Multiply Unit and Non-Unit Fractions
Multiply Unit and Non-Unit Fractions is a Grade 5 math skill from Illustrative Mathematics Chapter 3 (Multiplying and Dividing Fractions) that teaches students to multiply any two fractions using the rule (1/b) × (c/d) = c/(bd). Students multiply numerators together and denominators together. This bridges the gap between multiplying two unit fractions and multiplying two general fractions.
Key Concepts
Property To multiply a unit fraction by a non unit fraction, multiply the numerators together and the denominators together. For fractions $\frac{1}{b}$ and $\frac{c}{d}$: $$\frac{1}{b} \times \frac{c}{d} = \frac{1 \times c}{b \times d} = \frac{c}{bd}$$.
Examples $\frac{1}{3} \times \frac{2}{5} = \frac{1 \times 2}{3 \times 5} = \frac{2}{15}$ $\frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}$.
Explanation This skill extends the area model to multiply a unit fraction by a non unit fraction. For example, to find $\frac{1}{3}$ of $\frac{2}{5}$, you first model $\frac{2}{5}$ and then take $\frac{1}{3}$ of that shaded area. The resulting product is found by multiplying the numerators to find the number of shaded parts and multiplying the denominators to find the total number of parts in the whole. This bridges the gap between multiplying two unit fractions and multiplying two non unit fractions.
Common Questions
How do you multiply a unit fraction by a non-unit fraction?
Multiply the numerators together and multiply the denominators together. For (1/b) × (c/d): the product is (1 × c)/(b × d) = c/(bd). For example, (1/3) × (2/5) = (1 × 2)/(3 × 5) = 2/15.
What is the general rule for multiplying any two fractions?
Multiply numerators: a × c. Multiply denominators: b × d. The product is (a × c)/(b × d). For example, (3/4) × (1/2) = (3 × 1)/(4 × 2) = 3/8.
What chapter covers multiplying unit and non-unit fractions in Illustrative Mathematics Grade 5?
Multiplying unit and non-unit fractions is covered in Chapter 3 of Illustrative Mathematics Grade 5, titled Multiplying and Dividing Fractions.
How does an area model show multiplication of a unit fraction by a non-unit fraction?
Shade the non-unit fraction (like 2/5) in a rectangle to show the first fraction. Then take the unit fraction (like 1/3) of that shaded region. The overlap represents the product. The total pieces visible in the whole rectangle give the denominator.
What is the difference between a unit fraction and a non-unit fraction?
A unit fraction has a numerator of 1 (like 1/2, 1/3). A non-unit fraction has a numerator other than 1 (like 2/5, 3/4). Both follow the same multiplication rule: multiply numerators and multiply denominators.