Multiplying whole numbers and fractions
Multiplying whole numbers and fractions in Grade 6 Saxon Math Course 1 requires writing the whole number as a fraction over 1 before multiplying. For 4 × 3/5, rewrite as (4/1) × (3/5), then multiply numerators: 4 × 3 = 12, and denominators: 1 × 5 = 5, giving 12/5 = 2⅖. This uniform procedure works for any product of a whole number and a fraction. Unlike addition, no common denominator is needed — simply multiply numerators together and denominators together.
Key Concepts
Property A whole number can be written as a fraction by writing the whole number as the numerator of the fraction and 1 as the denominator of the fraction. Thus, the whole number 2 can be written as the fraction $\frac{2}{1}$.
Examples $5 \times \frac{3}{4} = \frac{5}{1} \times \frac{3}{4} = \frac{15}{4} = 3\frac{3}{4}$ $7 \times \frac{2}{5} = \frac{7}{1} \times \frac{2}{5} = \frac{14}{5} = 2\frac{4}{5}$ $\frac{1}{8} \times 6 = \frac{1}{8} \times \frac{6}{1} = \frac{6}{8} = \frac{3}{4}$.
Explanation How do you multiply a whole number by a fraction? Give the whole number a secret identity! By putting it over a 1, you turn it into a fraction without changing its value. Now it can hang out with the other fractions, and you can multiply straight across like you normally would. Sneaky and effective!
Common Questions
How do you multiply a whole number by a fraction?
Write the whole number over 1, then multiply numerators together and denominators together. Example: 3 × 2/7 = (3/1) × (2/7) = 6/7.
What is 5 × 3/4?
5/1 × 3/4 = 15/4 = 3¾.
Why is a common denominator not needed for multiplying fractions?
Common denominators are needed only for adding and subtracting fractions. Multiplication uses its own rule: top × top over bottom × bottom.
Do you ever cancel before multiplying?
Yes. If a numerator and any denominator share a common factor, you can cancel (simplify) before multiplying to keep numbers small.
How do you simplify 12/5 after multiplying?
12/5 is an improper fraction. Divide 12 ÷ 5 = 2 remainder 2, giving the mixed number 2⅖.