How to Add Fractions? – A Complete Guide

Adding fractions is quite different from simple addition in mathematics. A sum in math means combining whole numbers or amounts to find a total. On the other hand, adding fractions requires a specific approach to solve.

It is an important arithmetic operation that is essential for solving problems in various scenarios like measuring ingredients in a recipe, estimating dimensions, or calculating distances.

In this blog, we will guide you about everything related to the addition of fractions. So, keep reading!

Adding Fractions

Imagine a pizza divided into 4 equal slices. You have a slice of pizza that's 1/4th of the whole, and your friend has two pieces that are 2/4th of the same pizza. So, how much pizza do you have together? It is simply about figuring out the total of two portions of the same thing. When we add two or more fractions, it is equivalent to asking

"If we put these fractional parts together, what total portion do we get?"

How to Add Fractions?

Before you start to add fractions, first analyze the denominators, which represent the whole. If both portions have the same denominator, then the process is quite easy. You just need to add the numerators of both parts, and the denominator will remain the same. That's it.

But, addition will get a little tricky if the denominators are different. In this case, you have to create equivalent fractions with the same denominators. We will discuss this in the next section. For now, here is a general way of solving fractions.

Add 1/3 and 2/3

Step 1: Check the Denominators

First, look at the denominators (the bottom numbers) of the fractions you want to add. Here, both are 3 and 3.

Step 2: Find a Common Denominator

If the denominators are different, you will need to convert the ratios to the same denominator. The easiest way to do this is to find the least common multiple of the denominators. In this example, this step is not required.

Step 3: Add the Numerators

Now, simply add the numerators. Keep the denominator the same: 1/3 + 2/3 = 3/3.

Step 4: Simplify (if possible)

If the resulting amount can be simplified, you can reduce it to its lowest terms. This means dividing both the numerator and denominator by their greatest common factor (GCF). 3/3 will become 1.

So, adding 1/3 and 2/3 will return 1.

Adding Fractions with Like Denominators

When each portion has the same denominator, adding them is the simplest! Since the denominators are the same, you don't need to change them. The denominator of your answer will be the same as the denominators of the fractions you're adding. Then, you have to add up and simplify the numerators (the top numbers).

Let’s make this concept clear with a sum:

We are adding  3/8 and 2/8. These are like fractions due to the same denominator. 

⇒ 3/8 + 2/8

The denominator will remain unchanged, and we will add the numerator.

⇒ 3+2/8

⇒ 5/8

Therefore, 3/8 + 2/8 = 5/8.

Adding Fractions with Unlike Denominators

To combine fractions with unlike denominators, we require an extra step. All you need to do is express the fraction with a like denominator before adding the numerators.

Below are the steps to add two unlike fractions.

1. Convert each fraction to an equivalent fraction with the common denominator. To do this, multiply both the numerator and denominator of each fraction by the same number so that the denominator matches the least common multiple.
2. Once the fractions have the same denominator, add the numerators.
3. Keep the common denominator.
4. If the resulting fraction can be simplified, reduce it to its lowest terms.

Let’s learn it through an example.

We will add unlike fractions  13 and 14 with different denominators.

⇒ 1/3 + 1/4

Now, we will take LCM of 3 and 4 which is 12.

Now, we will convert the fractions

⇒ 1/3 = (1 x 4) / (3 x 4) = 4/12

⇒ 1/4 = (1 x 3) / (4 x 3) = 3/12

Then, we will add the numerators:

⇒ 4+ 3/12

⇒ 7/12

So, 1/3 + 1/4 = 7/12.

Note: To add a whole number to a fraction, express the whole number as a fraction with a denominator of 1. Then, follow the same steps, to sum up the two fractions. No need to stress about adding different types of fractions, let the Fraction Calculator handle the work for you!

Addition of Mixed Fractions

Mixed fractions combine whole numbers and fractions. Adding them requires a little extra attention, but it's easily manageable with a step-by-step approach.

Adding Mixed Numbers with Like Denominators

The process is quite simple when mixed numbers have the same fractional denominators. Below are the steps to add mixed numbers with like denominators.

1. First, add the whole number parts of the mixed numbers together.
2. Then, add the fractional parts together. The common denominator will remain the same.
3. Add the sum of the whole numbers and the sum of the fractions.

We will solve mixed fractions with the same denominators to elaborate it further.

2¹⁄₅ and 3²⁄₅

⇒2¹⁄₅ + 3²⁄₅

⇒ 2 + 3 = 5 (Adding the whole numbers)

⇒ 1/5 + 2/5 = 3/5  (Adding the fractions)

⇒ 5³⁄₅ (Combined results)

Hence, 2¹⁄₅ + 3²⁄₅ = 5³⁄₅.

