Unlock the Secrets to Simple Fractions: A Beginner's Guide
I was working with another family in the afternoon, and she was saying that her son had been doing fractions for his homework and she’d had to look up what an integer was.
So, I hope this (very short) glossary helps:
Integer: whole number
Denominator: the number at the bottom of the fraction
Numerator: the number at the top of the fraction
Common denominator: when the numbers at the bottom of the fraction are the same.
If you have common denominators and you are asked to add the fraction, it becomes as simple as just adding the top numbers together, the bottom numbers stay the same.
It’s a bit like saying, I have a cake cut into 8 pieces (that’s the bottom number, the denominator).
You take 2 pieces and I take 1 piece. The number of pieces we each take are the numerators. So, how many pieces did we take altogether? 2+1 =3
So, our answer will be 3/8 Three out of the 8 pieces have been taken.
It’s the same with subtracting. If we again have a cake that has been cut into 8 pieces, By the time I get to the table, you have again taken 2 pieces, so we have 6/8 pieces left.
When the cake was whole, we had 8 pieces, you took 2, this left us with 6 out of the 8 pieces, which as a fraction would be written as 6/8.
I then come along and take1 piece. (The number of pieces we each take are the numerators).
So, how many pieces that are left now is 6/8 – 1/8 = 5/8.
If the denominators are different, things get harder as we need them to match.
When we are presented with a question such as ½ + ¾ , we have 2 options on how to solve it:
We can either double everything on the left-hand side so that we have a 4 at the bottom of the fraction like we do on the right: 2/4 +3/4
Or we can multiply everything on the left by 4 (4/8) and everything on the right by 2 (6/8)
Then we can add he numerators together to get our final answer.
In the first example the answer would be 2/4 + ¾ (2+3=5) giving us the answer 5/4
In the second example we would add 4/8 + 6/8 (4+6 =10) giving us the answer 10/8.
We are often asked to give our answer in its simplest form, so because we are left with 2 even numbers in the second fraction, we can simplify this, by halving both numbers to 5/4, giving us the same answer as the previous method.
To subtract fractions, we need to use the exact same method except instead of adding the fractions, we subtract them.
This time we could use the question: 4/5 -1/2
Because neither of the bottom numbers go into the other, we will need to multiply them together:
5x2 =10
Our denominator for this question will be 10.
I often rewrite the bottom half of the question at this stage then just fill in the blanks as I work them out:
---- - ---- = -----
10 10 10
So, because I multiplied the 5 by 2, it means that I have to multiply everything in that fraction by 2. So, 4x2 =8. This will go on the top of our first fraction:
8
---- - ---- = -----
10 10 10
Then, because we multiplied the 2 by 5, we will also need to multiply the 1 by 5. This will go on the top of our second fraction:
8 5
---- - ---- = -----
10 10 10
Now we can simply work out 8-5, which gives us an answer of 3.
8 5 3
---- - ---- = -----
10 10 10
How can we help our children to learn their fractions?
One of my favourite games that I think I have mentioned before is Jenga. I love this game.
What I would suggest is that you write a fraction on one side of each brick. Then on a separate piece of paper write down 3 or 4 other fractions and cut them into individual playing cards.
Build your Jenga tower ready to play the game.
The first person takes a brick from the tower. They then choose a playing card from the pile.
They must now calculate the answer when the fraction on the playing card and the fraction on the Jenga tower are added together.
They then replace the card to the pile and the brick to the top of the tower.
The next person has a go.
They must do the same.
The game continues with each player taking it in turns to answer a question.
When one player causes the tower to fall, the game comes to an end with the other player winning.
It’s really good fun. Enjoy!
Other suggestions include things like playing snakes and ladders with every question on the board having an adding or subtracting fractions question written on it. We’ve also created a ‘lily pads’ game where, like ‘Tiddly-Winks’ you have to flick the counter onto a lily-pad. Again, a fractions question is there for you to answer.
The person with the most lily pads at the end of the game is the winner.
We use games like this in most of our tutoring sessions because I learned many years ago that learning needs to be engaging. But additionally, if we just give our children one activity, for example a worksheet, to help them to learn we are only helping them to create one memory. So, when they need to recall that information, their brain only has one place it can go to where it will find it.
However, if we use a variety of resources, we are providing our brains with multiple memories making it easier for our brain to find the information that it needs.
I can chat about this all day.
If you’re interested, please do reach out and ask.
I hope this has been helpful.
