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 teaches an efficient order for calculating a fraction times a whole number: multiply first, then divide by the denominator. For example, 2/3 x 12 = (2 x 12) / 3 = 24/3 = 8. Students can also reverse the order when early division simplifies the calculation.
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 compute 3/4 of 20 by multiplying then dividing?
Multiply the whole number by the numerator first: 20 x 3 = 60. Then divide by the denominator: 60 / 4 = 15. So 3/4 x 20 = 15.
Can you divide first then multiply when computing a fraction of a whole number?
Yes, if the whole number is divisible by the denominator. For 2/5 x 15, divide first: 15 / 5 = 3, then multiply: 3 x 2 = 6. This keeps numbers smaller.
Why learn both orders of multiply-then-divide and divide-then-multiply?
Choosing the order where division eliminates a common factor first keeps numbers small and reduces errors. Flexibility with both orders builds strategic mathematical thinking.
What Eureka Math Grade 5 chapter covers this fraction multiplication method?
Eureka Math Grade 5 covers the multiply-then-divide and divide-then-multiply strategies in its fraction multiplication chapters as efficient computational methods.
How is this related to the standard fraction multiplication algorithm?
Both methods compute the same result. The standard algorithm multiplies numerators and denominators; the multiply-then-divide approach computes (a x b)/c, which is equivalent.