Equivalent fractions explorer

What the explorer shows

Equivalent fractions are different names for the same amount. The top bar is cut into 2 to 6 equal parts with some of them shaded, such as 2/3. Underneath is the same bar after every part has been split into 2, 3, 4, 5 or 6 smaller pieces. Thick lines mark the original parts, dashed lines show the new cuts, and a purple dotted line runs down the edge of the shaded amount so you can see it has not moved. The readout gives the new name, such as 2/3 = 8/12.

Why splitting beats a rule

Many children learn "multiply the top and bottom by the same number" without knowing why it works. Splitting shows the reason. If each of the 3 parts is cut into 4 pieces, there are 3 × 4 = 12 pieces in the whole, and each of the 2 shaded parts becomes 4 shaded pieces, so 2 × 4 = 8 are shaded. Nothing has been added or taken away, so 2/3 and 8/12 must be the same amount. After seeing this a few times, the rule becomes a shortcut a child understands rather than a trick to remember.

Common mix-ups

• Adding the same number to the top and bottom. 2/3 is not equal to 3/4. Splitting multiplies both numbers, and the bar shows why adding does not keep the amount the same.
• Thinking bigger numbers mean a bigger fraction. 8/12 has bigger numbers than 2/3, but the shaded length is identical.
• Splitting only some of the parts. Every part must be split the same way, or the pieces are no longer equal and the fraction name is wrong.
• Believing equivalent fractions are only nearly equal. They are exactly equal: the dotted line does not move at all.

A 10-minute activity

• Minutes 1 to 3: choose 3 parts and shade 2. Split every part into 2, then 3, then 4. The child writes each name: 2/3, 4/6, 6/9, 8/12.
• Minutes 4 to 6: ask what pattern they see in the top numbers and in the bottom numbers, and why both change by the same factor.
• Minutes 7 to 9: press Challenge. Before splitting, the child predicts the missing top number and presses Check, then splits the bar to see why it is right.
• Minute 10: ask for a fraction equal to 1/2 that they did not make on screen, such as 50/100, and how they know.

Where it fits by grade

• Grade 3: simple equivalent fractions such as 1/2 = 2/4 and 4/6 = 2/3, explained with a visual fraction model (Common Core 3.NF.A.3).
• Grade 4: explaining why a/b = (n × a)/(n × b) with visual models, paying attention to how the number and size of the parts change (4.NF.A.1).
• Grade 5: using equivalent fractions to find common denominators before adding and subtracting.
• England: Year 3 pupils recognize and show equivalent fractions with small denominators, Year 4 pupils learn families of common equivalent fractions, and Year 5 pupils write equivalent fractions of a given fraction, including tenths and hundredths.

Learning more

Equivalent fractions is one of the skills on Eurekami's skill map. Lessons draw fraction bars from the numbers in each question, and Daily Practice brings the skill back when it starts to fade.