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MULTIPLYING FRACTIONS AND MIXED NUMBERS To multiply fractions: EXAMPLE ONE: 1. Multiply numerators. 2. Multiply denominators. 3. Reduce if possible OR 1. Reduce first by cross cancelling- divide numbers on the diagonals by common factors. 2. Multiply numerators. 2 3 3 8 x 6 24 = EXAMPLE TWO: 1 4 = x 7 9 = 35 54 ______________________________________________ EXAPMPLE ONE: 2 3 X 3 8 1 (cross cancel) 2 3 = 1 X 1 EXAMPLE TWO: 3. Multiply denominators. 4 7 To multiply mixed numbers: EXAMPLE ONE: 1. Change to improper fractions. 3 2. Cross cancel (reduce first). EXAMPLE TWO: 3. Multiply numerators. 2 X 3 10 3 8 = 4 1 4 2 (cross cancel) 4 7 = X 3 10 = 6 35 5 1 4 5 X 1 2 3 = 19 5 5 3 = 19 3 17 6 = 51 3 =6 8 8 X = 6 1 3 1 3 4. Multiply denominators. 5. Change back to a mixed number. 5 6 1 4 X 2 5 6 = 9 4 X 2 EXAMPLE THREE: 2 4 3 5 X 10 11 = 23 5 1 X 10 11 = 46 11 = 4 2 11 DIVIDING FRACTIONS AND MIXED NUMBERS To divide fractions, multiply by the reciprocal. Reciprocal of 2 3 is 3 2 Reciprocal of 5 is Reciprocal of 1 8 is 8 1 Reciprocal of 1. Keep the first fraction the same. 2. Change the division sign to multiplication. 3. Take the reciprocal (flip) of the second fraction. EXAMPLE ONE: 2 3 ÷ 3 4 4 5 X 4 3 = 2 9 2 15 ÷ 2 2 3 is EXAMPLE TWO: 4. Cross cancel if possible. 5. Multiply (follow multiplication rules). 9 2 1 5 8 9 4 5 3 X 1 15 2 1 = 6 =6 1 To divide mixed numbers: 1. Change the mixed number to improper fractions. EXAMPLE ONE: 3 2. Follow steps above. 1 3 ÷ = 2 5 7 3 ÷ = 2 5 5 7 X = 3 2 35 5 =5 6 6 EXAMPLE TWO: 2 3 1 ÷1 = 8 3 19 4 19 57 25 3 ÷ = X = =1 8 8 32 32 3 4 EXAMPLE THREE: 7 5 1 ÷3= 4 21 3 ÷ = 4 1 21 1 X = 3 4 1 7 3 =1 4 4