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3-6 Dividing Fractions and Mixed Numbers Note When dividing fractions, inverting the divisor (the fraction that follows the division sign) changes the operation to multiplication. Example: 2/3 � 3/4 = 2/3 x 4/3 | 3-6.1 Dividing Proper Fractions Procedure To divide proper fractions: - Invert the divisor (the fraction that follows the division sign) and change the operation to multiplication.
- Multiply the numerators and denominators.
- Reduce or simplfy the result as necessary.
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| | Example 3/4 � 1/2 = ? | Problem | | 3/4 � 1/2 = ? | - Invert the divisor and change the operation to multiplication..
| 3/4 � 1/2 = 3/4 x 2/1 | | - Multiply the numerators and denominators.
| 3/4 x 2/1 = 6/4 | | - Reduce or simplfy the result as necessary.
| 6/4 = 11/2 | | | Solution | | 3/4 � 1/2 = 11/2 | Example 1/6 � 2/3 = ? | Problem | | 1/6 � 2/3 = ? | - Invert the divisor and change the operation to multiplication..
| 1/6 � 2/3 = 1/6 x 3/2 | | - Multiply the numerators and denominators.
| 1/6 x 3/2 = 3/12 | | -
| 3/12 = 1/4 | | | Solution | | 1/6 � 2/3 = 1/4 | Examples and Exercises Use these interactive examples and exercises to strengthen your understanding and build your skills: Complete the division operation. Convert to a mixed number or reduce as necessary. | | 3-6.2 Dividing Mixed Fractions Procedure To divide mixed fractions: - Convert the mixed fractions to improper fractions.
- Complete the division
- Change division to multiplication
- Invert the divisor
- Multiply the numerators and denominators
- Reduce or simplfy the result as necessary
- Reduce if necessary
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| | Note A whole-number value can be converted to an improper fraction by setting it over 1. Examples: 5 = 5/1, 8 = 8/1, 10 = 10/1 | Example 3/16 � 2 = ? | Problem | | 3/16 � 2 = ? | - Convert the mixed fractions to improper fractions.
| 3/16 � 2 = 3/16 � 2/1 | | - Invert the divisor and change the operation to multiplication..
| 3/16 � 2/1 = 3/16 x 1/2 | | - Multiply the numerators and denominators.
| 3/16 x 1/2 = 3/32 | | | Solution | | 3/16 � 2 = 3/32 | Example 122/3 � 31/2 = ? | Problem | | 122/3 � 31/2 = ? | - Convert the mixed fractions to improper fractions.
| 122/3 � 31/2 = 38/3 � 7/2 | | - Invert the divisor and change the operation to multiplication..
| 38/3 � 7/2 = 38/3 x 2/7 | | - Multiply the numerators and denominators.
| 38/3 x 2/7 = 76/21 | | - Reduce or simplfy the result as necessary.
| 76/21= 3 13/21 | | | Solution | | 122/3 � 31/2 = 313/21 | Examples and Exercises Use these interactive examples and exercises to strengthen your understanding and build your skills: Complete the division operation. Convert to a mixed number or reduce as necessary. | |
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