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Monday, March 27, 2023

# Including Fractions with the Identical or Completely different Denominators

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

• You can not add the denominators, additionally known as backside numbers!
• You may solely add the numerators, additionally known as prime numbers!
• You may add the numerators solely when the denominators are the identical!
• If the denominators will not be the identical, search for a standard denominator earlier than including the numerators.

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

Let’s illustrate why it does not make sense so as to add the denominators utilizing a straightforward instance. The determine under reveals the mistaken means so as to add 1 / 2 and 1 / 2. This error is sort of widespread when studying fractions for the primary time! Discover that   1 + 1 / 2 + 2

 Discover that   1 + 1 / 2 + 2

In keeping with the determine above, if you happen to might 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 reveals. What have we realized to this point?

• You may 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 will we do then when including fractions with completely different denominators?

When the denominators are completely different. you have to discover equal fractions that give a standard denominator for each fractions. All you have to do is the search for the least widespread a number of (LCM) of the denominators.

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

• The denominator shouldn’t be the identical for each fractions, so we can not add 2 and three to get 5.
• You could search for a standard denominator after which you’ll be able to add the numerators.

Since 6 is the least widespread a number of of three and 6, you need to use 6 as a standard denominator.

If you happen to 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

Instance #3 will probably be so as to add the next:

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

As a rule of thumb, when the denominators would not have any widespread issue(s), you’ll be able to simply multiply them to get a standard denominator. Since 4 and 5 don’t have any widespread components, the widespread denominator is 4 occasions 5 = 20.

To get the identical denominator, here’s what it is best to do:

 Multiply the numerator and denominator of

 Multiply the numerator and denominator of

 You’re going to get

22
/
20

We present the maths on the identical line:

 is an equal fraction for

It has the identical denominator as

3
/
6

 What you might be actually including is

7
/
6

Instance #3 will probably be so as to add the next:

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

As a rule of thumb, when the denominators would not have any widespread issue(s), you’ll be able to simply multiply them to get a standard denominator. Since 4 and 5 don’t have any widespread components, the widespread denominator is 4 occasions 5 = 20.

To get the identical denominator, here’s what it is best to do:

Multiply the numerator and denominator of three / 5 by 4.

Multiply the numerator and denominator of two / 4 by 5

 You’re going to get

22
/
20

We present the maths on the identical line:

## Including fractions with entire numbers

Listed below are the steps to comply with when including a fraction to an entire quantity.

Step 1

Convert the entire quantity right into a fraction. You do that through the use of 1 as a denominator for the entire quantity.

Step 2

Search for the bottom widespread denominator. You simply have to multiply 1 and the opposite denominator to get the bottom widespread denominator.

Step 3

Multiply the numerator and the denominator of the fraction in step 1 by the bottom widespread denominator.

Step 4

Instance #4

3/5 + 8 = 3/5 + 8/1 = 3/5 + 40/5 = (3 + 40)/5 = 43/5

If you happen to perceive the lesson about sorts of fractions and the lesson about evaluating fractions, this lesson will probably be simple to comply with. Examine additionally fractions worksheets, the place yow will discover a wide range of worksheets about addition, subtraction, multiplication, and division of fractions in PDF format.