Finding a Fraction of a Fraction
Finding a fraction of a fraction in Grade 7 means multiplying two fractions together, because the word 'of' signals multiplication in math. In Saxon Math, Course 2, students learn that one fourth of one half = (1/4) × (1/2) = 1/8. Simply multiply numerators together and denominators together. This skill is used constantly when working with parts of parts — like finding half of your quarter share of a pizza — and forms the foundation for fraction multiplication in all subsequent math courses.
Key Concepts
Property To find a part of a fraction, like “one fourth of one half,” you multiply the fractions together. The word “of” is your secret code for multiplication in fraction problems, so this means $\frac{1}{4} \times \frac{1}{2}$.
Examples What fraction is half of $\frac{1}{3}$? This means you calculate $\frac{1}{2} \times \frac{1}{3} = \frac{1}{6}$. If you ate $\frac{1}{2}$ of your $\frac{1}{4}$ share of a pizza, you ate $\frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$ of the whole pizza. A quart is $\frac{1}{4}$ gallon. Half a quart is $\frac{1}{2}$ of $\frac{1}{4}$ gallon, which is $\frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$ of a gallon.
Explanation Imagine you have a manipulative piece for one half. Finding a fourth of it means you need an even smaller piece! You are taking a part of an existing part, which is why the final fraction is smaller than what you started with. It’s a piece of a piece!
Common Questions
How do you find a fraction of a fraction?
Multiply the two fractions by multiplying numerators together and denominators together. For example, 1/4 of 1/2 = (1×1)/(4×2) = 1/8.
Why does 'of' mean multiply in fraction problems?
In mathematics, 'of' is a signal word for multiplication. 'One fourth OF one half' means you are taking a portion of a portion, which is the operation of multiplication.
Can you show an example of finding a fraction of a fraction?
If you ate 1/2 of your 1/4 slice of pizza, you ate (1/2) × (1/4) = 1/8 of the whole pizza.
Do you always get a smaller fraction when you multiply two fractions?
When both fractions are less than 1, yes — the product is smaller than either factor. This makes intuitive sense: taking a part of a part always gives a smaller piece.
Where is finding a fraction of a fraction taught in Saxon Math Course 2?
This skill appears in Saxon Math, Course 2, as part of Grade 7 fraction multiplication content.
How is fraction of a fraction different from adding fractions?
Adding fractions combines equal-sized pieces and requires a common denominator. Multiplying fractions (fraction of a fraction) takes a portion of a portion and does not require a common denominator.
What mistakes do students make when finding a fraction of a fraction?
Common errors include adding the fractions instead of multiplying, or forgetting to simplify (reduce) the result to lowest terms.