Fractions of a set

A fraction can describe part of a group: 3 of 8 balloons are red, so 3/8 of the balloons are red. Quiz for kids, parent help below.

🧒 Kids: what fraction of the set?

Count the coloured ones and count them all. Then try the quiz!

▶ Quiz 🍕 More practice

3/8 are blue
2/6 = 1/3 are blue

💡 Trick: 5 of 9 stars are yellow? Coloured on top, total on the bottom: 5/9!

More fractions: Halves and quarters · Unit fractions · Number line · Fractions of a set · Fraction of a number · Fractions as division

For parents and teachers ↓

This part is for grown-ups: the key idea, pictures to draw, what to say, common mistakes, questions with answers and a free worksheet.

The trick: coloured over total

In a set, the whole is the group of things. The bottom number is how many things there are altogether, and the top number is how many have the feature you are asking about. So if 3 of 8 balloons are red, 3/8 of the balloons are red, and the other 5/8 are not. The things don’t have to be the same size or shape: each one counts as one equal share of the set.

Patterns to spot

See it: pictures to draw with your child

Draw these on paper or a whiteboard. A quick sketch makes the idea concrete before any rules.

3/8 blue, 5/8 white
3 of the 8 counters are blue: 3/8. The other 5/8 are white.
4/12 = 1/3
12 counters in 3 equal rows of 4: one row is blue, so 4/12 = 1/3.
2/5 of the class
A set can be drawn as a bar: each part is one child.

What your child already knows

Children already count sets of objects. The new step is to describe part of a set with a fraction, and to notice that the whole is now the group, not one shape. This is the bridge to finding a fraction of a number, such as 3/4 of 20, which grades 4 and 5 use all the time.

In real life: Count the family’s shoes: what fraction are trainers? Sort a bag of sweets by colour: what fraction are red? At the table, what fraction of the plates are empty?

Worked examples

Example 1: Name the fraction

  1. There are 9 stars.
  2. 5 are yellow.
  3. The total is 9 and 5 are yellow, so 5/9 of the stars are yellow and 4/9 are not.

Example 2: Simplify by grouping

  1. 12 eggs, 6 are brown.
  2. Put them in 2 equal groups of 6: one group is brown.
  3. So 6/12 = 1/2.

Example 3: Find the other part

  1. 3/10 of the children walk to school.
  2. 10/10 − 3/10 = 7/10 do not walk.

Common mistakes

Coloured over not colouredWrites 3/5 for 3 red out of 8 balloons.Fix: the bottom is the total, 8, not the other 5.
Mixing up the wholeUses one object as the whole instead of the set.Fix: ask “what is the whole here?” In a set, it is all the objects.
Thinking things must be the same sizeWon’t use fractions for a set of different toys.Fix: in a set, each object counts as one equal share, whatever its size.

What to say to your child

A short script for your first session. Pause after each line and let your child answer.

  1. “Here are 8 crayons. 3 are red. How many altogether?” (8.)
  2. “How many red?” (3.) “So 3 out of 8 are red. We write 3/8.”
  3. “What fraction are not red?” (5/8.)
  4. “If I take 1 red crayon away, how many are there now, and how many red?” (7 and 2: 2/7.)
  5. “Can you make a set where half are red?”

Questions to try (answers below)

Ask these out loud or write them down. The last one is a stretch.

  1. 4 of 10 apples are red. What fraction are red?
  2. 2 of 5 children are boys. What fraction are girls?
  3. 6 of 9 stars are gold. What fraction are gold?
  4. A box has 12 eggs; 3 are cracked. What fraction are not cracked?
  5. A set of 8 has half coloured. How many are coloured?
  6. What fraction of a week is Saturday and Sunday?
  7. All 6 cars are red. What fraction are red?
  8. 3 of 4 cats are black. 3/4 of how many?
  9. Stretch: 1/3 of a set of 15 marbles is blue. How many are blue?
Show the answers
  1. 4/10
  2. 3/5
  3. 6/9 = 2/3
  4. 9/12 = 3/4
  5. 4
  6. 2/7
  7. 6/6 = 1
  8. 4 cats
  9. 5

Games to play at home

Sock sort

Sort socks by colour and say the fraction of each colour.

Snack fractions

Ask what fraction of the snacks are left after eating some.

Family fractions

What fraction of the family wears glasses, or likes tea?

A 5-day plan for fractions of a set

Ten minutes a day is enough. Short, regular practice works far better than one long session.

By grade

Grade 3 (Common Core 3.NF.A.1) understands a fraction as a parts of size 1/b, and fractions of a set give children a second model besides shapes. Grade 4 (4.NF.B.4) and grade 5 use sets to find a fraction of a number. In India, fractions of a collection appear in class 3 and class 4 maths.

More for each grade: Grade 3 math and the CBSE class 3 maths guide; Grade 4 math and the CBSE class 4 maths guide.

What comes next

Next, find a fraction of a number, such as 3/4 of 20, using equal groups. Grouping sets is also a way into equivalent fractions.

Worksheet and more practice

Print a free worksheet with an answer key, or keep practicing online with fraction practice.

← Number lineFraction of a number →

More: fractions for kids · fraction wall · fraction calculator · fractions quiz · fraction levels · fraction games · fractions chart

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Questions parents ask

What is a fraction of a set?

A fraction that describes part of a group. If 3 of 8 balloons are red, 3/8 of the set is red.

What is the denominator in a fraction of a set?

The total number of objects in the set. The numerator is how many have the feature you are counting.

Do the objects in a set have to be the same size?

No. In a set, each object counts as one equal share of the whole group.

How do you simplify a fraction of a set?

Group the set into equal groups. 6 of 12 eggs are brown: in groups of 6, one group is brown, so 6/12 = 1/2.

What grade learns fractions of a set?

Grade 3, with fractions of numbers in grades 4 and 5.