Multiplying fractions
Multiplying fractions means multiplying the numerators together to get the new numerator and multiplying the denominators together to get the new denominator. The word 'of' in math indicates multiplication: one half of one half = (1/2) x (1/2) = 1/4. To multiply (1/2) x (3/4) x (1/5) = 3/40. This Grade 7 math skill from Saxon Math, Course 2 does not require finding a common denominator (unlike addition), making it one of the simpler fraction operations — and it directly enables compound probability, scaling, and ratio problem-solving.
Key Concepts
Property To multiply fractions, multiply the numerators to find the product's numerator, and multiply the denominators to find the product's denominator. The word "of" often means to multiply: $\frac{1}{2} \text{ of } \frac{1}{2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$.
Examples What is $\frac{1}{2}$ of $\frac{1}{3}$? We multiply straight across: $\frac{1 \times 1}{2 \times 3} = \frac{1}{6}$. To find $\frac{1}{2} \cdot \frac{3}{4} \cdot \frac{1}{5}$, multiply all numerators and all denominators: $\frac{1 \cdot 3 \cdot 1}{2 \cdot 4 \cdot 5} = \frac{3}{40}$. If you shade $\frac{1}{2}$ of a rectangle, then shade $\frac{1}{4}$ of that shaded part, you just found $\frac{1}{2} \times \frac{1}{4} = \frac{1}{8}$.
Explanation Multiplying fractions is like finding a piece of a piece. If you take half of a cookie, and then take half of that piece, you end up with a quarter of the original cookie. You're making the piece smaller! Just multiply the tops together and the bottoms together. Top times top, bottom times bottom!
Common Questions
How do I multiply fractions?
Multiply the numerators together and the denominators together. For (2/3) times (3/5): numerators 2 times 3 = 6, denominators 3 times 5 = 15, so the answer is 6/15 = 2/5.
Do I need a common denominator to multiply fractions?
No. Unlike addition and subtraction, fraction multiplication does not require a common denominator. Simply multiply numerators together and denominators together.
What does 'of' mean in math?
In math, the word 'of' means multiply. So 'one half of one third' means (1/2) times (1/3) = 1/6.
How do I multiply a fraction by a whole number?
Write the whole number as a fraction over 1, then multiply. For 3 times (2/5): (3/1) times (2/5) = 6/5 = 1 and 1/5.
When do students learn to multiply fractions?
Fraction multiplication is introduced in Grade 5 and reinforced in Grade 7. Saxon Math, Course 2 covers it in Chapter 6 with both numeric and word problem contexts.
How do I simplify before multiplying fractions?
Cross-cancel: if any numerator and any denominator share a common factor, divide both by that factor before multiplying. This reduces the work and gives a simpler result.
How does multiplying fractions connect to probability?
Compound probability multiplies the probability of each independent event. P(A and B) = P(A) times P(B), where each probability is a fraction. Fraction multiplication is the core operation.