Multiply Fractions and Mixed Numbers

Multiplying fractions is faster than adding them — there is no need to find a common denominator. Multiply across: tops together for the new numerator, bottoms together for the new denominator. The same rule covers fraction times fraction, fraction times whole number, and mixed-number multiplication once you switch the mixed numbers to improper fractions first.

Multiplying a Fraction by a Fraction

• Multiply the numerators together to get the new numerator.
• Multiply the denominators together to get the new denominator.
• Example: 1/2 times 1/3 = (1 x 1) / (2 x 3) = 1/6.
• Simplify the answer to lowest terms when possible.

The Area Model — Why It Works

• Draw a rectangle and split it into rows and columns by the two denominators.
• 1/2 x 1/3 means split one whole into 2 columns and 3 rows — that makes 6 small parts.
• Shade 1 of the 2 columns one way, and 1 of the 3 rows another way.
• The overlap (where both shadings meet) shows the product: 1 of the 6 small parts, or 1/6.

Multiplying a Fraction by a Whole Number

• Write the whole number over 1 to make it a fraction: 6 = 6/1.
• Multiply across: 2/3 x 6 = 2/3 x 6/1 = (2 x 6) / (3 x 1) = 12/3.
• Simplify: 12/3 = 4.
• Shortcut: just multiply the numerator by the whole number, keep the denominator, then simplify.

Multiplying Mixed Numbers

• First, change each mixed number into an improper fraction.
• 1 1/2 becomes 3/2 (because 2 x 1 + 1 = 3 over 2).
• 2 1/3 becomes 7/3 (because 3 x 2 + 1 = 7 over 3).
• Then multiply across as usual: 3/2 x 7/3 = 21/6 = 3 1/2 after simplifying.