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Chapter 1: Q10. (page 15)

Identify the additive inverse and multiplicative inverse for each number

10. -8

Short Answer

Expert verified

Additive inverse of -8 is 8 and multiplicative inverse of -8 is -18

Step by step solution

01

- Define additive inverse

Let 鈥�a鈥�be a real number such that

a+-a=0=-a+a

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

02

- Additive inverse of -8

Substitute -8for a

a=鈭�8

Multiply both sides by -1

鈭�1脳a=鈭�1脳鈭�8鈭�a=8

Thus additive inverse of -8is 8

03

- Define multiplicative inverse

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

a路1a=1=1a路a

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

04

- Multiplicative inverse of -8

Substitute -8for a

a=-8

Reciprocal on both sides

1a=1鈭�81a=鈭�18

Thus multiplicative inverse of -8 is -18 .

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