| Chapter 3 Fractions, Part 1 3-4 Converting Between Improper Fractions and Mixed Numbers 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 Use these interactive examples and exercises to strengthen your understanding and build your skills: | | 3-4.1 Converting Improper Fractions to Mixed Numbers Arithmetic opereations 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. These 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.
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Figure 3-6. Steps for converting an improper fraction to a proper mixed number.
| Example Convert 4/3 to a proper mixed number. | Problem | | 4/3 = ? | Divide the denominator into the numerator. | 4/3 = 1 R 1 | | Assemble the mixed number | 4/3 = 11/3 | | | Solution | | 4/3 = 11/3 | Example Convert 27/9 to a proper mixed number. | Problem | | 27/9 = ? | Divide the denominator into the numerator. | 27/9 = 3 R 0 | | Assemble the mixed number | 27/9 = 3 | | | Solution | | 27/9 = 3 | 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: 12/8 = 1 1/2
Examples and Exercises Use these interactive examples and exercises to strengthen your understanding and build your skills: | | 3-4.2 Converting Mixed Numbers to Improper 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. | | Example Convert the mixed number 3 1/2 to an improper fraction | Problem | | 3 1/2 = ? | Multiply the whole number times the denominator of the fraction. | 3 x 2 = 6 | | Add the numerator of the fraction to the result | 6 + 1 = 7 | | Assign the result to the numeratorof the imporper fraction and use the original denominator. | 7/2 | | | Solution | | 3 1/2 = 7/2 | Note: Any whole number can be converted to an improper fraction by setting it over 1. Example: 8 = 8/1 Examples and Exercises Use these interactive examples and exercises to strengthen your understanding and build your skills: | |
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