Everything you need to know about fractions
LikeAs a tutor for maths, I often find that KS1 and KS2 maths students struggle with understanding fractions, so I´ve created this simple guide that allows you to increase your understanding of the world of fractions.
What are fractions?
Imagine you have an object, perhaps a circle. The fraction 3/5 means that you if you split the circle into 5 equal pieces, you would have 3 of them. It helps to draw it out - lets use D's as the pieces.
There are 5: D D D D D
We have 3: D D D
I always think that it should be just over half of the circle (as 3 is just over half of 5), you can use your initiative to check whether your answer seems right.
Fractions to decimals
To convert a fraction to a decimal, follow this:
3/7
A decimal is always out of a total of 1, so we need to work out what 3/7 of 1 is, which will give us the answer. First, we must divide 1 by 7, as 7 is our bottom number. Then, we must multiply our answer by 3 as we have 3 of those 7ths. As such: 1 divided by 7 = 0.14. 0.14x3=0.42. Therefore 3/7 = 0.42. Remeber, we can see that 0.42 is just under half of 1, and 3/7 is also just under half, so we can use our initiative to check this and it seems right.
Fractions to percentages %
The same as a decimal, but instead of being out of 1, % are always out of 100. Therefore, we use the same procedure as with a fraction, but divide 100 by our bottom number instead of 1.
Adding/subtracting fractions
This requires getting the bottom number the same, and then adding or subtracting the top number from the other. i.e.
3/5 + 4/6
First, we must make both fractions out of the same number. The easiest way? Muliply our two bottom numbers togther:
5x6 = 30
Now our fractions are out of 30.
When we multiply the bottom, we must also multiply the top by THE SAME.
So to get our first fraction from /5 to /30, we had to multiply 5 by 6. So lets do it to the top too.
3x6/5x6 = 18/30
To get our second, we had to multiply 6 by 5, so lets do the same to the top
4x5/6x5 = 20/30
Now we can add them becasue they are out of the same number.
18/30 + 20/30 = 38/30 OR 1 and 3/30ths WHY? because 30/30 = 1, so we can simplify. We can also simplify further, because 8/30 is not the simplest form of this fraction. We can divide it by 2, so the answer is 1 and 4/15ths.
The same goes for subtraction, we follow the same procedure, finding a common BOTTOM NUMBER and subtracting the TOP NUMBERS. We call the top number the numerator and the bottom number the denominator, but don't let it be complicated!
I hope this makes sense, if anyone needs further explanation please feel free to reach out to me for private maths lessons. I can also show how to multiply and divide fractions, it follows a very similar pattern to adding and subtracting.
Thanks! Jack