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Mathematics · Fractions and decimals

Adding and subtracting fractions

Why isn't 1/2 + 1/3 equal to 2/5? Learn to add fractions with equal denominators, to bring different denominators to a common denominator, and to subtract fractions from a whole, using recipes and walks.

  • 20 min
  • 1 simulation
  • Mini quiz

Updated:

Preview

The question

Emre is making a cake. He needs 14\dfrac{1}{4} of a glass of sugar for the cake mixture and 38\dfrac{3}{8} of a glass of sugar for the syrup on top. There's exactly 1 glass of sugar in the cupboard. How much sugar will Emre use altogether, and how much will be left? Adding and subtracting fractions is the key to everyday questions like this.

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Fraction model

What is 1/4 + 3/8?

Set the number of parts, select the slices that show the sum and press Check.

Prediction

Predict first

Is the sum 1/4 + 3/8 less or more than half a pizza (1/2)?

It doesn’t matter whether you’re right; the simulation opens once you choose.

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Frequently asked

5 questions

Why isn't 1/2 + 1/3 equal to 2/5?

The denominator shows the size of the parts; adding denominators changes that size for no reason. 2/5 = 0.4, which is even smaller than 1/2 = 0.5 on its own, and adding something cannot make the result smaller. The correct answer is 3/6 + 2/6 = 5/6.

When the denominators are equal, why does the denominator stay the same?

You are putting together parts of the same size; their size does not change, only their number grows. In 2/7 + 3/7 you end up with 5 sevenths: 5/7. It is just like 2 apples and 3 apples making 5 apples.

How do I subtract a fraction from 1?

Write 1 as a fraction with the same denominator as the other fraction. For 1 − 5/8 you write 1 = 8/8, so 8/8 − 5/8 = 3/8. Then check by adding: 5/8 + 3/8 = 8/8 = 1.

Is my answer wrong if I don't simplify it?

No, 3/6 and 1/2 show the same amount, so an unsimplified answer is not wrong. Still, writing it in simplest form is a good habit: it is easier to read and compare, and "half full" is clearer than "3/6 of the bottle".

How can I tell whether my answer is right?

Estimate before you start. 1/4 and 3/8 are both less than a half, so their sum must be less than 1. If your answer does not match your estimate, there is a mistake somewhere. For subtraction, add the result back and see whether you get the number you started with.