Subscribe to our ▶️ YouTube channel 🔴 for the latest videos, updates, and tips.

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