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Operations on Fractions Objectives: …to add, subtract, multiply, and divide fractions. Assessment Anchor: 7.A.3.2 – Compute accurately with and without use of a calculator NOTES To add or subtract fractions: 1. You MUST have a COMMON DENOMINATOR!!!! a. If denominator is already the same, continue to step 2. b. If denominator is different: 1. Find a common denominator (LCM). 2. Write equivalent fractions using your common denominator. 2. Add or subtract the numerators. a. If you are able to subtract, continue to step 3. b. If you cannot subtract, you must BORROW! 1. Take one away from the whole number. 2. Add the numerator and denominator together to get a NEW numerator. 3. The denominator remains the same. 3. Add or subtract the whole numbers. 4. The denominator remains the same. ***Special Situation: If the fraction part of a mixed number is improper, you must change that improper fraction to a mixed number and add the original whole number to it. The most important words above are: COMMON DENOMINATOR Operations on Fractions EXAMPLES 1) 3 1 2 +1 5 3 ……original problem with unlike denominators 3 5 6 +1 15 15 ……equivalent fractions with like denominators 4 2) 3) 11 15 ……sum of original numbers 3 11 3 –1 12 4 …… original problem with unlike denominators 3 11 9 –1 12 12 …… equivalent fractions with like denominators 2 2 1 = 2 12 6 ……difference of original numbers (simplified) 93 + 35 4 6 4) 55 – 31 9 6 “Getting the LCD (least common denominator is great…but any common denominator will do just fine!” Operations on Fractions MORE EXAMPLES (with borrowing) 5) 7 3 3 –1 8 4 ……original problem with unlike denominators 7 3 6 –1 8 8 ……equivalent fractions with like denominators 6 11 6 –1 8 8 ……borrowing procedure 5 6) 5 8 ……difference of original numbers 5 1 1 –4 10 4 ……original problem with unlike denominators 5 2 5 –4 20 20 ……equivalent fractions with like denominators 4 22 5 –4 20 20 ……borrowing procedure 17 20 7) …… difference of original numbers 13 2 – 4 1 7 2 8) 9 5 12 – 17 9 Operations on Fractions Vocabulary alert!! RECIPROCAL – a number that can be multiplied by another number to make 1 MORE NOTES To multiply or divide fractions: 1. Rewrite any whole numbers OR mixed numbers as improper fractions. 2. IF multiplication, continue to step 3…IF division make the following changes first: a. Keep the first fraction the same. b. Change the division symbol to a multiplication symbol. c. Write the reciprocal of the second fraction. 3. Multiply the numerators. 4. Multiply the denominators. 5. Simplify final answer if possible ***Special Situation: When you have a multiplication symbol between two fractions, you are allowed to REDUCE or CANCEL common factors before multiplying the numerators and denominators. EXAMPLES 9) 6 7 × 41 6 7 × ……original problem 5 126 35 21 5 = ……change to improper fraction 18 5 or 3 3 5 ……multiply numerators and denominators ***SHOW CANCELLING OPTION!!! Operations on Fractions 10) 51 × 11 ……original problem 26 5 ……change to improper fraction 5 4 × 130 20 5 4 13 2 = or 6 1 2 ……multiply numerators and denominators ***SHOW CANCELLING OPTION!!! 11) 11 ÷ 12 ……original problem (DIVISION!) 4 3 ÷ 11 9 ……change to improper fraction 4 3 × 9 11 ……multiply by the reciprocal!!! 3 36 33 9 12 11 = or 1 1 11 ……multiply numerators and denominators ***SHOW CANCELLING OPTION!!! 12) 62 ÷4 ……original problem (DIVISION!) 20 3 ÷ 4 1 ……change to improper fraction 20 3 × 1 4 ……multiply by the reciprocal!!! 3 20 12 = 5 3 or 1 2 3 ……multiply numerators and denominators ***SHOW CANCELLING OPTION!!! Operations on Fractions 13) 41 × 31 14) 71 × 31 15) 81 ÷ 62 16) 1 11 ÷ 16 4 3 3 3 2 13 7