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.


Answers:


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

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Rational Numbers

Introduction of 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

Rational Numbers in Descending Order

Representation of Rational Numbers on the Number Line

Rational Numbers on the Number Line

Addition of Rational Number with Same Denominator

Addition of Rational Number with Different Denominator

Addition of Rational Numbers

Properties of Addition of Rational Numbers

Subtraction of Rational Number with Same Denominator

Subtraction of Rational Number with Different Denominator

Subtraction of Rational Numbers

Properties of Subtraction of Rational Numbers

Rational Expressions Involving Addition and Subtraction

Simplify Rational Expressions Involving the Sum or Difference

Multiplication of Rational Numbers

Product of Rational Numbers

Properties of Multiplication of Rational Numbers

Rational Expressions Involving Addition, Subtraction and Multiplication

Reciprocal of a Rational  Number

Division of Rational Numbers

Rational Expressions Involving Division

Properties of Division of Rational Numbers

Rational Numbers between Two Rational Numbers

To Find Rational Numbers