How to add fractions
How to add fractions

How to add fractions with different denominators?

If the denominators are not the same, then you have to use equivalent fractions that do have a common denominator. To do this, you need to find the least common multiple (LCM) of the two denominators.

To add fractions with unlike denominators, rename the fractions with a common denominator. Then add and simplify.

How to add fractions with whole numbers?

As you may recall, a mixed number consists of an integer and a proper fraction. Any mixed number can also be written as an improper fraction, in which the numerator is larger than the denominator, as shown in the following example:

Example 1

To add mixed numbers, we first add the whole numbers together, and then the fractions.

If the sum of the fractions is an improper fraction, then we change it to a mixed number. Here's an example. The whole numbers, 3 and 1, sum to 4. The fractions, 2/5 and 3/5, add up to 5/5, or 1. Add the 1 to 4 to get the answer, which is 5.

Example 2

If the denominators of the fractions are different, then first find equivalent fractions with a common denominator before adding. For example, let's add 4 1/3 to 3 2/5. Using the techniques we've learned, you can find the least common denominator of 15. The answer is 7 11/15.

Subtracting mixed numbers is very similar to adding them. But what happens when the fractional part of the number you are subtracting is larger than the fractional part of the number you are subtracting from?

Here's an example: let's subtract 3 3/5 from 4 1/3. First you find the LCD; here it's 15.

4 1/3 - 3 3/5

4 5/15 - 3 9/15


Write both fractions as equivalent fractions with a denominator of 15.

3 + 1 5/15 - 3 9/15

3 + 20/15 - 3 9/15


Since you're trying to subtract a larger fraction from a smaller one, you need to "borrow" a one from the integer 4, change it to 15/15, and add it to the fraction.

3 20/15 - 3 9/15



Now the answer is 11/15.

How to add fractions with the same denominators?

To add fractions, the denominators must be equal. Complete the following steps to add two fractions.

  1. Build each fraction (if needed) so that both denominators are equal.
  2. Add the numerators of the fractions.
  3. The new denominator will be the denominator of the built-up fractions.
  4. Reduce or simplify your answer, if needed.
  5. Factor the numerator.
  6. Factor the denominator.
  7. Cancel-out fraction mixes that have a value of 1.
  8. Re-write your answer as a simplified or reduced fraction.

REMEMBER: We DO NOT add denominators

That’s all there is to it!

What is a Fraction?

Definition Of fractions:- A fraction is a part of a whole number, and a way to split up a number into equal parts. It is written as the number of equal parts being counted, called the numerator, over the number of parts in the whole, called the denominator. ... The size of fractions can also be compared to find the smallest or the largest fraction.

What Are the Types of fractions?

Based on numerator and denominator, apart from these three major types of fractions, there are three more types of fractions namely like & unlike fractions and equivalent fractions. Hence, there are in total six types of fractions as:

  1. Proper fraction
  2. Improper fraction
  3. Mixed fraction
  4. Like fractions
  5. Unlike fractions
  6. Equivalent fractions

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