Question

II. Name the property used in each of the following:

1. -7/11 x 3/5 = 3/5 x -7/11

2. -2/3 ( ¾ + -1/2) = -2/3 x ¾ + -2/3 x -1/2

3. 1/3+ (4/9 +-4/3) = (1/3+ 4/9) + -4/3

4. -2/7 +0=0+-2/7 = -2/7

5. 3/8 x 8/3=1 = 8/3 x 3/8



III .Simply each of the following by suitable properties

1. -4/5 x 3/7 x 15/16 x -14/9

2. [½ x ¼] + [½ x 6]

3. [1/5 x 2/15] - [2/5 x 1/5]



IV. Find three rational numbers between

1. -1 and -2 2. -3/2 and 5/3 3. 5/7 and 6/7

V. Solve the following equations.

1. x/3 + 5/2 = -3/2

2. 2y +9=4

3. 9x - 5 = 3 (x-1) +7​

Answer 1

Step-by-step explanation:

• Name the property used in each of the following:

1. By Commutativity of multiplication
2. By Distributivity
3. By Associativity of addition
4. By Closure property of zero
5. By multiplicative inverse

• Simply each of the following by suitable properties

1. -4/5 x 3/7 x 15/16 x (-14/9)

By suitable rearrangement

= (-4/5 × 15/6) × (-14/9 × 3/7)

= (-2 ) × (-2/3)

= 4/3

2. [½ x ¼] + [½ x 6]

By Distributivity

= 1/2(1/4 + 6)

= 1/2(1/4 + 24/4)

= 1/2(25/4)

= 25/8

3. [1/5 x 2/15] - [2/5 x 1/5]

By Distributivity

= 1/5(2/15 - 1/5)

= 1/5(2/15 - 3/15)

= 1/5(-1/15)

= -1/75

• Solve the following equations.

1. x/3 + 5/2 = -3/2

=> (x-15)/6 = -3/2

=> x-15 = -3/2 × 6

=> x-15 = -1/4

=> x = 1/4 + 15

=> x = 1/4 + 60/4

=> x = 61/4

2. 2y +9=4

=> 2y = 4-9

=> 2y = -5

=> y = -5/2

3. 9x - 5 = 3 (x-1) +7

=> 9x-5 = 3x - 3 + 7

=> 9x - 3x = -3 + 7 -5

=> 6x = -1

=> x = -1/6