Adding fractions: how to add two parts?
To add parts, they must be comparable. This is the purpose of adding fractions. If your parents allow you and your sibling to eat half a pizza, but your sibling has already eaten 1/8, the following should keep you from being duped.
What is the use of adding fractions?
Adding fractions makes it possibleadd two numbers expressed in fractional form. But for that, we must first find the common denominator. Indeed, fractions express a part of a whole, a part of a whole. So you need to make sure we’re talking about the same set before adding the parts.
The size of a number (the numerator) in fractional writing is relative to the size of the unit (the integer or denominator). We therefore need to find the common denominator (the set we are talking about) to add two fractions.
The concepts to master to add two fractions
It’s impossible understanding of fractional addition if you don’t have in mind what each digit of a fraction means. Before giving you all the keys to adding two fractions, read these definitions carefully.
Recall the definition of fraction
A fraction expresses the part of a whole. It is one notion proportional to another. We can therefore only understand what the part, also called the numerator, or the unit represents with respect to a set, also called the denominator, for example 3/4 is a fraction in which the unit 3 refers to the set 4. therefore expressing three quarters.
When the denominator, i.e. the whole, is expressed out of 100, a fraction expresses a percentage. 50/100 is a fraction that can also be expressed as a percentage, i.e. 50%.
What is the numerator?
The numerator is the first digit expressed in the fraction. It evokes the part, unit or proportion that one seeks to express.
For example, in the fraction 6/8, the numerator is the number 6.
What is the denominator?
The denominator is the second digit expressed in the fraction. It evokes the whole to which the part refers. For example, in the fraction 6/8, 8 is the denominator.
Imagine you want compare two slices of pizza. Your brother first cut the pizza into two portions and took one, then he took half. He tells you that you have to cut the rest of the pizza in half to get even half a slice. Do you have the vague impression that you have been deceived? It’s normal: you don’t have the same common denominator. Half a slice of pizza does not equal half a slice of half a pizza.
How to add two fractions?
To add two fractions, you must first relate the two fractions to a common denominator, which makes it possible to relate the two parts to the same whole, thus in a sense to compare comparable things.
How do you add two fractions with the same denominator?
In some cases you are lucky, because the denominator is already common.
Let’s go back to the pizza example. Your mother knows that you could argue with your brother about which of you will eat more pizza. So she takes matters into her own hands and automatically cuts the pizza into 8s. And she allows you and your brother to eat 6/8ths of the pizza, because she wants to keep one portion for herself and one for your father.
Add a fraction with the same denominator. Knowing that one part equals 1/8, how much did you eat if you take three parts?
Just add the numerators to get the result. In this case: 1/8 + 1/8 + 1/8 = 3/8
To add two fractions, you must first relate the two fractions with a common denominator.
How to add two fractions with a distinct denominator?
the calculating a fractional addition with different denominator it’s more complicated. You must first reduce fractions to the same denominator before adding numerators.
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 multiple of the other. There are several scenarios.
With one denominator a multiple of the other denominator
For example, you need to add 3/4 + 4/8.
Knowing that 8 is the multiple of 4, you just need to reduce the fraction to the lowest denominator, which is 4.
This will give 3/4 + 2/4 = 5/4
The two denominators have a common multiple
This method of calculation is possible if in the tables there is a multiple common to the two denominators.
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 multiples
When neither of these rules apply, the common denominator is the product of the two denominators.
Examples of adding fractions to practice
To never have the smallest portion of pizza in the family again, it’s best to train by doing concrete addition exercises for fractions.
To help you, try solving these additions in fractional writing:
- 3/8 + 6/16 =
- 2/8 + 5/6 =
- 5/5 + 2/15 =
- 2/12 + 4/12 =
To master the addition of fractions, there is no mystery: it takes practice. And if you want to learn more about these concepts, check out our articles on percentage calculation and cross product.