Area with Fractions
Find the area of a rectangle with fractional side lengths by tiling with unit-fraction squares; show that the area equals the product of the side lengths
What a learner can do afterwards
- Tile a 2/3 × 3/4 rectangle with 1/12 squares and count to find area = 6/12 = 1/2
- Explain why the number of unit-fraction tiles equals the product of the two fractions
- Calculate the area of a rectangle with sides 1 1/2 and 2/3 using fraction multiplication
The lesson
You already know how to multiply fractions. Today you will use that skill to find the area of a rectangle when the length and width are both fractions, like a rug that is 2/3 meter long and 3/4 meter wide.
A rectangle is 2/3 m long and 3/4 m wide. Line up 2 of the 3 columns and 3 of the 4 rows. That covers 6 of the 12 tiles, so the area is 6/12 square meters, which is the same as 1/2 square meter.
A garden bed is 1 1/2 m long and 2/3 m wide. First write 1 1/2 as 3/2. Then multiply: 3/2 x 2/3 = 6/6 = 1. The bed's area is 1 square meter, the same answer tiling would give.
Turn mixed numbers into improper fractions before you multiply. Then estimate first: since 2/3 and 3/4 are both less than 1, the area has to be smaller than 3/4. That helps you catch mistakes.
Area with fraction sides follows the same rule as always, length times width, and tiling with tiny fraction squares shows exactly why it works.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.