For more information, please see full course syllabus of Pre Algebra

Start learning today, and be successful in your academic & professional career. Start Today!

Loading video...

This is a quick preview of the lesson. For full access, please Log In or Sign up.

For more information, please see full course syllabus of Pre Algebra

For more information, please see full course syllabus of Pre Algebra

### Dividing Rational Numbers

- Two numbers are reciprocals if their product is 1. Examples are 2/3 and 3/2.
- In order to divide fractions, you must find the reciprocal of the second fraction and then multiply numerators and denominators.
- In order to divide decimals, the divisor cannot contain a decimal. To clear the divisor of the decimal, move the decimal to the right; move the decimal in the dividend the same number of places.

### Dividing Rational Numbers

Find the reciprocal of [4/7].

[7/4]

Find the reciprocal of 3.

- 3 = [3/1]

[1/3]

Find the reciprocal of −[8/9].

− [9/8]

[8/3] ÷[2/3] =

- [8/3] ×[3/2] =
- [24/6] =

4

−[5/2] ÷[15/10] =

- − [5/2] ×[10/15] =
- − [50/30] =

− [5/3]

− [9/4] ÷− 4 =

- − [9/4] ×− [1/4] =

[9/16]

3[3/8] ÷− 2.1 =

- 3[3/8] ÷− 2[1/10] =
- [27/8] ÷− [21/10] =
- [27/8] ×− [10/21] =
- [9/4] ×− [5/7] =
- − [45/28] =

− 1[17/28]

21.6 ÷2.7 =

- 2.7| ― 21.6 =
- 27| ― 216 =

8

You have a 15[2/3] pound bag of rice that you want to split evenly for the next 7 weeks. How many pounds of rice do you get each week?

- 15[2/3] ÷7 =
- [47/3] ×[1/7] =
- [47/21] =

2[5/21] pounds

A runner needs to run a total distance of 17[1/3] miles, and he wants to take 5 breaks on the way after running the same distance each time. How far does the runner have to run before he takes a break?

- If the runner takes 5 breaks, then the distance he needs to run is split into 6 equal parts.
- 17[1/3] ÷6 =
- [52/3] ×[1/6] =
- [26/3] ×[1/3] =
- [26/9] =

2[8/9] miles

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Dividing Rational Numbers

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- What You'll Learn and Why
- Vocabulary
- Finding the Reciprocal
- Dividing Rational Numbers
- Example 1: Dividing Rational Numbers
- Example 2: Dividing Rational Numbers
- Example 3: Dividing Rational Numbers
- Dividing Rational Numbers in Word Problems
- Extra Example 1: Dividing Decimals
- Extra Example 2: Dividing Fractions
- Extra Example 3: Search Committee
- Extra Example 4: Stake

- Intro 0:00
- What You'll Learn and Why 0:05
- Topics Overview
- Vocabulary 0:22
- Reciprocal
- Finding the Reciprocal 0:56
- Example: Reciprocal of 2/3
- Example: Reciprocal of 8
- Example: Reciprocal of -1/2
- Dividing Rational Numbers 1:28
- Example 1: Dividing Rational Numbers
- Example 2: Dividing Rational Numbers
- Example 3: Dividing Rational Numbers
- Dividing Rational Numbers in Word Problems 3:56
- Example: Chocolate Peanuts
- Extra Example 1: Dividing Decimals 5:17
- Extra Example 2: Dividing Fractions 7:09
- Extra Example 3: Search Committee 8:34
- Extra Example 4: Stake 10:18

0 answers

Post by Aaron Dhaemers on February 25, 2013

Department stores sometimes advertise a clearance sale: â€œTake Â½ of Â½â€â€¦ In practice, this means a 75% discount off the original price. But mathematically, half of half works out to 1. What's up with this?

1 answer

Last reply by: Professor Fung

Mon Sep 24, 2012 4:53 AM

Post by Michael Trow on September 22, 2012

75 / 2.25 is 33.3 recurring so it should be 34, right?

1 answer

Last reply by: mickaole walden

Sat Mar 9, 2013 12:18 PM

Post by Michael Trow on September 22, 2012

31 multiplied by 2.25 = 69.75 not 75 !

0 answers

Post by Samvel Karapetyan on May 20, 2012

31 stakes to build the fence!