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Grades 3 to 6 (Years 4 to 7 in England)

Fractions practice, from grade 3 to grade 6

Free fractions practice problems from across grades 3 to 6, checked as you go, plus a printable fractions worksheet with answers. Below the practice set is a guided tour of fractions in the order children learn them, with an example for each step and a page for each topic.

The method, step by step

  1. Read the question and decide what the whole is.
  2. Decide the operation: compare, add, subtract, multiply or divide.
  3. To compare, add or subtract, rename the fractions with a common denominator first; to multiply or divide, you don't need one.
  4. Change mixed numbers into improper fractions before you multiply or divide.
  5. Work out the answer, then write it in simplest form.
  6. Check the size: is the answer roughly what you expected?

CCSS 4.NF.A.1CCSS 3.NF.A.3.BCCSS 4.NF.A.2CCSS 4.NF.B.3CCSS 5.NF.A.1CCSS 5.NF.A.2England: Y4 FractionsEngland: Y5 FractionsEngland: Y6 FractionsEngland: KS3 Number

Worked example

A recipe needs 3/4 cup of milk. You have 1/3 cup. How much more milk do you need?

  1. This is a subtraction: 3/4 − 1/3.
  2. The least common multiple of 4 and 3 is 12.
  3. 3/4 = 9/12 and 1/3 = 4/12.
  4. 9/12 − 4/12 = 5/12.
  5. 5 and 12 share no common factor except 1, so you need 5/12 cup more.

Practice now

Question 1 of 100 correct

1/5 × 1/8 = ? Give your answer in simplest form.

Print a worksheet with answersShare to Google ClassroomFree, no sign-up. Nothing you type is saved.

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Fractions practice problems with answers

The practice set below mixes problems from grade 3 to grade 6: missing numbers, multiple choice, putting fractions in order and short word problems. Every answer is checked straight away, with hints and worked steps. Print a fresh worksheet with answers whenever you want one on paper.

For 4th grade fractions practice, focus on steps 3 to 7 of the tour below and the first half of step 9. For 5th grade, review those and add steps 8 to 10. Each topic has its own page, linked at the bottom of this one, with its own practice set and worksheet.

1. What a fraction is (grade 3)

A fraction names equal parts of a whole. The denominator says how many equal parts the whole is cut into, and the numerator says how many of those parts you have. Example: 3/4 means 3 parts, each of size 1/4, and 4/4 is one whole.

2. Fractions on a number line (grade 3)

A fraction is a number with its own place on the number line, not just a slice of pizza. Split the space from 0 to 1 into equal jumps and count them. Example: 5/4 is five jumps of 1/4 from 0, just past 1.

3. Equivalent fractions (grades 3 and 4)

Different fractions can name the same amount. Multiply the numerator and denominator by the same number to make an equivalent fraction. Example: 2/3 = 8/12, because both parts were multiplied by 4. Almost everything that follows depends on this step.

4. Comparing fractions (grades 3 and 4)

With the same denominator, more parts means more. With different denominators, rename both fractions with a common denominator or compare each one with 1/2. Example: 3/4 = 9/12 and 5/6 = 10/12, so 3/4 < 5/6.

5. Adding and subtracting with like denominators (grade 4)

When the pieces are the same size, add or subtract the numerators and keep the denominator. Example: 3/8 + 4/8 = 7/8, and 7/10 − 3/10 = 4/10, which simplifies to 2/5.

6. Mixed numbers and improper fractions (grade 4)

An improper fraction such as 11/4 is more than one whole, and 2 3/4 is the same amount written as a mixed number. Example: 2 3/4 = (2 × 4 + 3)/4 = 11/4, and 17/5 = 3 2/5, because 17 ÷ 5 = 3 remainder 2.

7. Simplifying fractions (grades 4 to 6)

Divide the numerator and denominator by their greatest common factor to write a fraction in simplest form. Example: 12/18 = 2/3, dividing both by 6. From here on, final answers are usually expected in simplest form.

