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Chapter 1: Q11. (page 15)

Identify the additive inverse and multiplicative inverse for each number

11. 13

Short Answer

Expert verified

Additive inverse of 13 is -13 and multiplicative inverse of 13 is 3

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 13

Substitute 13for a

a=13

Multiply both sides by -1

鈭�1脳a=鈭�1脳13鈭�a=鈭�13

Thus additive inverse of 13is -13

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 13

Substitute 13for a

a=13

Reciprocal on both sides

1a=1131a=3

Thus multiplicative inverse of 13is 3

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