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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