8. Adding and subtracting with unlike denominators (grade 5)

Rename both fractions with a common denominator, then add or subtract the numerators. Example: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. The classic mistake, 1/2 + 1/3 = 2/5, adds the tops and the bottoms.

9. Multiplying fractions (grades 4 and 5)

In grade 4, children multiply a fraction by a whole number: 3 × 2/5 = 6/5. In grade 5 they multiply two fractions by multiplying the numerators and multiplying the denominators: 2/3 × 3/4 = 6/12 = 1/2. No common denominator is needed.

10. Dividing fractions (grades 5 and 6)

Grade 5 starts with unit fractions and whole numbers: 1/3 ÷ 2 = 1/6, and 4 ÷ 1/3 = 12, because each whole holds 3 thirds. In grade 6, children divide a fraction by a fraction by multiplying by the reciprocal: 3/4 ÷ 3/8 = 3/4 × 8/3 = 24/12 = 2.

How this order matches school

This order follows the US Common Core: fractions as numbers in grade 3 (3.NF); equivalence, comparing, like denominators and multiplying by a whole number in grade 4 (4.NF); unlike denominators, multiplying, and dividing with unit fractions in grade 5 (5.NF); and dividing fractions by fractions in grade 6 (6.NS.A.1). In England the same ideas run from Year 3 to Year 6, and dividing one fraction by another comes in Key Stage 3.

How parents can help

If your child is stuck on a step, go back one step first: trouble with unlike denominators is often really trouble with equivalent fractions. Keep practice short and regular, use measuring cups and rulers, and ask your child to explain answers out loud. If you want help choosing what to practice, Eurekami's Daily Practice starts with a short placement test that steps back to find the missing skill.

Common mistakes

  • Adding the tops and the bottoms: 1/2 + 1/3 is 5/6, not 2/5.
  • Thinking a bigger denominator means a bigger fraction: 1/8 is smaller than 1/3.
  • Changing only the denominator when renaming: 2/3 is 8/12, not 2/12.
  • Multiplying mixed numbers part by part: 2 1/2 × 1 1/2 is not 2 1/4. Change to improper fractions first: 5/2 × 3/2 = 15/4 = 3 3/4.
  • Flipping the wrong fraction when dividing: keep the first fraction, flip the second, then multiply.
  • Stopping before simplest form: 6/12 should be written as 1/2.

Questions people ask

What order should kids learn fractions in?
Usually: what a fraction is, fractions on a number line, equivalent fractions, comparing, adding and subtracting with like denominators, mixed numbers, then unlike denominators, multiplying and dividing. Each step leans on the ones before it.
Do you need a common denominator to multiply fractions?
No. Multiply the numerators and multiply the denominators: 2/3 × 3/4 = 6/12 = 1/2. You need a common denominator to add, subtract or compare.
What fractions should a 4th grader know?
In Common Core, grade 4 covers equivalent fractions, comparing fractions with different denominators, adding and subtracting with like denominators (including mixed numbers) and multiplying a fraction by a whole number, with denominators 2, 3, 4, 5, 6, 8, 10, 12 and 100.
What fractions should a 5th grader know?
Grade 5 adds and subtracts fractions with unlike denominators, including mixed numbers, multiplies fractions, and divides unit fractions by whole numbers and whole numbers by unit fractions.
Can you do fractions practice online free without signing up?
Yes. The practice set on this page needs no sign-up, and nothing is saved.
Is there a free fractions practice worksheet with answers?
Yes. Use the Print a worksheet button on this page for a fresh worksheet every time, with an answer key showing answers only or answers with worked steps.
My child keeps getting fractions wrong. Where should we start?
Go back to equivalent fractions and comparing fractions. Many later mistakes trace back to those two skills, and the steps above show what comes before each one.

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Fractions Practice Problems With Answers | Eurekami