Question

SOLVE THE FOLLOWING :-

1. What are the multiplicative and additive identities of rational numbers?

2. Write the additive inverse of 19/-6 and -⅔.

3. Write the multiplicative inverse of -13/19 and -7.

4. Mention any 4 rational numbers which are less than 5.

5. Find any five rational numbers between -3/5 and 1/3.

6. Use appropriate property and find

(-2/3 × 1/5) + ( 2/3 × 1/5 )

7. Which property you use to compute 1/4 × (3 × 4/7) as (1/4 × 3 ) × 4/7 ? Justify.

8. Represent -2/11, -5/11, and -9/11 on the number line.​

Answer 1

Explanation:

1. Additive identity of rational numbers = 0

Multiplicative identity of rational numbers = 1

2.Given number = 19/-6

=> -19/6

Additive inverse of -19/6 = 19/6

Given number = -2/3

Additive inverse = 2/3

3. Given number = -13/19

Multiplicative inverse = -19/13

Given number=-7

Multiplicative inverse = -1/7

4.Rational numbers less than 5 are 4,3,2,1

5.Given numbers are -3/5 .and 1/3

-3/5 =

(-3/5) × (3/3)

=(-3×3)/(5×3)

=-9/15

1/3=(1/3)×(5/5)

=(1×5)/(3×5)

=5/15

Required rational numbers -8/15 , -7/15 , -6/15 , -5/15 , -4/15,....1/15,2/15,3/15,4/15

6.(-2/3 × 1/5) + ( 2/3 × 1/5 )

=> (2/3)×(-1/5)+(2/3)×(1/5)

=> (2/3)[(-1/5)+(1/5)]

=> (2/3)[(-1+1)/5]

=> (2/3)(0/5)

=> (2/3)(0)

=> 0

Distributive Property under addition over Multiplication in rational numbers

7. 1/4×(3 ×4/7) and (1/4×3 )×4/7

=> (1/4)×(3×4/7)

=> (1/4)×(12/7)

=> 12/28

=> 3/7-----(1)

(1/4 × 3 ) × 4/7

=> (3/4)×(4/7)

=> 3/7 -------(2)

From (1)&(2)

1/4 × (3 ×4/7) = (1/4 × 3 ) × 4/7

This property is known as Associative Property in rational numbers

8.Given numbers are -2/11, -5/11, and -9/11

See the above attachment