P3 Equivalent Fractions: Same Pizza, Different Slices

A plain pizza lands on a paper plate. It is cut into 4 slices, then into 8. One slice lifts away and settles back. Nothing was added and nothing was eaten, yet the numbers describing it keep changing. That small puzzle is the whole of equivalent fractions.

That is Pizza Slices, a 30-second Primary 3 episode of our Topic Explainers series. Watch it first (there is no voice-over, so it works with the sound off), then read on.

Pizza Slices: same amount, different cut. Slice it, compare it, simplify it.

The episode makes three moves with one pizza. First, the same amount is cut three ways: 1/2, 2/4 and 4/8 all cover the same half. Next, two equal pizzas showing 3/4 and 2/3 are both recut into twelfths so their slices can be counted and compared. Last, a pizza in 12 slices with 4 shaded has its slices joined in groups of 4, which shows that 4/12 is the same as 1/3.

All three are Primary 3 skills in the MOE syllabus: equivalent fractions, comparing unlike fractions with denominators up to 12, and writing a fraction in its simplest form.

The method

The big idea fits in one sentence: cutting a pizza into more slices changes the numbers, not the amount of pizza.

If every slice of a half is cut into two, there are twice as many slices in the whole pizza and twice as many in the shaded part. So 1/2 becomes 2/4. Cut each slice in two again and it becomes 4/8. The numerator (the top number, the slices we have) and the denominator (the bottom number, the slices in the whole) are both multiplied by the same number.

The reverse also works. Joining slices in equal groups divides the top and the bottom by the same number. That is how we simplify.

So there is one rule, used two ways:

To find an equivalent fraction, multiply the numerator and the denominator by the same number.
To simplify, divide the numerator and the denominator by the same number.

Comparing fractions then becomes easy. When two fractions have different denominators, the slices are different sizes, so you cannot compare them by counting. Recut both into slices of the same size first, and then the bigger count is the bigger fraction.

Worked examples

Worked example 1: same amount, different cut

Three equal pizzas each have half shaded. One is cut into 2 slices, one into 4 and one into 8.

Step 1: Read each fraction.

Slices in the pizza	Slices shaded	Fraction
2	1	`1/2`
4	2	`2/4`
8	4	`4/8`

Step 2: Check with the rule. From 1/2 to 2/4, both numbers are multiplied by 2. From 1/2 to 4/8, both are multiplied by 4.

Step 3: Check with the picture. The shaded part covers exactly half of every pizza. So 1/2 = 2/4 = 4/8.

The picture and the numbers must always agree. If your child ever writes an equivalent fraction that a drawing does not support, the drawing wins and the working needs another look.

Worked example 2: which is more pizza, 3/4 or 2/3?

Two equal pizzas. One has 3/4 shaded, the other 2/3. Which is more?

Step 1: Notice the problem. Quarters and thirds are different sizes, so "3 slices against 2 slices" does not tell us anything yet.

Step 2: Find a slice size that works for both. We need a number that both 4 and 3 go into. Count in 4s (4, 8, 12) and in 3s (3, 6, 9, 12): the first match is 12. Cut both pizzas into twelfths.

Step 3: Recut each fraction.

Four quarters become twelve twelfths, so each quarter is cut into 3. Multiply top and bottom by 3: 3/4 = 9/12.
Three thirds become twelve twelfths, so each third is cut into 4. Multiply top and bottom by 4: 2/3 = 8/12.

Step 4: Compare. Now the slices are the same size. 9 slices is more than 8 slices, so 3/4 is more than 2/3. We can write it as 3/4 > 2/3.

It is a close call, which is exactly why the recut is worth doing. By eye, many children would not be sure.

Worked example 3: simplify 4/12

A pizza is cut into 12 slices and 4 are shaded. What is the fraction in its simplest form?

Step 1: Write the fraction. 4 of 12 slices are shaded: 4/12.

Step 2: Look for equal groups. Join the slices in groups of 4. The 12 slices make 3 big slices, and the 4 shaded slices make exactly 1 big slice.

Step 3: Divide top and bottom by the same number. 4 ÷ 4 = 1 and 12 ÷ 4 = 3, so 4/12 = 1/3.

Step 4: Check that it is simplest. 1 and 3 have no common factor other than 1, so no further joining is possible. The simplest form is 1/3.

If your child divides by 2 first, that is fine too: 4/12 = 2/6, then 2/6 = 1/3. It takes one more step, and arrives at the same place.

Common mistakes

Changing only one number. Writing 1/2 = 2/2 or 1/2 = 1/4. Ask, "If we cut every slice in two, what happens to the slices we have, and to the slices in the whole?" Both must change.
Thinking a bigger denominator means a bigger fraction. A child may say 1/8 is more than 1/2 because 8 is bigger than 2. More slices means smaller slices. Ask, "Would you rather have one slice of a pizza cut into 2, or one slice of a pizza cut into 8?"
Comparing numerators with different denominators. Saying 3/4 is more than 2/3 "because 3 is bigger than 2" gives the right answer for the wrong reason, and the same reasoning goes wrong on 3/5 and 2/3. Insist on the recut: same slice size first.
Adding instead of multiplying. Writing 1/2 = 3/4 by adding 2 to the top and bottom. Adding the same number does not keep the amount the same; multiplying does. A quick drawing shows 3/4 is more than half.
Stopping before the simplest form. 4/12 = 2/6 is correct but not simplest. Ask, "Can we still join the slices into equal groups?"

Parent tips

Cut real food. A pizza, a round pancake, a chapati or a square sandwich works well. Cut it in half, then cut each piece in half again, and ask your child to name the fraction of the same part at each step.
Fold paper strips. Fold one strip into halves, another into quarters and another into eighths, and line them up. Shading 1/2, 2/4 and 4/8 side by side makes the equal lengths visible.
Play "who gets more?" Give two fractions, such as 2/3 and 3/4, or 3/5 and 7/10. Your child finds a shared slice size, recuts, and decides. Then swap roles and let your child set one for you.
Join to simplify. Draw a pizza in 12 slices and shade some. Ask your child to group the slices into 2s, 3s, 4s or 6s until the shaded part fits into whole groups, then write the simpler fraction.
Always say "the same amount". When your child writes 2/4, ask them to say "two quarters is the same amount as one half". Saying it aloud keeps the meaning attached to the numbers.

Keep each round short, and let your child draw first and calculate second. That is the concrete, pictorial, abstract order of Singapore math teaching: real food, then a drawing, then the numbers. For the way fractions build from P2 to P6, our fractions parent guide gives the bigger picture, and Primary 3 sample questions explained walks through the shape of a P3 paper.

A worked solution for every question

Near the end of the episode, a worked-solution page unlocks three rows: "Every question has a worked solution. Open a hint when you want a step."

That is how fractions practice works in Singapore Math Drills. With progressive hints and worked solutions, every question can be opened up step by step, and every question has a full worked solution to read afterwards. If your child gets 3/4 against 2/3 wrong, the worked solution shows the recut into twelfths, so the method is right there next to the mistake.

Practice is calm by design too: no guilt-tripping over a missed day and no dark patterns, and your child's progress is only ever measured against their own. Slice it, compare it, simplify it.

Try a sample

Try a free interactive worksheet and see how calm practice feels, with no signup or credit card required.

Try a free Singapore math sample