Find a fraction of a quantity

Quantity Split

Build 60% of 60 marbles on the board, then work out 60% of 40 without it.

Per cent means "out of a hundred", so 60% is $\frac{60}{100}$. Both numbers divide by 20, which leaves $\frac{3}{5}$ - the same share, with far fewer groups to cut. The bottom number is how many equal groups the whole pile is cut into and the top number is how many of those groups you keep. $40÷5=8$, so one group holds 8 marbles, and 3 groups hold $3\times 8=24$. The groups add straight back up to 40 with nothing left over.

1. Step 1. Cut it up. Cut 60 marbles into 5 equal groups.
2. Step 2. Take your share. Now light up 3 of those 5 groups.
3. Step 3. A new pile. The board is covered. What is 60% of 40 marbles?

Open Quantity Split on its own page to share it

Area Grid

Slide the coral band to $\frac{2}{3}$ and the teal band to $\frac{3}{4}$. Where they cross is $\frac{2}{3}\times \frac{3}{4}$.

This engine’s own main skill is Multiplying Fractions. It practises find a fraction of a quantity alongside it.

Cutting the square into 3 rows and 4 columns makes $3\times 4=12$ equal cells, and the two bands cross over $2\times 3=6$ of them. That is the whole reason you multiply the tops and multiply the bottoms: the tops count the rows and columns the overlap covers, and the bottoms count the rows and columns the square was cut into. $\frac{6}{12}$ cancels by 6 to $\frac{1}{2}$, the same rectangle regrouped into bigger pieces. Notice the overlap is smaller than either band on its own - taking a fraction OF something always shrinks it, which is why adding the two fractions can never be the answer.

1. Step 1. Build it. Slide the coral band to $\frac{2}{3}$ of the height and the teal band to $\frac{3}{4}$ of the width.
2. Step 2. Cancel it. The overlap covers 6 of the 12 cells. Pull the simplify handle as far as it will go.
3. Step 3. Without the square. The square is covered. What is $\frac{3}{5}\times \frac{2}{3}$?

Open Area Grid on its own page to share it