Equivalent Fractions Simulation

About this experiment

Equivalent fractions look different but are the same amount, like 1/2, 2/4 and 3/6. Shade an orange fraction strip, then split every piece into 2 or 3 smaller pieces: the number of pieces changes, but the shaded amount stays exactly the same. Compare it with a blue strip, follow the dashed line down the fraction wall to find every equal fraction up to twelfths, and switch to circles to see the same idea as slices of a pizza.

Learning goals

Recognise that a fraction is a number of equal parts of one whole
Show that fractions such as 1/2, 2/4 and 4/8 are equivalent
Make equivalent fractions by multiplying the top and bottom by the same number
Simplify a fraction by dividing the top and bottom by the same number
Compare two fractions using a fraction wall

How to use it

1Start with 1/2 in orange. Press Split each piece in 2. What fraction is shaded now? Did the shaded amount change?
2Split again. Write down the three fractions you have made. What happens to the top and bottom numbers each time?
3Follow the dashed line down the fraction wall. Which other rows have a piece that ends exactly on the line?
4Make 3/4 in orange and 6/8 in blue. Are they equal? Now try 2/3 and 3/4: which is bigger?
5Make 6/9 and press Simplify. What number did both parts get divided by?
6Switch to Circles and compare 3/4 with 9/12 as slices of a pizza.

The model

\frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4}

Multiply the top and bottom by the same number to get an equivalent fraction

\frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3}

Divide both by the same number to simplify

\frac{a}{b} = \frac{c}{d} ⟺ a \times d = b \times c

A quick check that two fractions are equal (for older pupils)

Assumptions

All pieces in a strip or circle are exactly the same size, and every strip is the same length: one whole.
Fractions go up to twelfths so the pieces stay big enough to see.
Equality is checked exactly with whole numbers, never with rounded decimals.

Try this in class

Q1Mia ate 2/8 of a pizza and Tom ate 1/4 of the same size pizza. Who ate more?
Q2Why can you not split 1/2 into an equivalent fraction with 5 as the bottom number?
Q3Find three fractions that are equal to 2/3.
Q4Which is bigger, 5/6 or 7/8? How can the fraction wall help you decide?
Q5Is 3/6 in its simplest form? How do you know?

Frequently asked questions

Why does splitting the pieces not change the amount?

Each piece is cut into smaller pieces of the same size, so there are more pieces, but the shaded part covers exactly the same area of the whole. The top and bottom numbers are both multiplied by the same number.

What does simplest form mean?

A fraction is in its simplest form when no whole number bigger than 1 divides both the top and the bottom exactly. For example 2/3 is simplest, but 4/6 is not because both numbers can be divided by 2.

Why use a fraction wall?

Every row is the same whole cut into a different number of equal pieces. Lining the rows up makes it easy to see which fractions are equal and which are bigger, without any calculation.