Strange as it might seem, adding and subtracting fractions is little bit harder than multiplying and dividing them, because before we can add or subtract fractions, we have to do a little bit more work.

We all know that a half plus a half equals a whole:

Because each of the fractions on the left are “halves”, we can just add up the numerators to give this answer. Just a note here, whenever the numerator and the denominator are equal, we have “one whole”, and it doesn’t matter how big the numbers are, if they are the same, we have “one whole”. To add and subtract fractions we have to make sure first of all that the denominators of the same.



Now this is a slightly different case, here we just can’t simply add up 5 and 2 because our denominators aren’t the same. We need to make the denominators the same, this is called “finding a common denominator” and it involves finding a number that we can multiply one or both of the denominators by to make them the same. Now in this particular case it is quite easy, if we multiply the denominator 3 x 2, we have a denominator of 6 but we also have to remember to multiply the numerator by 2 otherwise we have changed the value of the fraction.



Now we have this expression:



from here we can add up the numerators (notice that we don’t have to add up the denominators) and this gives us the following improper fraction which we would then have to convert to a mixed number:



Notice that when we converted our improper fraction into a mixed number, we were able to simplify the fractional part. Whenever possible, this is should always be done.

When we subtract one fraction from another, we do exactly the same thing with the denominators if they are not already equal, and then subtract one of the numerators from the other. I will use the same fractions as above, but this time carry out a subtraction:



Step 1 - find the common denominator and convert:



In this particular case we have finished, the answer is 1/6.


Exercises


Carry out these additions and subtractions, simplify your answers as mixed numbers and / simplest form fractions: