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Multiplying &
Dividing Mixed Numbers
To multiply or divide mixed numbers, first convert each
mixed number to an improper fraction.
Multiply
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First,
multiply the two numerators of the fractions.
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Then,
multiply the two denominators of the fractions.
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Then,
simplify the resulting fraction.
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Finally,
convert the improper fraction from the previous step to a mixed number.
Example:
4 3/5 X 2 7/8 = ?
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Convert
both mixed numbers to improper fractions:
4 3/5 = 23/5
2 7/8 = 23/8
23/5 X 23/8 = ?
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Multiply
the numerators ( 23 X 23 = 529)
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Next,
multiply the denominators( 5 X 8 = 40)
23/5 X 23/8 = 529/40
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Convert
to a mixed number
529/40 = 13 9/40
Divide
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First,
invert the divisor (the second fraction) – this means turn the fraction
upside down. 23/8 becomes 8/23.
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Then,
multiply the two fractions following the steps from above.
Example:
4 3/5 ÷ 2 7/8 = ?
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Convert
both mixed numbers to improper fractions:
4 3/5 = 23/5
2 7/8 = 23/8
23/5 ÷ 23/8 = ?
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Invert
the divisor ( 23/8 becomes 8/23)
Now multiply the two fractions:
23/5 X 8/23
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Multiply
the numerators ( 23 X 8 = 184)
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Next,
multiply the denominators( 5 X 23= 115)
23/5 X 8/23 = 184/115 (This fraction is already
simplified.)
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Convert
to a mixed number
184/115 = 1 69/115
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