How to find the reciprocal of a fraction

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ACT Math › How to find the reciprocal of a fraction

Questions 1 - 6
1

Find the negative reciprocal of the following:

Explanation

The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number). The negative reciprocal takes the negative of that number.

Reciprocal

Negative Reciprocal

2

What is the reciprocal of ?

This fraction doesn't have a reciprocal.

Explanation

The reciprocal of a fraction is simply exchanging the denominator and numerator of a fraction.

You can double check that it works by making sure the product of a fraction and its reciprocal is 1.

3

What is the reciprocal of the fraction 3/727?

727/3

–3/727

–727/3

3/727

242

Explanation

The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number). The negative reciprocal takes the negative of that number.

3/727

Reciprocal 727/3

4

What is the opposite reciprocal of 25/127?

–127/25

–25/127

127/25

25/127

–5

Explanation

The reciprocal of a fraction is just switching the numerator (top number) and the denominator (bottom number). The opposite reciprocal takes the negative of that number.

5

What is the slope of any line perpendicular to 4_y_ = 2_x_ + 7 ?

Explanation

First, we must solve the equation for y to determine the slope: y = (2/4)x + 7/4

By looking at the coefficient in front of x, we know that the slope of this line has a value of 1/2. To find the slope of any line perpendicular to this one, we take the negative reciprocal of it:

slope = m , perpendicular slope = –1/m

slope = 1/2 , perpendicular slope = –2

6

Find the reciprocal of the following fraction

Explanation

The reciprocal is defined such that a faction times its recprocal is 1. For you this just means turn the fraction upside down, ie the numerator is the denominator and vice versa.

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