Lesson 4: Solve word problems using fraction and decimal multiplication.

Property

To multiply a decimal by a fraction, you can convert the decimal to its equivalent fraction and then multiply the two fractions. For a decimal $0.a$, the equivalent fraction is $\frac{a}{10}$. For a decimal $0.ab$, the equivalent fraction is $\frac{ab}{100}$.

Examples

• To calculate $0.5 \times \frac{3}{4}$, convert $0.5$ to $\frac{1}{2}$:

• To find the value of $0.25$ of $\frac{4}{5}$, convert $0.25$ to $\frac{1}{4}$:

• A recipe calls for $\frac{2}{3}$ cup of sugar. If you only make $0.75$ of the recipe, how much sugar do you need?

Explanation

This skill provides an alternative strategy for multiplying decimals and fractions. Converting a decimal to a fraction can sometimes make the calculation easier, especially if the decimal has a simple fractional equivalent like $0.5 = \frac{1}{2}$ or $0.25 = \frac{1}{4}$. Once both numbers are in fraction form, you can multiply the numerators and the denominators as usual. This method avoids decimal multiplication and allows for potential simplification before or after multiplying.

Property

To multiply a number by a fraction, you can first convert the fraction into its decimal equivalent by dividing the numerator by the denominator. Then, perform the multiplication with the resulting decimal. For a fraction $\frac{a}{b}$, the decimal equivalent is $a \div b$.

Examples

• To calculate $\frac{2}{5}$ of $15.5$, first convert the fraction to a decimal: $\frac{2}{5} = 2 \div 5 = 0.4$. Then multiply: $0.4 \times 15.5 = 6.2$.
• A baker has a $12.5$ liter container of milk. She uses $\frac{3}{4}$ of the milk for a batch of muffins. To find out how much milk she used, convert $\frac{3}{4}$ to $0.75$ and multiply: $0.75 \times 12.5 = 9.375$ liters.

Explanation

This skill focuses on a strategy for multiplying fractions and decimals. When a problem requires you to find a fractional part of a decimal quantity, it can be easier to convert the fraction into a decimal first. This allows you to perform a standard decimal multiplication, which can be simpler than working with both number types. This method is especially useful when the fraction converts to a terminating decimal, like $\frac{1}{2}=0.5$ or $\frac{4}{5}=0.8$.

Property

When quantities are in a ratio $a:b$, the whole can be represented as $a+b$ equal units. The fractions representing each part of the whole are $\frac{a}{a+b}$ and $\frac{b}{a+b}$. To solve, find the value of one unit, then multiply to find the unknown quantity.

Examples