Multiply a Fraction by a Whole Number: Multiply then Divide
Multiply a Fraction by a Whole Number: Multiply then Divide is a Grade 5 math skill from Eureka Math that presents an alternative procedure for multiplying fractions by whole numbers. Students first multiply the whole number by the numerator, then divide by the denominator, rather than converting to a fraction first. This method often simplifies calculation by allowing early cancellation.
Key Concepts
To multiply a fraction by a whole number, multiply the numerator by the whole number and place the product over the original denominator. $$\frac{a}{b} \times c = \frac{a \times c}{b}$$.
Common Questions
How do you multiply a fraction by a whole number using the multiply-then-divide method?
Multiply the whole number by the numerator first, then divide by the denominator. For example, 3/4 x 20: multiply 20 x 3 = 60, then divide by 4 = 15.
Why is multiplying then dividing sometimes easier than converting to a fraction first?
If the whole number is divisible by the denominator, you can simplify early. For example, 2/5 x 15: divide 15 by 5 first to get 3, then multiply by 2 = 6, which avoids large intermediate numbers.
Is multiply-then-divide the same as the standard fraction multiplication algorithm?
Yes, it produces the same result. (a/b) x c = (a x c) / b = ac/b. The order of multiplication and division can be rearranged by the commutative and associative properties.
What Eureka Math Grade 5 chapter covers this fraction multiplication method?
Eureka Math Grade 5 covers the multiply-then-divide method in its fraction multiplication chapters as an alternative strategy alongside the standard algorithm.
When should students use the multiply-then-divide method?
Use this method when the whole number and the denominator share a common factor, allowing simplification before multiplying, which keeps numbers smaller and reduces errors.