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Chapter 1: Q47. (page 16)

Identify the additive inverse and multiplicative inverse for each number

47. 43

Short Answer

Expert verified

Additive inverse of 43 is -43 and multiplicative inverse of 43 is 34

Step by step solution

01

- Define additive inverse

Let 鈥榓鈥� be a real number such that

a+-a=0=-a+a

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

02

- Additive inverse of 43

Substitute 43 for a

a=43

Multiply both sides by -1

鈭�1脳a=鈭�1脳43鈭�a=鈭�43

Thus additive inverse of 43is -43

03

- Define multiplicative inverse

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

a路1a=1=1a路a

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

04

- Multiplicative inverse of 43

Substitute 43 for a

a=43

Take reciprocal on both sides

1a=1431a=34

Thus multiplicative inverse of 43is 34

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