SME
Grade 5 Math · Problem type
Area of a rectangle with fractional sides
Use this for “A rug is 3/4 yard by 2/3 yard. What is its area?”
Diagram
3/4 of the columns and 2/3 of the rows overlap in 6 of the 12 small pieces: 6/12.
The product is 6/12.
This is an example. Type your own values to start a new problem.
Length numerator
Length denominator
×
Width numerator
Width denominator
=
Area numerator
Area denominator
Formulas
3 × 2 = 6
Length numerator × width numerator = area numerator
4 × 3 = 12
Length denominator × width denominator = area denominator
Assumptions
•
Area = length × width, even when the sides are fractions.
•
Tile the rectangle with unit rectangles: the picture shows the fraction of a square yard covered.
•
Multiply the numerators and multiply the denominators. Sides are fractions of a unit, denominators 2 to 12.
Step-by-step
WE KNOW
Length numerator: 3
Length denominator: 4
Width numerator: 2
Width denominator: 3
FIND
area numerator, area denominator
Step 1 · Find area numerator
3 × 2 = ?
Length numerator × width numerator = area numerator
Multiply the numerators: the tiles along the length times the tiles along the width.
Area numerator = 6
Step 2 · Find area denominator
4 × 3 = ?
Length denominator × width denominator = area denominator
Multiply the denominators: how many tiles fill one square unit.
Area
denominator
=
12
(area
6
12
=
1
2
square
unit)
Check
Put the numbers back in. Both sides should match.
3 × 2 = 6 ✓
3
4
×
2
3
=
6
12
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.