What are fractions?

A fraction is a number for part of something: equal parts of a whole, part of a group, or a point between whole numbers.

Fractions mean equal parts

When a pizza is cut into 4 equal slices and you eat 1, you have eaten one quarter of the pizza, written 1/4. A fraction tells you how many equal parts the whole was cut into, and how many of those parts you are talking about.

The word that matters most is equal. If one slice is bigger than the others, the slices are not quarters. Children who understand equal parts find every later fraction idea easier, from comparing to adding.

Fractions are also numbers. 1/2 sits half-way between 0 and 1, just as 5 sits between 4 and 6. Seeing fractions as numbers is a big step in grade 3.

See it: pictures to draw with your child

Copy these onto paper or a whiteboard. A quick sketch makes the idea concrete before any written method.

3/4 of a whole
Part of a whole: 3 of 4 equal parts are shaded.
3/8 of a set
Part of a set: 3 of the 8 counters are blue.
013/4
A point on a number line: 3/4 is three quarter-jumps from 0.

Three ways to see a fraction

All three describe the same number. Moving between them helps children see that a fraction is one idea, not three different tricks.

How to read and write fractions

A fraction has two numbers separated by a line. The bottom number, the denominator, is how many equal parts make one whole. The top number, the numerator, is how many of those parts we have. More in numerator and denominator.

Explore fractions on the fraction wall

Tap pieces to shade them. Each row is one whole, cut into equal parts.

One whole, and fractions bigger than 1

When every part is shaded, the fraction equals 1: 4/4, 6/6 and 10/10 are all one whole. Children enjoy spotting this: the top and bottom numbers are the same.

Fractions can also be bigger than 1. Five quarters is one whole pizza and one more slice: 5/4. That can be written as the mixed number 1 1/4, which grade 4 and 5 explore in improper fractions and mixed numbers.

Where children meet fractions

Fractions are everywhere once you look: half past three, a quarter of a cake, three quarters full, half price, a 1/2 cup of flour, 3/4 of the way to school. Talking about these at home gives children a feel for fraction sizes long before they meet the rules.

A good habit is to ask “is that more or less than half?” Children who can judge sizes against 1/2 make far fewer mistakes when comparing and adding fractions later.

Quiz: name the fraction

Look at each picture or number line. Type the top number, then the bottom number.

Where this fits: fractions step by step

  1. Halves and quarters
  2. What are fractions (this page)
  3. Unit fractions
  4. Numerator and denominator
  5. Fractions on a number line
  6. Fractions of a set
  7. Equivalent fractions
  8. Simplifying fractions
  9. Comparing fractions
  10. Ordering fractions
  11. Improper fractions and mixed numbers
  12. Adding fractions
  13. Subtracting fractions
  14. Finding a common denominator
  15. Adding mixed numbers
  16. Subtracting mixed numbers
  17. Fraction of a number
  18. Fractions × whole numbers
  19. Multiplying fractions
  20. Fractions as division
  21. Dividing fractions by whole numbers
  22. Dividing fractions
  23. Fractions to decimals
  24. Fraction word problems

What to say to your child

A short script for teaching it the first time. Pause after each line and let your child do the next step.

  1. “Here is one sandwich. Let’s cut it so 4 people get the same.” (Cuts into 4 equal parts.)
  2. “Each piece is one quarter. We write 1/4.”
  3. “If you eat 3 pieces, how much have you eaten?” (3/4.)
  4. “How much is left?” (1/4.)
  5. “Can you find something at home cut into equal parts?”

More worked examples

Example 1: naming a shape

A chocolate bar has 6 equal pieces and 5 are eaten. 5/6 of the bar is eaten and 1/6 is left.

Example 2: naming a set

There are 10 children and 7 wear glasses. 7/10 of the children wear glasses.

Example 3: on a number line

0 to 1 is split into 5 equal parts. A point 2 parts from 0 is at 2/5.

Example 4: one whole

A pie is cut into 8 slices and all 8 are eaten: 8/8 = 1 whole pie.

Practice questions (answers below)

Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.

  1. A pizza has 4 equal slices; 1 is eaten. What fraction is eaten?
  2. 6 equal parts, 5 shaded. What fraction is shaded?
  3. What is 3/3 equal to?
  4. 3 of 7 cars are red. What fraction are red?
  5. How do you say 5/8?
  6. Is 1/2 more or less than 1/3?
  7. What fraction is not shaded if 2/5 is shaded?
  8. How many sixths make a whole?
  9. Where is 1/2 on a number line from 0 to 1?
  10. Stretch: what is 5 quarters as a mixed number?
Show the answers
  1. 1/4
  2. 5/6
  3. 1
  4. 3/7
  5. five eighths
  6. More
  7. 3/5
  8. 6
  9. Half-way
  10. 1 1/4

Common mistakes

Unequal partsCalls a shape cut into 3 different-sized pieces “thirds”.Fix: fractions need equal parts. Fold or measure to check.
Counting the wrong totalWrites 3/5 for 3 shaded out of 8 parts.Fix: the bottom is all the parts, shaded and unshaded: 3/8.
Bigger bottom means bigger fractionThinks 1/8 is more than 1/2.Fix: more parts means smaller parts. Compare on the fraction wall.

How to teach it at home

Sandwich fractions

Cut food into equal parts and name the fraction eaten.

Clock fractions

Talk about half past and quarter past.

Fraction spotting

Find fractions in recipes, signs and measuring jugs.

By grade

More for each grade: Grade 2 math and the CBSE class 2 maths guide; Grade 3 math and the CBSE class 3 maths guide.

Worksheets and practice

Fractions of shapes worksheet, page 1

Fractions of shapes worksheet: printable PDF with an answer key. · Make a fresh test

Fraction practice · fraction calculator · fraction wall · fractions quiz · fraction levels · fraction games · fractions for kids

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Questions parents ask

What is a fraction in simple words?

A number for part of something. It tells how many equal parts the whole is cut into (bottom number) and how many of those parts you have (top number).

Why must fraction parts be equal?

Because a fraction names one size of piece. If the pieces are different sizes, a name like “one quarter” doesn’t mean anything.

Can a fraction be bigger than 1?

Yes. 5/4 is one whole and one more quarter. It can also be written as the mixed number 1 1/4.

How do you read fractions?

Say the top number, then the bottom number as a part name: 3/4 is “three quarters” or “three fourths”, 5/8 is “five eighths”.

What grade learns fractions?

Grade 1 and 2 meet halves and quarters, and grade 3 learns fractions as numbers in depth. Fractions continue up to grade 6.