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Chapter 1: Q12. (page 15)

Identify the additive inverse and multiplicative inverse for each number

1.5

Short Answer

Expert verified

Additive inverse of 1.5is -1.5 and multiplicative inverse of 1.5 is 23

Step by step solution

01

- Define additive inverse

Let 鈥榓鈥� be a real number such that

a+-a=0=-a+a

Then 鈥�-a鈥� is the additive inverse of 鈥榓鈥�

02

- Additive inverse of 1.5

Substitute 1.5for a

a=1.5

Multiply both sides by -1

鈭�1脳a=鈭�1脳1.5鈭�a=鈭�1.5

Thus additive inverse of 1.5 is -1.5

03

- Define multiplicative inverse

Let 鈥榓鈥� be a real number with a=0 such that

a路1a=1=1a路a

Then 鈥�1a鈥� is the multiplicative inverse of 鈥榓鈥�

04

- Multiplicative inverse of 1.5

Substitute 1.5for a

Convert it from decimal form to fraction

a=1.5=1510=32

Reciprocal on both sides

1a=1321a=23

Thus multiplicative inverse of 32is 23

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