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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.
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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: | |
