When including fractions there are 4 essential issues you have to know and it is extremely essential to maintain these in thoughts to keep away from frequent pitfalls.

• You can not add the denominators!
• You’ll be able to solely add the numerators!
• You’ll be able to add the numerators solely when the denominators are the identical!
• If the denominators are usually not the identical, search for a typical denominator earlier than including the numerators.

## Why cannot you add the denominators when including fractions?

Let’s illustrate why it doesn’t make sense so as to add the denominators utilizing a straightforward instance. The determine beneath exhibits the flawed method so as to add 1 / 2 and 1 / 2. This error is sort of frequent when studying fractions for the primary time!

 Discover that   1 + 1 / 2 + 2
 Discover that   1 + 1 / 2 + 2

In accordance with the determine above, should you may add the denominators, it could imply that including half and half will nonetheless give half. Does this make sense? After all not!

 ≠   1 + 1 / 2 + 2
 ≠   1 + 1 / 2 + 2

Everyone knows that half a pizza plus one other half of the identical pizza is the same as 1 pizza as the next determine exhibits. What have we realized up to now?

• You’ll be able to solely add the numerators when the denominators are the identical for each fractions.
• Since we do not add the denominators, the denominator stays the identical.

Instance #1

Observe that each fractions have the identical denominator, which is 2. This implies you’ll be able to add the numerators (3 + 1 = 4) and your denominator will keep the identical.

4
/
2

=   2

Observe that each fractions have the identical denominator, which is 2. This implies you’ll be able to add the numerators (3 + 1 = 4) and your denominator will keep the identical.

4
/
2

=   2

## What can we do then when including fractions with totally different denominators?

When the denominators are totally different. you have to discover equal fractions that give a typical denominator for each fractions.

Did you make the next observations for instance #2 beneath?

• The denominator just isn’t the identical for each fractions, so we can not add 2 and three to get 5.
• It’s worthwhile to search for a typical denominator after which you’ll be able to add the numerators.

For those who multiply the numerator and the denominator of two / 3 by 2, you’ll get 4 / 6

 is an equal fraction for and it has the identical denominator as

 What you might be actually including is (Add 4 and three and the reply is

Our closing instance will likely be so as to add the next:

Discover that it isn’t straightforward to multiply one denominator by a quantity to get the second denominator as we did earlier than in instance #2.

To get the identical denominator, here’s what it’s best to do as a substitute:

 Multiply the numerator and denominator for
 Multiply the numerator and denominator for
 You’ll get

22
/
20

We present the maths on the identical line:

Verify additionally Including combined numbers

For those who multiply the numerator and the denominator of two / 3 by 2, you’ll get 4 / 6.

 is an equal fraction for

It has the identical denominator as

3
/
6

 What you might be actually including is

Add 4 and three and the reply is

7
/
6

Our closing instance will likely be so as to add the next:

Discover that it isn’t straightforward to multiply one denominator by a quantity to get the second denominator as we did earlier than in instance #2.

To get the identical denominator, here’s what it’s best to do as a substitute:

Multiply the numerator and denominator for 3 / 5 by 4.

Multiply the numerator and denominator for 2 / 4 by 5

 You’ll get

22
/
20

We present the maths on the identical line:

For those who perceive the lesson about varieties of fractions and the lesson about evaluating fractions, this lesson will likely be straightforward to observe.

## Including fractions quiz. See if you will get 100%

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