Question

The product of additive inverse and multiplicative inverse of -1/4 is​

Answer 1

Answer:

Step-by-step explanation:

Additive inverse : 1/4

Multiplication inverse: -4

Product= (1/4) * (-4) = -1

Answer 2

The product of additive inverse and multiplicative inverse of -1/4 is​ -1.

Concept used:

Additive inverse:

• Additive inverse is also called the opposite of the integer.
• For e.g : (+7) + (-7) = 0 and (-16) + (+ 16) = 0
• We observe that for integer (+7), there is an integer (-7) which when added to (+7) gives us the sum as zero (identity).
• For an integer (-16), there is an integer (+16) such that their sum is Zero.
• (-7) is called the additive inverse of (+7) and (+16) is the additive inverse of -16.
• From the above, we observe that for every integer there exists its additive inverse or opposite such that their sum is Zero (identity).
• Hence, if a is any integer, then a + (- a) = (- a) + a = 0 and - a is called the additive inverse of a and vice versa.

Multiplicative Inverse:

The product of an integer and its multiplicative inverse is 1. That is if a is a non-zero integer then $\frac{1}{a}$ is called the multiplicative inverse of a.

For example, the multiplicative inverse of 12 is $\frac{1}{12}$ and 12 × $\frac{1}{12}$ = 1

Similarly, $(-8) \times \frac{1}{-8} = 1$

Given:  -1/4

To find: The product of additive inverse and multiplicative inverse of -1/4

Solution:

Step 1: Write the additive inverse and multiplicative inverse of -1/4 :

Additive inverse of $\frac{-1}{4} = \frac{1}{4}$

The multiplicative inverse of $\frac{-1}{4} = \frac{-4}{1} = - 4$

Step 2: Find the product of additive inverse and multiplicative inverse of -1/4 :

Product of additive inverse and multiplicative inverse of -1/4 :

Additive inverse of $\frac{-1}{4}$ × multiplicative inverse of $\frac{-1}{4}$ = $\frac{1}{4} \times -4 = - 1$

Hence, the product of additive inverse and multiplicative inverse of -1/4 is - 1.

Learn more on Brainly:

Multiply 6/13 by the reciprocal of -7/16.

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Name the property under multiplication used in each of the following:

(i) -4/5 x 1 = 1 x (-4/5) = -4/5

(ii) -13/17 x -2/7 = -2/7 x -13/17

(iii) -19/29 x 29/-19 = 1

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