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Multiplying Fractions
including Mixed Fractions with Mixed Numbers

The product of multiplying fractions always results with proportion that increases if the factors are greater than 1 and no factors are equal to zero:

1. 1 (one) multiplied by any non-zero fraction equals the non-zero fraction:
    1/5 × 1 = 1/5
2. 1 (one) multiplied by all non-zero fractions equals the product of all non-zero fractions not equal to 1:
    2/3 × 1 × 1/2 = 2/6 = 1/3
3. Fraction multiplication by zero equals zero: 2/3 × 5/8 × 0 = 0

The denominator of a fraction can never equal zero. A zero denominator is undefined math.

Dividing and multiplying fractions are each opposite math operations of the other.

How to Multiply Fractions

There are 3 steps for fraction multiplication:

1.  Multiply all numerators.
2.  Multiply all denominators.
3.  Simplify fractions answers by reducing fractions to make them  proper fractions.

1/5 × 2/3 = 2/15

Numerator multiplication: 1 × 2 = 2

Denominator multiplication: 5 × 3 = 15

1

5

×

2

3

=

 2

15

Multiplying Mixed Fractions

One and one half apples is

1 1/2 as a mixed fraction.

Solving mixed fraction math problems:

2 4/6 × 1 3/4 =

1. Convert mixed numbers to improper fractions:
   2 4/6 × 1 3/4 = 16/6 × 7/4 =
2. Reduce fractions if possible, keeping them improper fractions:
   8/3 × 7/4 =
3. Multiply numerators by numerators and denominators by denominators:
   56/12 =
4. Simplify fractions answer:
   56/12 = 28/6 = 14/3 = 4 2/3

Multiplying multiple fractions:

3 1/2 × 1 3/5 × 2/3 = 7/2 × 8/5 × 2/3 =
 112/30 = 56/15 = 3 11/15

8 quarters of orange is 2 whole oranges.

Multiplying Fractions and Mixed Numbers

3 × 1 3/5 × 2/3 = 3/1 × 8/5 × 2/3 =
 48/15 = 16/5 = 3 1/5

The process is the same as multiplying mixed fractions. The integer 3 is written as an improper fraction by dividing 3 by 1.

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