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## Fraction Operations

### Mathematics, Grade 7

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#### Study Guide Fraction Operations Mathematics, Grade 7

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FRACTION OPERATIONS Fraction operations are the processes of adding, subtracting, multiplying and dividing fractions and mixed numbers. A mixed number is a fraction with a whole number. Adding fractions is common in many everyday events, such as making a recipe and measuring wood. In order to add and subtract fractions, the fractions must have the same denominator. If the fractions do not have the same denominator, a common denominator must be found before the fractions can be added or subtracted. Once the fractions have the same denominator the fractions are added, by adding the numerators only and leaving the denominators the same. Multiplying fractions is the operation of multiplying two or more fractions together to find a product. Multiplying fractions is used when finding the area of various shapes. Dividing fractions is the operation of dividing two fractions or mixed numbers to find a quotient. Mixed numbers can be used in all operations, but a mixed number must be changed into an improper fraction first before performing the operation. All fractions should be in simplified form. Equations may contain fractions and must be solved using inverse operations. How to use fraction operations When adding or subtracting fractions, the denominators must be the same. If the fractions have the same denominator, they can be added or subtracted. If the fractions do not have the same denominator, one must be found before the fractions can be added or subtracted. Ex. Add 4/18 + 3/9 4/18 + 6/18 = 10/18 = 5/9 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
When multiplying fractions, simply multiply the numerators first to find the resulting numerator and then the denominators to find the resulting denominator. When multiplying fractions, the resulting fraction should always be reduced to lowest terms if possible. When dividing fractions, the first fraction stays the same, the sign changes to multiplication and the second fraction is changed to its reciprocal. A reciprocal is the fraction flipped so when the two fractions are multiplied together, the result is 1. Ex. Multiply: 5/6 · 4/5 = 20/30 =2/3 Divide: 1/3 ÷ 4/7 = 1/3 · 7/4 = 7/12 When evaluating mixed fractions, the mixed fraction must be changed into an improper fraction before evaluating. The same rules apply to mixed fractions. When operating with mixed fractions, the result may be an improper fraction, which would then have to be changed back into a mixed number for the final answer. Ex. Add: 1 2/3 + 3 7/8 = 5/3 + 31/8 = 40/24 + 93/24 = 133/24 = 5 13/24 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
Try This! 1. Add the fractions: 3/5 + 7/15 = ? 8/14 + 3/28 = ? 2 2/3 + 6 1/5 = ? 4 7/8 + 1 3/4 = ? 2. Subtract the fractions: 8/9 - 2/3 = ? 15/16 - 4/8 = ? 5 9/10 - 3 2/5 = ? 4 4/8 - 1 1/4 = ? 3. Multiply the fractions: 6/10 · 2 /3 = ? 7/9 · 4/5 = ? 2 6/9 · 3 1/4 = ? 1 1/2 · 2 2/3 = ? 4. Divide the fractions: 6/7 ÷ 2/3 = ? 8/12 ÷ 3/4 = ? 5 1/2 ÷ 1 1/2 = ? 6 2/3 · 4 1/4 = ? 5. Solve the equations for x: x + 3/4 = 11/12 x - 2 3/20 = 2 4/5 1 7/9 · x = 4/18 2 5/6 ÷ x = 1 5/12 © Copyright NewPath Learning. All Rights Reserved. Permission is granted for the purchaser to print copies for non-commercial educational purposes only. Visit us at www.NewPathLearning.com.
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