How would you add 4/15 to 3/5?

4/15 and 3/5 are both fractions - a fraction is less than a whole (like a piece of cake rather than the whole cake!!)

The top number of a fraction is called a numerator and the bottom number is a denominator.

If the denominators (on the bottom) are the same- we can simply add the numerators. So 1/5 + 2/5 = 3/5.

When adding or subtracting fractions that have different denominators - we need to do a bit more work!!

We need to get the denominators to be the same. We can't just pick any old number and put it at the bottom because we can't change the value of the fraction - (we can't suddenly transform a 1/5 of a piece of cake into a 1/2 - I know - too bad!!) Soooo....

We look at the denominators and we find a number they can both divide into - a number that is in both their timetables.

1 X 15 = 15 1 X 5 = 5

2 X 15 = 30 2 X 5 = 10

3 X 5 = 15

We found it ..... 15. This is called a common denominator. Now we can't just make it 4/15 + 3/15 because that is changing the value of the second fraction.

4/15 + 3/5 = 4/15 + ?/15 = ?/15

We ask ourselves - what did we need to do to the 5 to get to a denominator of 15? We multiplied by 3. So - we do the same to the numerator ..... 3 X 3 = 9

4/15 + 3/5 = 4/15 + 9/15 = 13/15

Before we pat ourselves on the back we need to check if the fraction is in its simplest form. We do this by checking if the same number can be divided into the numerator and the denominator. I usually start with 2 - and no it can't go into either, what about 3? - no, what about 5 ? - no. - So we can safely say this is the simplest form! If the answer had been something like 10/15, then 5 goes into 10 twice and into 15 three times so the simplest form would have been 2/3.

Now have a go with the next 2. Scroll down for the answers. If you get them correct - that's great - if you don't - no worries - just look back through the example given and have another go. If you still can't quite get it - check out the link to a youtube video on adding fractions with different denominators.

https://www.youtube.com/watch?v=tDQipFjAoT8

A ) 1/4 + 2/3 =

B) 1/2 + 3/8 =

Answers:

A) 11/12

B) 7/8

If you can add fractions with different denominators you can also subtract them in the same way!!

Next time we will look at what to do with mixed numbers (whole numbers and fractions) and improper fractions (with a bigger numerator than the denominator!) - Not as hard as it might sound!

Change it so they both share the same denominator (/15's), then add across. x 4 by 3 on the top to do so.

Firstly, we need to make sure the Denominators (the bottom parts) match.

So, we can keep 4/15 as it is. But, we need to multiply both parts (the numerator and the denominator) of the other fraction by 3 (so the Denominators are the same on both fractions)

3 x 3 = 9

5 x 5 = 15

Now we have 2 fractions which are easy to add together: 4/15 + 9/15 = 13/15

Sometimes, you can simplify the final fraction, but not in this case (as 13 are 15 have no common factors! :)