How to Add Fractions Between Them: 13 Steps

2024 Author: Samantha Chapman | [email protected]. Last modified: 2023-12-17 09:13

Knowing how to add fractions is something that can be very useful. Not only because it is part of the school curriculum - from elementary to high school - but also because it is a practical skill. Read on to learn more. In a few minutes you will be an expert.

Steps

Method 1 of 2: Adding fractions with the same denominator

Step 1. Check the denominators (bottom numbers) of each fraction

If the numbers are the same, then you are working with fractions that have the same denominator. Otherwise, skip to the section below.

• Here are two problems that we will work on in this section. In the last step, you will be able to understand how they were added together.
• Example 1: 1/4 + 2/4
• Example 2: 3/8 + 2/8 + 4/8

Step 2. Take the two numerators (top numbers) and add them together

The numerator is the number at the top of the fraction. Regardless of the number of fractions, if they all have the same bottom number, add the top numbers together.

• Example 1: 1/4 + 2/4 is our equation. 1 and 2 are the numerators. So 1 + 2 = 3.
• Example 2: 3/8 + 2/8 + 4/8 is our equation. 3 and 2 and 4 are the numerators. From here 3 + 2 + 4 = 9.

Step 3. Start putting the new fraction together

Take the sum of the numerators found in Step 2; this sum will be the new numerator. Take the denominator the same in all fractions. Leave it as it is. This is the new denominator. In the case of the sum of fractions with the same denominator, it will always remain the same as the old denominator.

• Example 1: 3 is the new numerator and 4 the new denominator. The result will be 3/4. 1/4 + 2/4 = 3/4.
• Example 2: 9 is the new numerator and 8 the new denominator. The result will be 9/8. 3/8 + 2/8 + 4/8 = 9/8.

Step 4. Simplify if necessary

Simplify the new fraction so that it is written in the simplest form possible.

• If the numerator is greater of the denominator, as in example 2, we can remove at least an integer. Divide the number above by the number below. When we divide 9 by 8, we will have 1 and the remainder of 1. Put the whole number in front of the fraction and the remainder as the numerator of the new fraction, leaving the denominator unchanged.

9/8 = 1 1/8

Method 2 of 2: Adding fractions with different denominators

Step 1. Check the denominators (bottom numbers) of each fraction

If the denominators are different numbers, then you are dealing with different denominators. You will have to find a way to make the denominators equal to each other. This guide will help you.

• Here are two problems that we will work on in this section. In the last step, you will be able to understand how they were added together.
• Ex. 3: 1/3 + 3/5
• Ex. 4: 2/7 + 2/14

Step 2. Find a common denominator

You will need to find a multiple of both denominators. An easy method is to multiply the two denominators together. If one of the two numbers is a multiple of the other, you will only need to multiply one of the fractions.

• Example 3:

  3 x 5 = 15. Both fractions will have a denominator equal to 15.

• Ex. 4:

  14 is a multiple of 7. We will then simply have to multiply 7 by 2 to get 14. Both fractions will have a denominator equal to 14.

Step 3. Multiply both numbers in the first fraction by the bottom number in the second fraction

We do not change the value of the fraction, but simply its appearance. It is always the same fraction.

• Example 3:

  1/3 x 5/5 = 5/15.

• Ex. 4:

  For this fraction, we just need to multiply the first fraction by 2, because this gives us the common denominator.

  2/7 x 2/2 = 4/14

Step 4. Multiply both numbers of the second fraction by the bottom number of the first fraction

Again, we do not change the value of the fraction, but simply its appearance. It is always the same fraction.

• Example 3:

  3/5 x 3/3 = 9/15.

• Ex. 4:

  It is not necessary to multiply the second fraction as well, because both fractions already have common denominators.

Step 5. Place the two fractions with the new numbers close together

We haven't added them up yet, but we will soon! What we did was to multiply each fraction by the number 1. Our goal was to have the same denominators.

• Example 3:

  instead of 1/3 + 3/5, we have 5/15 + 9/15

• Ex. 4:

  instead of 2/7 + 2/14, we have 4/14 + 2/14

Step 6. Add the numerators of the two fractions together

The numerator is the top number of the fraction.

• Example 3:

  5 + 9 = 14. 14 will be our new numerator.

• Ex. 4:

  4 + 2 = 6. 6 will be our new numerator.

Step 7. Take the common denominator found in step 2 and put it at the bottom, under the new numerator

Or, use the denominator found in the changed fractions - it's the same number.

• Example 3:

  15 will be the new denominator.

• Ex. 4:

  14 will be the new denominator.

Step 8. Write the new numerator at the top and the new denominator at the bottom

• Example 3:

  14/15 is the result of 1/3 + 3/5 =?

• Ex. 4:

  6/14 is the result of 2/7 + 2/14 =?

Step 9. Simplify and reduce

Simplify by dividing both the numerator and denominator by the greatest common factor of each number.

• Example 3:

  14/15 cannot be simplified.

• Ex. 4:

  6/14 can be reduced to 3/7 by dividing both the numbers above and below by 2, the greatest common factor.

Advice

• You must always have the same denominators before adding the numerators.
• Do not add the denominators. Once you find a common denominator, don't change it.