# 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

**Solution:**

(i) -4/5 × 1 = 1 × -4/5 = -4/5

∴ 1 is the multiplicative identity in the above expression.

Thus, the property of Multiplicative Identity is used here.

(ii) -13/17 × -2/7 = -2/7 × -13/17

In general, a × b = b × a for any two rational numbers.

Thus, the property of Commutativity of Multiplication is used here.

(iii) -19/29 × 29/-19 = 1

For a rational number a/b, the multiplicative inverse is the reciprocal of that number which is b/a.

Thus, the property of Multiplicative Inverse is used here.

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

**Video Solution:**

## 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

NCERT Solutions Class 8 Maths Chapter 1 Exercise 1.1 Question 5

**Summary:**

The properties used in each of the following: (i) -4/5 × 1 = 1 × -4/5 = -4/5 (ii) -13/17 × -2/7 = -2/7 × -13/17 and (iii) -19/29 × 29/-19 = 1 are Multiplicative Identity, Commutativity of Multiplication, and the Multiplication Inverse respectively.

**☛ Related Questions:**

- Multiply 6/13 by the reciprocal of -7/16. The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product an identity
- Tell what property allows you to compute 1/3 × (6 × 4/5) as (1/3 × 6) × 4/3? The Associative property tells us that we can add/multiply the numbers in an equation irrespective of the grouping of those numbers.
- Is 8/9 the multiplicative inverse of -1 (1/8)? Why or why not?
- Is 0.3 the multiplicative inverse of 3 (1/3)? Why or why not?

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