rational Number

Worksheet on Division of Rational Numbers

Worksheet on Finding Rational Numbers between Two Rational Numbers

Worksheet on Word Problems on Rational Numbers

Objective Questions on Rational Numbers

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Relation between Diameter Radius and Circumference |Problems |Examples

Apr 22, 24 05:19 PM

Relation between diameter radius and circumference are discussed here. Relation between Diameter and Radius: What is the relation between diameter and radius? Solution: Diameter of a circle is twice

2. ### Circle Math | Terms Related to the Circle | Symbol of Circle O | Math

Apr 22, 24 01:35 PM

In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We…

3. ### Preschool Math Activities | Colorful Preschool Worksheets | Lesson

Apr 21, 24 10:57 AM

Preschool math activities are designed to help the preschoolers to recognize the numbers and the beginning of counting. We believe that young children learn through play and from engaging

4. ### Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

Apr 20, 24 05:39 PM

There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

5. ### What are Parallel Lines in Geometry? | Two Parallel Lines | Examples

Apr 20, 24 05:29 PM

In parallel lines when two lines do not intersect each other at any point even if they are extended to infinity. What are parallel lines in geometry? Two lines which do not intersect each other

Rational Numbers

What is Rational Numbers?

Is Every Rational Number a Natural Number?

Is Zero a Rational Number?

Is Every Rational Number an Integer?

Is Every Rational Number a Fraction?

Positive Rational Number

Negative Rational Number

Equivalent Rational Numbers

Equivalent form of Rational Numbers

Rational Number in Different Forms

Properties of Rational Numbers

Lowest form of a Rational Number

Standard form of a Rational Number

Equality of Rational Numbers using Standard Form

Equality of Rational Numbers with Common Denominator

Equality of Rational Numbers using Cross Multiplication

Comparison of Rational Numbers

Rational Numbers in Ascending Order

Representation of Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

To Find Rational Numbers