AI Tutor
Imagine baking a huge party recipe that calls for 1121\frac{1}{2} batches of brownies, where each batch needs 2142\frac{1}{4} cups of cocoa.
To find the total cocoa needed, we must multiply these two mixed numbers together: 112×2141\frac{1}{2} \times 2\frac{1}{4}.
Can we just multiply the whole numbers and then multiply the fractions? Let's check why that shortcut breaks down.

The 3-Step Strategy

A mixed number combines a whole number and a fraction, like 1121\frac{1}{2}. An improper fraction writes that exact same value as a single fraction where the top number is bigger than or equal to the bottom, like 32\frac{3}{2}.
In Standard Algorithm Step 1, convert each mixed number to an improper fraction using the relationship abc=(a×c)+bca\frac{b}{c} = \frac{(a \times c) + b}{c}. For 1121\frac{1}{2}, this gives (1×2)+12=32\frac{(1 \times 2) + 1}{2} = \frac{3}{2}.
For 2142\frac{1}{4}, multiply (2×4)+1=9(2 \times 4) + 1 = 9, which gives 94\frac{9}{4}.
Now that both are standard fractions, what happens when we multiply them straight across?

Multiplying Across

In Standard Algorithm Step 2, multiply the improper fractions by multiplying numerators together and denominators together: pq×rs=p×rq×s\frac{p}{q} \times \frac{r}{s} = \frac{p \times r}{q \times s}.
We get 3×92×4=278\frac{3 \times 9}{2 \times 4} = \frac{27}{8}.