Question

Maltipicative propertys of rational numbers

Answer 1

Answer:

Commutative property of multiplication of rational numbers: Two rational numbers can be multiplied in any order. Associative property of multiplication of rational numbers: While multiplying three or more rational numbers, they can be grouped in any order

Answer 2

Answer:

For any rational number a/b, we have (a/b × 1) = (1 × a/b) = a/b

1 is called the multiplicative identity for rationals. 

For example:

(i) Consider the rational number 3/4. Then, we have 

(3/4 × 1) = (3/4 × 1/1) = (3 × 1)/(4 × 1) = 3/4 and ( 1 × 3/4 )

= (1/1 × 3/4 ) = (1 × 3)/(1 × 4) = 3/4 

Therefore, (3/4 × 1) = (1 × 3/4) = 3/4. 

(ii) Consider the rational -9/13. Then, we have

(-9/13 × 1) = (-9/13 × 1/1) = {(-9) × 1}/(13 × 1) = -9/13 

and (1 × (-9)/13) = (1/1 × (-9)/13) = {1 × (-9)}/(1 × 13) = -9/13

Therefore, {(-9)/13 × 1} = {1 ×(-9)/13} = (-9)/13

Existence of multiplicative inverse property:

Every nonzero rational number a/b has its multiplicative inverse b/a. 

Thus, (a/b × b/a) = (b/a × a/b) = 1

b/a is called the reciprocal of a/b. 

Clearly, zero has no reciprocal. 

Reciprocal of 1 is 1 and the reciprocal of (-1) is (-1) 

For example: 

(i) Reciprocal of 5/7 is 7/5, since (5/7 × 7/5) = (7/5 × 5/7) = 1 

(ii) Reciprocal of -8/9 is -9/8, since (-8/9 × -9/8) = (-9/8 × -8/9 ) =1

(iii) Reciprocal of -3 is -1/3, since

(-3 × (-1)/3) = (-3/1 × (-1)/3) = {(-3) × (-1)}/(1 × 3) = 3/3 = 1 

and (-1/3 × (-3)) = (-1/3 × (-3)/1) = {(-1) × (-3)}/(3 × 1) = 1 

Note: 

Denote the reciprocal of a/b by (a/b)-1

Clearly (a/b)-1 = b/a 

Step-by-step explanation:

Hope it helps you