Fractions for Parents part 1
If your child is starting fractions at school and you realise that you have forgotten everything you once knew on fractions then this is for you.
Fractions recap part 1 (Header)
1. Terminology (header)
A very quick terminology recap: the number on top of the fraction is the numerator and the number below the line is the denominator.
If the number on top is bigger than the one below then we have an improper fraction. (7/4). And if it’s a number written next to a fraction it’s called a mixed numeral.
2. Simplifying fractions (header)
Here is six tenths. This fraction can be simplified because both the numerator and the denominator can be divided by the same number – in this case 2. Six divided by 2 is 3 and 10 divided by 2 is 5: Three fifths can’t be simplified any further because apart from 1 you can’t divide both 3 and 5 by the same number and arrive at a whole number.
If your child struggles with this concept, you might like to use pizza to help explain.
This is a quarter (or a fourth) of a pizza. Now we have 2 quarters of a pizza. But it’s clear from just looking at it that 2/4 of a pizza is the same as half a pizza.
If the denominators are the same then addition is very easy – you just add the numerators.
For example, what is three sevenths plus two sevenths? The denominators are the same, so we just add the numerators together to get 5: the answer is five sevenths.
If the denominators aren’t the same you need to find a common denominator.
For example what is one sixth plus one quarter.
Now, the lowest common denominator is the lowest number that is a multiple of both denominators. Many of you will instantly know that 12 is the lowest common denominator here: as 12 is divisible by both 4 and 6, but no lower number is.
However, if you’re not sure – or if your child is not sure – a foolproof way is to simply multiply the denominators as this guarantees that the new denominator will be a multiple of both. So in this case, it’s six times four which is 24.
I’ll do this sum using both methods. First, with 12 as the common denominator:
We had to multiply six by 2 to get 12, so we also multiply the numerator by 2 and one sixth becomes two twelfths. We had to multiply 4 by 3 to get to 12, so we multiply this numerator by 3: 3 quarters becomes 9 twelfths.
Now we have the same denominator so we can add the numerators. 3 plus 9 = 11. The answer is 11 twelfths.
Now using the other method.
We multiplied 6 by 4 to get 24, so we also multiply the numerator by 4, giving us 4. And for this one we multiplied 4 by 6 to get to 24 so we multiply the numerator by 6, giving us 18.
Now we can add the numerators to give us 22 over 24.
Both 22 and 24 are divisible by 2, so we can simplify: 22 divided by 2 is 11and 24 divided by 2 is 12 – giving us the same answer as above: 11/12.
4. Improper fractions and mixed numerals
Let’s do a simple sum: 4/5 plus 3/5. The denominator is the same so we can just add the numerators giving us an answer of seven fifths.
This is an improper fraction; there is nothing wrong with this, but usually it is peferable to express it as a mixed number.
Conceptually, once we reach five fifths we have a whole number. That leaves us with 2 fifths left over, so we can write it as 1 and 2 fifths.
Here’s a more complex example: Convert 25/7 to a mixed numeral.
The process is to divide 25 by 7. Given that 3 times 7 = 21, the answer is 3, with 4 left over. So of our original 25 sevenths, 21 of the sevenths equals 3, and there are 4 sevenths left over. So the mixed numeral is 3 and 4 sevenths.
Again, if your child is having difficulty with the concept of mixed numerals, pizza can help.
Imagine 3 halves of a pizza: 1 half is here, another half is here and another half is here. Thus we have 3 over 2, 3 halves of pizza, but by looking at the picture it is clear that another way of saying this is that we have one and a half pizzas.
Okay, that’s enough fractions for the moment – I’m going to have a pizza!