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Multiplying/Dividing Fractions To Multiply fractions: 1. Change a mixed number or whole number so that it is a ratio of two integers (i.e. an improper fraction). Put whole number over 1. Change mixed number to an improper fraction by multiplying the whole number times the denominator, then add the numerator of the fraction part to the product, and put the sum over the denominator. 2. Simplify a numerator and a denominator if 5 3 12 ? 6 23 5 1. For 3 : 3x6 18 5 23 , giving ; 6 6 12 For 12: the fraction is 1 Ex1. 2. 23 x 12 6 1 Since 12 6 2 & 6 6 1 23 x 2 1 1 3. possible by dividing the numerator and denominator by the same number. 3. Multiply the numerator times the other numerator and multiply the denominator times the other denominator. 4. If the products result in an improper fraction, then change it to a mixed number (by dividing the numerator by the denominator); add the whole numbers sum to the fraction part. 5. Simplify the fraction if needed. To Divide fractions: 1. Change mixed number or whole number so that it is a ratio of two integers (i.e. an improper fraction). Put whole number over 1. Change mixed number to an improper fraction by multiplying the whole number times the denominator, then add the numerator of the fraction part to the product, and put the sum over the denominator. 2. Change the division sign to a multiplication sign and change the divisor (the 2nd term) to its reciprocal (i.e. “flip” the Ex2: 23 2 46 x 46 Answer: 46 1 1 1 8 3 x 9 14 1. Step 1 is not needed since it’s already in a ratio of two integers. 2. 8 x 3 9 14 Since 8/2=4 & 14/2=7 Since 3/3=1 & 9/3=3, then 4 x1 2 7 3. Ex3. 4 1 4 x 3 7 21 33 1 Answer: 4 21 5 6 1. 33 11 & 1x6 6,6 5 11 , then 1 6 2. 33 11 33 6 x 1 6 1 11 (Note - The reciprocal of 11 6 is ) 6 11 3. 33 x 6 1 11 Since 33 11 3 & 11 11 1 Then 3 x 6 1 1 Multiplying/Dividing Fractions numerator and the denominator). 3. Simplify a numerator and a denominator if possible by dividing the numerator and denominator by the same number. 4. Use the rule for multiplying fractions: multiply a numerator times a numerator and multiply a denominator times a denominator. 5. If it’s an improper fraction, then change to mixed number (i.e. divide the numerator by the denominator) and add the whole numbers to the sum. 4. Ex4: 3 6 18 x 18 Answer: 18 1 1 1 8 6 9 27 1. Step 1 is not needed since it’s already in a ratio of two integers. 2. 8 27 8 6 x = 9 6 9 27 3. 8 x 27 9 6 Since 8/2=4 & 6/2=3 Since 9/9=1 & 27/9=3, then 4 x 3 1 3 6. Simplify the fraction if needed. 4. 4 3 12 x 1 3 3 5. 12 4 3 Answer: 4