Area is length × width, whether the sides are whole numbers or not.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Counting the small tiles
A 1/2 by 1/3 rectangle is one tile in a whole cut into sixths. Its area is 1/6.
With bigger fractions
A 2/3 by 3/4 rectangle covers 6 of the 12 tiles, so its area is 6/12, or 1/2.
Area still means covering with unit squares
A rectangle 1/2 wide and 2/3 tall has an area of 1/2 × 2/3 = 1/3 of a square unit. Area is still length times width; the sides simply happen to be fractions. The formula did not change because the numbers got smaller.
Seeing it in a unit square
Draw a unit square. Cut it into halves one way and thirds the other, giving 6 small rectangles. The piece measuring 1/2 by 2/3 covers 2 of those 6, which is 1/3. The grid makes the multiplication visible rather than asserted.
Sides that are mixed numbers
For a rectangle 2 1/2 by 1 1/3, convert to improper fractions first — 5/2 and 4/3 — then multiply to get 20/6 = 3 1/3 square units. Multiplying the whole parts and the fraction parts separately misses two of the four pieces and is a very common error.
Where this comes up
Rooms, garden beds, fabric and tiles rarely have whole-number dimensions. A floor 12 1/2 feet by 9 3/4 feet needs exactly this calculation before you can order carpet. The fractional case is the normal case outside a textbook.
Step 2: Try It Yourself
Tap and try it out.
Area · squares inside
12
Perimeter · walk around
14
3 × 4 = 12 · 3 + 4 + 3 + 4 = 14
Area counts the units inside. Perimeter measures the walk all the way round.
Step 3: Watch an Example
One step at a time.
Watch Ana Find an Area
Ana finds the area of a rectangle 2/3 by 3/4.
- Step 1
She uses area = length × width, as always.
Step 4: Your Turn
Practice makes it stick.
The Small Tile
Problem 1 of 2
A rectangle 1/2 by 1/4. What is the bottom number of its area?
The Garden Patch
Problem 2 of 2
A patch 3/4 m by 2/5 m. What is the bottom number of its area?
Area of a Fraction Rectangle
1 of 4
1/3 by 1/5. What is the bottom number of the area?
2 of 4
2/3 by 1/2. What is the top number of the area?
3 of 4
3/5 by 2/3. What is the bottom number of the area?
4 of 4
Does the area formula change for fractional sides?
Step 5: Quick Check
Show what you know.
Question 1 of 2
1/2 by 2/5. What is the bottom number of the area?
Question 2 of 2
How do you find the area of a rectangle?
What You Learned
- Area is length × width, fractions included.
- Multiply the tops, then the bottoms.
- A rectangle with sides under 1 has an area under both.