Solving Fraction of a Remainder Problems
Fraction of a remainder problems require finding a fraction of what remains after an initial portion has been taken, by multiplying the second fraction by the remaining portion of the whole. Using a tape diagram helps visualize the two-step process. This Grade 5 math skill from Eureka Math Chapter 23 covers multiplication of a fraction by a fraction.
Key Concepts
To find a fraction of a remainder, you multiply the second fraction by the part that remains from the whole. If an initial fraction $\frac{a}{b}$ is taken from a whole, the remainder is $(1 \frac{a}{b})$ of the whole. The final part, which is a fraction $\frac{c}{d}$ of the remainder, is calculated as: $$ \text{Part} = \frac{c}{d} \times \left(1 \frac{a}{b}\right) \times \text{Whole} $$.
Common Questions
What is a fraction of a remainder problem?
A fraction of a remainder problem involves two steps: first finding what remains after taking a fraction of the whole, then taking a different fraction of that remaining amount.
How do you solve a fraction of a remainder problem?
Subtract the first fraction from 1 whole to find the remaining fraction, then multiply the second fraction by that remainder and by the whole amount to find the final answer.
What is an example of a fraction of a remainder problem?
A baker makes 40 muffins, sells 2/5 in the morning, then sells 1/3 of the remaining muffins. The remainder is 3/5 of 40 equals 24 muffins. Selling 1/3 of 24 equals 8 muffins sold in the afternoon.
How does a tape diagram help with fraction of a remainder problems?
A tape diagram visually partitions the whole into the first fraction and the remainder, then re-partitions just the remainder according to the second fraction, preventing the common error of taking the second fraction from the original total.