Home › Math exercises › Fractions

Mathematics · ESO

Exercises on fractions step by step

Add, subtract, multiply, and divide fractions with solved and explained examples. Review the theory and practice with instant correction until you can do them without thinking.

Practice for free

5-day trial · no card required · instant grading

Fractions: quick theory

A fraction a/b represents a part of a whole: the numerator (a) indicates how many parts we take, and the denominator (b) indicates how many parts the whole is divided into.

Adding or subtracting: if the denominators are different, they are converted to a common denominator (the least common multiple) and the numerators are added or subtracted.

Multiplying: numerator by numerator and denominator by denominator. Dividing: you multiply the first by the reciprocal of the second (flip the second fraction). Finally, it is best to simplify.

Step-by-step solved exercises on fractions

Solved examples to show you the method. Then, practice with instant correction.

Exercise 1Calculate 2/3 + 1/4.

Step-by-step solution

  1. Common denominator: lcm(3, 4) = 12.
  2. We convert: 2/3 = 8/12 and 1/4 = 3/12.
  3. We add the numerators: 8/12 + 3/12 = 11/12.
Result: 2/3 + 1/4 = 11/12.

Exercise 2Calculate 3/5 · 10/9.

Step-by-step solution

  1. We multiply straight across: (3·10)/(5·9) = 30/45.
  2. Simplify by dividing by 15: 30/45 = 2/3.
Result: 3/5 · 10/9 = 2/3.

Exercise 3Calculate 4/7 ÷ 2/3.

Step-by-step solution

  1. Dividing is multiplying by the reciprocal: 4/7 · 3/2.
  2. We multiply: (4·3)/(7·2) = 12/14.
  3. Simplify by 2: 12/14 = 6/7.
Result: 4/7 ÷ 2/3 = 6/7.

Do you want to practice fractions for real?

Hundreds of fractions exercises with instant correction that tells you where you went wrong and how to do it right.

Start for free
Instant feedback

The AI reviews each of fractions's exercises in seconds and explains the mistake step-by-step.

Hundreds of exercises

From fractions and the entire syllabus, ordered by difficulty so you can make progress.

You see your progress

You know what you master and what you struggle with. Go into the exam having truly practiced.

This topic is studied in:

1st year of ESO2nd year of ESO3rd year of ESO

Frequently asked questions about fractions

How do you add fractions with different denominators?

Find a common denominator (the least common multiple of the denominators), convert both fractions, and add the numerators while keeping the common denominator.

How do you divide two fractions?

Multiply the first fraction by the reciprocal of the second (swap the numerator and denominator of the second) and then simplify.

Can I practice these exercises for free?

Yes. With Refuerzo.ai you practice fractions with hundreds of exercises and step-by-step instant correction. You get a 5-day free trial with no card required.

Master fractions by practicing

Create your account in one minute. No card required, no commitment.

Try Refuerzo.ai for free

Already have an account? Log in