# Using appropriate properties find:

(i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6

(ii) 2/5 × (-3/7) -1/6 × 3/2 + 1/14 × 2/5

**Solution:**

Rational numbers numbers are in the form of p/q, where p and q can be any integer and q ≠ 0.

By using commutative property of multiplication and addition we proceed with the questions.

(i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6

= 3/5 × (-2/3) + 5/2 - 3/5 × 1/6 [By commutativity of multiplication]

= 3/5 × (-2/3) - 3/5 × 1/6 + 5/2 [By commutativity of addition]

Rearranging to take 3/5 common

= 3/5 × (-2/3 - 1/6) + 5/2

= 3/5 × (-5/6) + 5/2

= -1/2 + 5/2

= 2

(ii) 2/5 × (-3/7) - 1/6 × 3/2 + 1/14 × 2/5

Taking 2/5 as common

= 2/5 × [(-3/7) + 1/14] - 1/6 × 3/2 [By distributive property of multiplication]

= 2/5 × (-3 × 2 + 1)/14 - 1/6 × 3/2

= 2/5 × (-5/14) - 1/6 × 3/2

= -1/7 - 1/4

= -(4 + 7)/28

= -11/28

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 1

**Video Solution:**

## Using appropriate properties find: (i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6 (ii) 2/5 × (-3/7) -1/6 × 3/2 + 1/14 × 2/5

NCERT Solutions Class 8 Maths Chapter 1 Exercise 1.1 Question 1

**Summary:**

Using appropriate properties, the resultant answer for the expressions are: (i) -2/3 × 3/5 + 5/2 - 3/5 × 1/6 and (ii) 2/5 × (-3/7) -1/6 × 3/2 + 1/14 × 2/5 are 2 and -11/28 respectively.

**☛ Related Questions:**

- Write the additive inverse of each of the following (i) 2/8 (ii) -5/9 (iii) -6/-5 (iv) 2/-9 (v) 19/-6.
- Verify that -(-x) = x for. (i) x = 11/15 (ii) x = -13/7
- Find the multiplicative inverse of the following (i) -13 (ii) -13/19 (iii) 1/5 (iv) -5/8 × -3/7 (v) -1 × -2/5 (vi) -1.
- Name the property under multiplication used in each of the following: (i) -4/5 × 1 = 1 × -4/5 = -4/5 (ii) -13/17 × -2/7 = -2/7 × -13/17 (iii) -19/29 × 29/-19 = 1

visual curriculum