Convert Fractions to Decimals to Multiply
Convert Fractions to Decimals to Multiply is a Grade 5 math skill from Eureka Math that teaches students to multiply by first converting fractions to their decimal equivalents. For example, 1/4 x 36 can be computed as 0.25 x 36 = 9. This strategy leverages decimal multiplication fluency and connects fraction and decimal representations of the same numbers.
Key Concepts
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 $\frac{4}{5}=0.8$.
Common Questions
How do you convert a fraction to a decimal before multiplying?
Divide the numerator by the denominator to get the decimal equivalent. For example, 3/4 = 0.75. Then multiply: 0.75 x 8 = 6.
What common fractions should Grade 5 students know as decimals?
Students should know 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/10 = 0.1, 1/100 = 0.01. These benchmarks allow quick conversion for multiplication.
Why convert fractions to decimals for multiplication?
Students who are more comfortable with decimal multiplication can use this as an alternative strategy. It also reinforces the equivalence of fractions and decimals.
What Eureka Math Grade 5 chapter covers converting fractions to decimals for multiplication?
Eureka Math Grade 5 covers the fraction-decimal connection for multiplication in its decimal and fraction chapters, building flexibility with multiple representations.
What is the decimal equivalent of 2/5?
2/5 = 0.4. Divide 2 by 5: 2.0 ÷ 5 = 0.4. Alternatively, 2/5 = 4/10 = 0.4.