Multiply a fraction by a whole number

Key Rules:

• 1. To multiply a fraction by a whole number, multiply only the numerator: 3 x 25 = 65, which is 1 15.

Remember:

• •Multiply tops together and bottoms together; to divide, flip the second fraction and multiply.

Don’t Forget...

• •Finding a common denominator before multiplying two fractions. A common denominator belongs to adding and subtracting; multiplication works directly on the tops and bottoms, so 12 x 13 means half of a third, which is 16.
• •Flipping the wrong fraction when dividing, or flipping both. Only the fraction you are dividing by becomes its reciprocal: 34 divided by 25 becomes 34 x 52, and flipping 34 as well changes the answer.
• •Multiplying the whole-number parts and the fraction parts of mixed numbers separately. 2 12 x 1 14 is not 2 x 1 plus 12 x 14, because the whole and fraction parts must also multiply across each other; converting to improper fractions handles every part correctly.

Worked Example:

Work out 2 12 divided by 1 14.

Convert both mixed numbers to improper fractions: 2 12 = 52 and 1 14 = 54.

Dividing by 54 is the same as multiplying by its reciprocal, 45, so the calculation becomes 52 x 45.

Multiply the numerators and the denominators: 5 x 42 x 5 = 2010.

Simplify: 2010 = 2.

Answer: 2

Why It Works:

Multiplying the denominators counts how many equal pieces the whole splits into when you take a fraction of a fraction, and multiplying the numerators counts how many of those pieces you take. Dividing by a fraction asks how many times it fits into the total, and multiplying by the reciprocal gives exactly that, because a fraction times its own reciprocal makes 1.

Another Example:

Write 3a/4 divided by 2/b as a single fraction.

The reciprocal of 2/b is b/2, so the division becomes 3a/4 x b/2.

Multiply the numerators and the denominators: 3a x b4 x 2 = 3ab/8.

Answer: 3ab/8