Area of a rectangle with fractional sides

The idea

The area of a rectangle with fractional sides equals the product of its sides, so the product of two fractions is the area of the rectangle having the two fractions as its sides.

A very small garden

A rectangle 3 m long and 2 m broad has area 3 × 2 = 6 square metres. Now a tiny garden is 1/2 m long and 1/4 m broad.

What is the area of the tiny garden?

• 1/8 square metre
• 3/4 square metre
• 1/4 square metre

Make the garden, count its area

The big square is 1 m by 1 m, so its area is 1. Make each garden and compare the counted area with the product of the sides.

Area = length × breadth, with fractions too

The first garden is 1/2 m by 1/4 m. Eight such gardens make the whole square of area 1, so one garden has area 1/8. And 1/2 × 1/4 = 1/8.

In every row, length × breadth gives the area you counted.

The area of a rectangle with fractional sides equals the product of its sides. So the product of two fractions is the area of the rectangle that has the two fractions as its sides.

• Length | Breadth | Area counted
• 1/2 | 1/4 | 1/8
• 3/4 | 2/3 | 1/2
• 2/5 | 5/6 | 1/3

Notes

The area of a rectangle with fractional sides equals the product of its sides. So the product of two fractions is the area of the rectangle that has the two fractions as its sides.

Check yourself

A table top is 3/4 m long and 1/2 m broad. What is its area in square metres? Type a fraction like 5/6.

Answer: 3/8

3/4 × 1/2 = 3/8 square metres.

A rectangle is 1/2 m long and 1/4 m broad. How many such rectangles fit in a square of side 1 m?

A rectangle is 2/3 m long and 3/5 m broad. What is its area in square metres? Type a fraction like 5/6.

Answer: 2/5

2/3 × 3/5 = 6/15 = 2/5 square metres.

A square has each side 1/3 m. What is its area?

• 4. Four would be quarters. One rectangle is a quarter cut in half again, so more fit.
• 6. That adds 2 + 4. The square holds 2 × 4 = 8 of them.
• 8 — correct. Yes! The area of one is 1/8. 8 × 1/8 = 1, the whole square.
• 2/3 square metre. That is 2 × 1/3. For area we multiply the two sides: 1/3 × 1/3.
• 1/9 square metre — correct. Yes! Area = side × side. 1/3 × 1/3 = 1/9
• 1/6 square metre. That is 1/3 × 1/2. Both sides are 1/3, so the area is 1/3 × 1/3.