   top

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 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 Example

 Problem Convert the mixed number 3 1/2 to an improper fraction Procedure 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/? 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:

[../../../../free-ed/blurb_footer.asp]