Multiplying Using Unit Fractions
Multiplying using unit fractions is a Grade 5 math skill in enVision Mathematics, Chapter 8: Apply Understanding of Multiplication to Multiply Fractions. Students decompose a fraction a/b and multiply by the unit fraction 1/b first, then scale by a: (a/b) x n = a x ((1/b) x n). This approach connects the meaning of numerators and denominators to the multiplication process.
Key Concepts
Property To multiply a fraction by a whole number, you can decompose the fraction and multiply by the unit fraction first. $$\frac{a}{b} \times n = a \times \left(\frac{1}{b} \times n\right)$$.
Examples $\frac{3}{4} \times 8 = 3 \times \left(\frac{1}{4} \times 8\right) = 3 \times 2 = 6$ $\frac{2}{5} \times 15 = 2 \times \left(\frac{1}{5} \times 15\right) = 2 \times 3 = 6$ $\frac{5}{6} \times 12 = 5 \times \left(\frac{1}{6} \times 12\right) = 5 \times 2 = 10$.
Explanation This method breaks down the multiplication into two simpler steps. First, find the unit fraction part of the whole number, which is like dividing the whole number by the denominator. Then, multiply that result by the numerator. This strategy is very useful because it often allows you to work with smaller, more manageable numbers.
Common Questions
How do you multiply a fraction by a whole number using unit fractions?
Decompose the fraction into its unit fraction and numerator: (a/b) x n = a x (1/b x n). First multiply the unit fraction 1/b by n, then multiply that result by a.
What is (3/4) x 8 using unit fractions?
(1/4) x 8 = 2, then 3 x 2 = 6. So (3/4) x 8 = 6.
What is a unit fraction?
A unit fraction has a numerator of 1, like 1/2, 1/3, or 1/5. Any fraction a/b can be seen as a copies of the unit fraction 1/b.
Where is multiplying with unit fractions taught in enVision Grade 5?
Chapter 8: Apply Understanding of Multiplication to Multiply Fractions in enVision Mathematics, Grade 5.
Why is it useful to think of fractions as multiples of unit fractions?
It deepens understanding of what numerators and denominators mean, and provides a flexible strategy for fraction multiplication and reasoning about fraction size.