### All ACT Math Resources

## Example Questions

### Example Question #491 : Arithmetic

What is the reciprocal of the fraction 3/727?

**Possible Answers:**

3/727

727/3

–3/727

242

–727/3

**Correct answer:**

727/3

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

### Example Question #1 : Reciprocals

What is the opposite reciprocal of 25/127?

**Possible Answers:**

–5

–127/25

25/127

–25/127

127/25

**Correct answer:**

–127/25

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.

### Example Question #1 : How To Find The Reciprocal Of A Fraction

Find the negative reciprocal of the following:

**Possible Answers:**

**Correct answer:**

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

### Example Question #1 : Reciprocals

What is the slope of any line perpendicular to 4*y* = 2*x* + 7 ?

**Possible Answers:**

**Correct answer:**

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

### Example Question #5 : Reciprocals

Find the reciprocal of the following fraction

**Possible Answers:**

**Correct answer:**

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.

### Example Question #6 : Reciprocals

What is the reciprocal of ?

**Possible Answers:**

This fraction doesn't have a reciprocal.

**Correct answer:**

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.