Area with Fractions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Area with Fraction Sides

Mathematics · Fractions · ages 10-11
Name ______________________   Date ____________

  1. A rectangle is 2/3 of a unit long and 3/4 of a unit wide. What is its area?

    • 5/12 square unit
    • 6/12, which is 1/2 square unit
    • 1 square unit
    • 5/7 square unit

  2. To find the area of a rectangle with fraction side lengths, what do you do to the two side lengths?

    • Add them
    • Multiply them
    • Divide them

  3. Each of the 12 tiles in a square cut into 3 columns and 4 rows is 1/12 of the whole square.

    Circle one:   True   False

  4. A square is cut into 3 columns and 4 rows to make equal tiles. How many tiles are there in all?

    • 7
    • 12
    • 9

  5. True or false: when you tile a rectangle whose sides are fractions, the number of small tiles you count is always the same as the product you get from multiplying the two fractions.

    Circle one:   True   False

  6. A garden bed is 1 1/2 m long and 2/3 m wide. What is its area?

    • 1 m²
    • 2 1/6 m²
    • 1/3 m²

  7. A rectangle is 2/3 m long and 3/4 m wide. If a whole square is tiled with 3 columns and 4 rows (12 tiles), how many tiles does the rectangle cover?

    Answer: ______________

  8. A rectangle is 5/6 of a unit long and 3/4 of a unit wide. Imagine a unit square split into 24 equal squares, 6 across and 4 down, where each small square has area 1/24. How many of these small squares does the rectangle cover?

    Answer: ______________

  9. Ben says a rectangle with sides 1/2 m and 1/3 m has an area of 5/6 m² because he added the fractions. What is his mistake?

    • He should subtract: the correct area is 1/6 m²
    • His answer is correct
    • He should multiply: the correct area is 1/6 m²

  10. A rectangle is 3/5 m long and 1/2 m wide. Tile a whole square into 5 columns and 2 rows (10 tiles). How many tiles does the rectangle cover?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Area with Fraction Sides W1-mt_gx6KQK5-Kx-s1

  1. 6/12, which is 1/2 square unit · Tiling with 1/12 squares gives 6 tiles, and 6/12 is 1/2. Multiplying 2/3 times 3/4 gives the same answer.
  2. Multiply them · Area always comes from multiplying length times width, even when the sides are fractions.
  3. True · Cutting a whole into 12 equal parts means each part is 1/12.
  4. 12 · 3 rows times 4 columns makes 12 equal tiles.
  5. True · Counting tiles multiplies the numerators, and multiplying fractions multiplies the numerators too. They are the same move.
  6. 1 m² · Change 1 1/2 to 3/2, then multiply: 3/2 x 2/3 = 6/6 = 1 m². Forgetting the whole number part would wrongly give 1/3.
  7. 6 · 2 of the 3 columns and 3 of the 4 rows covers 2 x 3 = 6 tiles.
  8. 15 · The tile count is 5 times 3, which is exactly the numerators multiplied. That is why multiplying the fractions counts the same tiles.
  9. He should multiply: the correct area is 1/6 m² · Area comes from multiplying side lengths, not adding: 1/2 x 1/3 = 1/6 m².
  10. 3 · 3 of the 5 columns and 1 of the 2 rows covers 3 x 1 = 3 tiles out of 10, matching 3/5 x 1/2 = 3/10.
Worksheet · LightMySky