Students looking for different properties of Multiplication of Rational Numbers can get all of them in one place. Utilize the Worksheet on Properties of Multiplication of Rational Numbers and kick start your preparation. Assess your strengths and weaknesses by solving the Rational Numbers Multiplication Properties Worksheet. Make use of the Rational Numbers Worksheets and understand different concepts underlying.

The Questions covered in the Worksheet for Properties of Multiplication of Rational Numbers include closure property, commutative property, associative property, the existence of multiplicative identity property, the existence of the multiplicative inverse property, distributive property of multiplication over addition, and multiplicative property of 0.

1. Multiply the following Rationals

(i) -5/13 by 21/(-30)

(ii) -3/10 by -15/32

(iii) -4/25 by -4/12

**Solution:**

(i) -5/13 by 21/(-30)

= (-5/13)/(21/-30)

= (-5/13)*(-30/21)

= (-5*-30)/13*21

= 150/273

= 50/91

(ii) -3/10 by -15/32

= (-3/10)/(-15/32)

= -3/10*32/-15

= -3*32/10*-15

= -96/-150

= 16/25

(iii) -4/25 by -4/12

= (-4/25)/(-4/12)

= -4/25*12/-4

= (-4*12)/(25*-4)

= -48/-100

= 48/100

= 12/25

2. Verify each of the following:

(i) 4/11 × (-7)/3 = (-7)/3× 4/11

(ii) (-6)/10 × 1/4 = 1/4 × (-6)/10

**Solution:**

(i) 4/11 × (-7)/3 = (-7)/3× 4/11

4/11 × (-7)/3 = 4*(-7)/11*3 = -28/33

(-7)/3× 4/11 = -7*4/3*11 = -28/33

Therefore, 4/11 × (-7)/3 = (-7)/3× 4/11

(ii) (-6)/10 × 1/4 = 1/4 × (-6)/10

(-6)/10 × 1/4 = -6*1/10*4 = -6/40

1/4 × (-6)/10 = 1*-6/4*10 = -6/40

(-6)/10 × 1/4 = 1/4 × (-6)/10

3. Fill in the Blanks

(i) (-13)/10 × 18/30 = 18/30 × (_____)

(ii) -32 × (-7)/11 = (-7)/11 × (_____)

(iii) {15/3 × -20/18} × (-3)/6 = (_____) × {(-20)/18 × (-3/6)}

**Solution:**

(i) (-13)/10

We know multiplication obeys the Commutative Property i.e. a*b = b*a

(ii) -32

We know multiplication obeys the Commutative Property i.e. a*b = b*a

(iii) 15/3

We know Multiplication of Rational Numbers is Associative i.e. a/b x (c/d x e/f) = (a/b x c/d) x e/f.

4. Find the Multiplicative Inverse of the following

(i) -4/5

(ii) -6/7

(iii) 11/-12

(iv) 15/8

**Solution:**

Multiplicative Inverse of a Rational Number is nothing but the Reciprocal of the Rational Number. Product of a Rational Number and its Multiplicative Inverse results in 1.

(i) 5/-4

(ii) 7/-6

(iii) -12/11

(iv) 8/15

5. Name the Property of Multiplication illustrated by the following statements

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

(ii) -8/13 × -12/5 = -12/5 × -8/13

(iii) (-15)/7 × 1 = 1 × (-15)/ 7= (-15)/7

(iv) (-1)/12 × 12/-1 = 12/-1 × (-1)/12 = 1

(v) 4/5*0 = 0

(vi) (-5)/2 × {(-3)/4 + 7/5} = {(-5)/2 × (-3)/4} + {(-5)/2 × 7/5}

**Solution:**

(i) Associative Property

(ii) Commutative Property

(iii) Multiplicative Identity Property

(iv) Multiplicative Inverse Property

(v) Multiplicative Property of 0

(vi) Distributive Property

6. Verify the following

(3/4 × 11/5) × 7/12 = 3/4 ×(11/5 × 7/12)

**Solution:**

(3/4 × 11/5) × 7/12 = (3*11/4*5) × 7/12

= 33/20*7/12

= 33*7/20*12

= 241/240

3/4 ×(11/5 × 7/12) = 3/4 ×(11*7/5*12)

= 3/4 *(77/60)

= 3*77/4*60

= 241/240