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Chapter 3—Fractions

3-4 Converting Between Improper Fractions and Mixed Numbers

When you complete the work for this section, you should be able to:
  • Convert any improper fraction to a mixed number and reduce the fraction where necessary.
  • Convert any mixed number to an improper fraction.

You are getting ready to do some basic arithmetic operations--addition, subtraction, multiplication, and division--with fractions and mixed numbers. These operations often require you to convert between improper fractions and mixed numbers. To begin, here is a review of the basic definition.

Definitions

  • A proper fraction is one where the numerator is smaller than the denominator.

Examples: 1/2, 1/3, 2/3, -5/8

  • An improper fraction is one where the numerator is greater than, or equal to, the denominator.

Examples: 3/2, 8/3, -16/5, 7/7

  • A mixed fraction is one that includes an integer as well as a fractional part.

Examples: 11/2, 2 3/4, 6 5/8, -4 1/4

Examples and Exercises

Identifying Improper Fractions

Use these interactive examples and exercises to strengthen your understanding and build your skills:

Converting Improper Fractions to Mixed Numbers

Arithmetic operations with fractions often result in fractions in an improper form. You should finish the work be converting this answer to a proper proper fractions (and reducing if possible). Suppose an addition operation results in an improper fraction such as 11/3. Converting to a mixed number, the answer becomes 3 2/3. This section describes how to make this important kind of conversion.

Procedure

Converting improper fractions to mixed numbers

Step 1: Divide the denominator into the numerator.

Use ordinary whole-number division that produces a quotient and a remainder.

Step 2: Assemble the mixed number.

  • The whole-number part of the mixed number is the whole-number part of the quotient from Step 1.
  • The numerator of the fraction part of the mixed number is the remainder from the quotient in Step 1.
  • The denominator of the fraction part of the mixed number is the denominator of the original improper fraction.

Note: If there is no remainder in Step 1, then the mixed-number part is a whole number. There is no fraction part.

Example:

10/5 = 2

fig0304_01.jpg (41463 bytes)

Steps for converting an improper fraction to a proper mixed number.

 

Examples

Sometimes the fractional part of these conversions needs to be reduced.

Example: Convert 12/8 to a mixed number.

Doing the division: 12/8 = 1 R 4
Assembling the mixed number: 12/8 = 1 4/8
Reducing the fraction:  1 4/8 = 1 1/2

Examples and Exercises

Converting Improper Fractions to Mixed Numbers

Use these interactive examples and exercises to strengthen your understanding and build your skills:

Converting Mixed Numbers to Improper Fractions

Converting mixed numbers to improper fractions is often necessary for setting up arithmetic operations with fractions.

Procedure

Converting mixed numbers to improper fractions.

Step 1: Multiply the whole number by the denominator and add the numerator. This becomes the numerator of the improper fraction.
Step 2: Set the denominator of the improper fraction equal to the denominator of the fraction in the mixed number.

Note: A whole number can be expressed as an improper  fraction by putting that number over 1.

Example:

14  = 14/1

fig0304_02.jpg (50867 bytes)

Example

Problem

Convert the mixed number 3 1/2 to an improper fraction

Procedure
  1. Multiply the whole number times the denominator of the fraction, and assign the result to the numerator of the improper fraction and use the original denominator.

3 x 2 + 1 = 7

3 1/2 = 7/?

  1. Set the denominator of the improper fraction equal to the denominator of the fraction in the mixed number.

3 1/2 = 7/2

Solution

3 1/2 = 7/2

Examples and Exercises

Converting Mixed Numbers to Improper Fractions

Use these interactive examples and exercises to strengthen your understanding and build your skills:

David L. Heiserman, Editor

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All Rights Reserved

Revised: June 06, 2015