We can solve it further like so:

5³⁄₅ ⇒ 2⁸⁄₅

Adding Mixed Numbers with Unlike Denominators

When mixed numbers have different fractional denominators, you need to find a common denominator for the fractional parts before adding. It involves the following steps.

1. Find the lowest common multiple denominators of the fractional parts.
2. Convert the fractional parts to equivalent fractions with the common denominator.
3. Add the whole number of parts together.
4. Add the fractional parts together in the sum.
5. Like the previous instances, combine the sum of the whole numbers and the sum of the fractions.

Now, we will solve mixed fractions with different denominators to elaborate it further.

Add 1¹⁄₆ and 2¹⁄₃

⇒ 1¹⁄₆ + 2¹⁄₃

First, we will separate the whole numbers from the fraction for simplification. And then, we will solve them separately.

⇒ 1 + 2 = 3 (Adding the whole numbers)

Now, we will solve the fraction part

⇒ 1/6 + 1/3 

The lowest common multiple of 6 and 3 is 18.

Convert the fractions

⇒ 1/6 = (1 x 3) / (6 x 3) = 3/18

⇒ 1/3 = (1 x 6) / (3 x 6) = 6/18

 ⇒ 3/18 + 6/18 = 3+ 6/18

⇒ 9/18

Combine the resulting whole number and fraction ⇒ 3⁹⁄₁₈

Thus, 1¹⁄₆ + 2¹⁄₃ = 3⁹⁄₁₈

Practice Questions for Learners to Add Fractions

We have provided a step-by-step guide for adding each type of fraction. So, here are some questions for practice. We have also added the answer at the end, which you can match after solving.

Fractions with Like Denominators:

1. 1/5 + 2/5 = ?
2. 3/7 + 2/7 = ?
3. 4/9 + 1/9 = ?
4. 5/11 + 3/11 = ?
5. 2/6 + 3/6 = ?

Fractions with Unlike Denominators:

1. 1/2 + 1/4 = ?
2. 1/3 + 1/6 = ?
3. 1/4 + 1/5 = ?
4. 2/3 + 1/5 = ?
5. 3/8 + 1/4 = ?

Mixed Numbers with Like Denominators:

1. 1¹⁄₃ + 2¹⁄₃ = ?
2. 3²⁄₇ + 1³⁄₇ = ?
3. 2⁴⁄₉ + 3²⁄₉
4. 4¹⁄₅ + 2³⁄₅ = ?
5. 1⁵⁄₁₁ + 3⁴⁄₁₁ = ?

Mixed Numbers with Unlike Denominators:

1. 1¹⁄₂ + 2¹⁄₄ = ?
2. 2¹⁄₃ + 1¹⁄₆ = ?
3. 3¹⁄₄ + 1¹⁄₅ = ?
4. 1²⁄₃ + 2¹⁄₅ = ?
5. 2³⁄₈ + 1¹⁄₄ = ?

Fractions and Whole Numbers:

1. 3 + 1/2 = ?
2. 2 + 2/5 = ?
3. 1/4 + 5 = ?
4. 4 + 3/7 = ?
5. 2/9 + 6 = ?

Bonus Challenge Questions:

1. 1/2 + 1/3 + 1/6 = ?
2. 2¹⁄₄ + 1¹⁄₃ + 3¹⁄₆ = ?
3. If you have 1/3 of a cake and your friend has 2/9 of the same cake, how much cake do you have together?
4. A recipe calls for 1¹⁄₂ cups of flour and 3/4 cup of sugar. How many cups total are needed?

Answer Key

Fractions with Like Denominators:

1. 3/5
2. 5/7
3. 5/9
4. 8/11
5. 5/6

Fractions with Unlike Denominators:

1. 3/4
2. 1/2
3. 9/20
4. 13/15
5. 5/8

Mixed Numbers with Like Denominators:

1. 3²⁄₃
2. 4⁵⁄₇
3. 5⁶⁄₉(or 5²⁄₃)
4. 6⁴⁄₅
5. 4⁹⁄₁₁

Mixed Numbers with Unlike Denominators:

1. 3³⁄₄
2. 3¹⁄₂
3. 4⁹⁄₂₀
4. 3¹³⁄₁₅
5. 3⁵⁄₈

Fractions and Whole Numbers:

1. 3¹⁄₂
2. 2²⁄₅
3. 5¹⁄₄
4. 4³⁄₇
5. 6²⁄₉

Bonus Challenge Questions:

1. 1
2. 6⁷⁄₁₂
3. 5/9
4. 2¹⁄₄