Lesson 3: Find the product of a whole number and a mixed number using the distributive property.

Property

To multiply a whole number ($a$) by a mixed number ($b\frac{c}{d}$), first represent the mixed number as the sum of its whole and fractional parts. Then, apply the distributive property to multiply the whole number by each part.

Examples

Property

To solve a word problem involving the multiplication of a whole number and a mixed number, identify the whole number and the mixed number from the context. Set up the multiplication expression and use the distributive property to find the product.
$c \times (a + \frac{b}{d}) = (c \times a) + (c \times \frac{b}{d})$

Examples

• A baker uses $2 \frac{1}{4}$ cups of flour for one cake. How much flour is needed for 3 cakes?

$3 \times 2 \frac{1}{4} = 3 \times (2 + \frac{1}{4}) = (3 \times 2) + (3 \times \frac{1}{4}) = 6 + \frac{3}{4} = 6 \frac{3}{4}$ cups.

• A runner jogs $4 \frac{1}{2}$ miles each day. How many miles does she jog in 5 days?

$5 \times 4 \frac{1}{2} = 5 \times (4 + \frac{1}{2}) = (5 \times 4) + (5 \times \frac{1}{2}) = 20 + \frac{5}{2} = 20 + 2 \frac{1}{2} = 22 \frac{1}{2}$ miles.

Explanation

This skill applies the multiplication of whole numbers and mixed numbers to real-world scenarios. First, read the problem carefully to identify the quantities you need to multiply. Then, use the distributive property to break the mixed number into its whole and fractional parts and multiply each by the whole number. Finally, add the partial products together to find the total and answer the question in the context of the problem.