Skip to content
Brainsladder

Find the Area of a Rectangle with Fractional Side Lengths

Students find the area of a rectangle with fractional side lengths by tiling it with unit squares having fractional side lengths (e.g., 1/2 by 1/2 unit squares) and by applying the area formula. They connect the tiling approach to the multiplication of fractions.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

Find the Area of a Rectangle with Fractional Side Lengths

Grade 5 · Multiplying Fractions · question 1 of 3

0 of 20

20 rungs. A star at the top.

23142314CDEF

Find the area of rectangle CDEF in square units.

Find the area.

Your answer:

How it is taught

0:00 of 4:22

Area is still length times width when the sides are fractions.

Unit-fraction tiles can fill that same rectangle.

Read it: A part of a part

2/3 × 3/4 is 2/3 of 3/4. Cut a whole 3 down and 4 across: 12 cells. The two shades cross on 6 of them, so 2/3 × 3/4 = 6/12, which is 1/2 in simplest form.

  1. Shade the first fraction one way: 2 of the 3 rows.
  2. Shade the second fraction the other way: 3 of the 4 columns.
  3. The cells inside both shades, over all the cells, are the product: 6/12 = 1/2.

Multiplying the denominators counts the cells in the whole: 3 × 4 = 12.

Multiplying the numerators counts the cells inside both shades: 2 × 3 = 6.

A part of a part is smaller than either part: 1/2 is less than 2/3 and less than 3/4.

Multiply the numerators for the top and the denominators for the bottom, then simplify: 2/3 × 3/4 = 6/12 = 1/2.

Adding the fractions instead of multiplying them: 2/3 + 3/4 = 17/12, more than either.

Multiplying takes a part of a part, so the product is smaller: 2/3 × 3/4 = 1/2.

A rectangle is 2/3 unit by 1/9 unit. What is its area in square units? — 2/27. Cut the whole 3 by 9: 27 cells. The shades cross on 2 cells: 2/27.

3/4 × 1/2

Picture a little rug — three-fourths of a unit long and one-half of a unit wide. How much floor does it cover?

Here it is. The long side is three-fourths, and the short side is one-half.

Let's tile it with little one-fourth-by-one-fourth squares. The long side is cut into three pieces.

Grade 5 · Tile a 3/4 by 1/2 rectangle to find its area

Now cut the short side in half. We have a tidy grid!

Count the squares: one, two, three, four, five, six.

Each little square is one-fourth times one-fourth — that's one-sixteenth of a square unit.

Six tiles, each one-sixteenth, makes six-sixteenths — which simplifies to three-eighths.

The area formula agrees: three-fourths times one-half. Multiply tops and bottoms to get three-eighths.

Both ways match! The area is three-eighths of a square unit. Nicely done!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics
Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal
1 star — one skill mastered, every rung of its ladder climbed
Climbing now
Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free