AI Tutor
Imagine you have 12\frac{1}{2} of a chocolate bar, and you decide to give 34\frac{3}{4} of your piece to a friend. How much of the whole chocolate bar does your friend get?
In math, the word of usually means multiplication. Finding 34\frac{3}{4} of 12\frac{1}{2} means we are calculating 34×12\frac{3}{4} \times \frac{1}{2}.
Why draw a grid every time when there is a simple calculation pattern? Let's look at the rule that powers this model.

The Multiplication Rule

To multiply fractions, multiply the numerators (top numbers) together, and multiply the denominators (bottom numbers) together.
ab×cd=a×cb×d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
For example, to solve 25×37\frac{2}{5} \times \frac{3}{7}, multiply tops: 2×3=62 \times 3 = 6. Multiply bottoms: 5×7=355 \times 7 = 35. The product is 635\frac{6}{35}.
Unlike fraction addition, you do not need a common denominator to multiply. But what happens when the numbers get huge?

Simplify Before You Multiply

Consider 512×815\frac{5}{12} \times \frac{8}{15}. If you multiply straight across, you get 40180\frac{40}{180}, which takes work to reduce.
Instead, we can use cross-simplifying — dividing any top number and any bottom number by their greatest common factor before multiplying.