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.

The right way to add fractions!

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.
The reply is  

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.
The reply is  

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

Simply add 12 and 10 and your reply is   

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

Simply add 12 and 10 and your reply is   

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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