# Fraction addition: how to add two parts?

In order to add parts, they must be comparable. This is the purpose of adding fractions. If your parents let you and your brother have half a pizza, but your brother has eaten 1/8 of his, the following things will keep you from being fooled.

## What’s the point of adding fractions?

The addition of fractions allows for**add two numbers expressed in fractional form**. But for that, we must first find a common denominator. Indeed, fractions express a part of the whole, a part of the whole. Therefore, it is important to make sure that we are talking about the same set before adding the parts.

The size of the number (quantum) in writing fractions is relative to the size of the unit (whole, or denominator). Therefore, we must find a common denominator (the set we are talking about) to add two fractions.

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## Concepts that must be mastered to add two fractions

Impossible **understand fraction addition** if you don’t remember what each fractional digit expresses. Before giving you all the keys to adding two fractions, read these definitions carefully.

## Fraction definition reminder

Fractions stated **part of a set**. This is an idea comparable to others. Therefore, we can only understand what is represented by the part, also called the quantifier, or the unit with respect to a set, also called the denominator. For example, 3/4 is a fraction where the unit 3 corresponds to the set 4. So we express three quarters .

When the denominator, which is the whole, is expressed out of 100, the fraction represents a percentage. 50/100 is a fraction that can also be expressed as a percentage, or 50%.

## What’s the numerator?

The numerator is **the first digit is expressed as a fraction**. It evokes the part, unit or proportion that someone wants to express.

For example, in the fraction 6/8, the numerator is 6.

## What is the denominator?

The denominator is the second digit in the fraction. It gives rise to the whole to which the part refers. For example, in the fraction 6/8, the denominator is 8.

Imagine what you want **compare two slices of pizza.** Your brother first cut the pizza in half, and took one slice, so he took half a slice. He tells you that you have to cut the rest of the pizza in half to get half slices as well. Do you have the faint impression of being conned? That’s normal: you don’t have a common denominator. Half a slice of pizza is not the same as half a slice of pizza.

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## How do you add two fractions?

To add two fractions, you must first relate the two fractions by a common denominator, which makes it possible to relate the two parts to the same set, therefore, to compare comparables.

## How do you add two fractions with the same denominator?

In some cases, you’re lucky, because the denominator is common.

Let’s return to the pizza example. Your mother knows that you may fight with your brother over which of the two of you will eat the most pizza. So he takes matters into his own hands and automatically cuts the pizza into 8. And he allows you and your brother to eat 6/8 of the pizza, because he wants to keep one serving for himself and one for your father.

You will be adding fractions with the same denominator. Knowing that one part is equal to 1/8, how much would you eat if you took three parts?

Just add the quantifier to get the result. In this case: 1/8 + 1/8 + 1/8 = 3/8

To add two fractions, you must first **Connect the two fractions with the same denominator.**

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## How do you add two fractions with different denominators?

that **calculate the addition of fractions with different denominators **more complicated. You must first reduce the fractions to a common denominator before adding the quantifiers.

## How to find the common denominator of two fractions?

To do this, find the least common multiple in the denominator. One of the denominators is **many of the others**. There are several scenarios.

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## With one denominator a multiple of the other denominator

For example, you need to add 3/4 + 4/8.

Knowing that 8 is a multiple of 4, you just need to reduce the fraction to its lowest denominator, which is 4.

This will give 3/4+ 2/4 = 5/4

## Both denominators have the same multiple

This way of calculating is possible if multiples that are equal to the two denominators are found in the multiplication table.

For example, we want to add 1/8 and 7/6. Knowing that 8 × 3 = 24 and 6 × 4 = 24, the common denominator is 24.

## The two denominators have no common multiple

When neither of these rules apply, the common denominator is the product of the two denominators.

## Examples of adding fractions for practice

In order to never again have the smallest portion of pizza in the family, it is best to practice by doing the concrete addition exercise.

To help you, try solving this addition while writing fractions:

- 3/8 + 6/16 =
- 2/8 + 5/6 =
- 5/5 + 2/15 =
- 2/12 + 4/12 =

Mastering addition of fractions is no mystery: it takes practice. And if you want to learn more about this idea, check out our articles on percentage calculations and cross multiplication.