Algorithm for Multiplying Unit Fractions
The algorithm for multiplying unit fractions states that you multiply the numerators together and the denominators together. Since unit fractions have 1 as the numerator, 1/3 x 1/4 = (1x1)/(3x4) = 1/12. The product of two unit fractions is always another unit fraction with a denominator equal to the product of the two original denominators. This 6th grade skill from enVision Mathematics Grade 6 builds the conceptual foundation for all fraction multiplication and helps students understand why multiplying fractions produces a smaller result.
Key Concepts
Property To multiply two unit fractions, multiply their denominators. The numerator of the product is always 1.
Examples $\frac{1}{2} \times \frac{1}{3} = \frac{1}{2 \times 3} = \frac{1}{6}$ $\frac{1}{4} \times \frac{1}{5} = \frac{1}{4 \times 5} = \frac{1}{20}$.
Explanation A unit fraction is a fraction with a numerator of 1. When you multiply two unit fractions, you are finding a part of a part. The product is found by multiplying the numerators (which is always $1 \times 1 = 1$) and multiplying the denominators. This is a special case of the general rule for multiplying any two fractions.
Common Questions
What is the algorithm for multiplying unit fractions?
Multiply the numerators and multiply the denominators. For unit fractions: 1/3 x 1/4 = (1x1)/(3x4) = 1/12.
What is a unit fraction?
A unit fraction has 1 as its numerator and a positive whole number as its denominator. Examples: 1/2, 1/3, 1/7. They represent one equal part of a whole divided into that many parts.
Why is the product of two unit fractions always smaller than either factor?
Multiplying by a fraction less than 1 reduces the quantity. Taking 1/3 of 1/4 means taking one-third of something already smaller than 1, so the result (1/12) is smaller than both.
What grade covers multiplying unit fractions?
The algorithm for multiplying unit fractions is introduced in 6th grade enVision Mathematics Grade 6, building toward multiplying general fractions and mixed numbers.
How does multiplying unit fractions extend to all fraction multiplication?
The same algorithm applies: multiply numerators and multiply denominators. 2/3 x 3/4 = (2x3)/(3x4) = 6/12 = 1/2. Unit fractions are the simplest case of this universal rule.
What is a real-world example of multiplying unit fractions?
If a recipe uses 1/3 of a cup and you want to make 1/4 of the recipe, you need 1/3 x 1/4 = 1/12 of a cup.