Get your Math Help with Fractions

Why do fractions have such a bad reputation? Why do we hate fractions so much?

To be honest and frank, we are simply not taught it properly at primary school. And to be blunt again...primary school teachers can't even articulate maths to little kids that REALLY don't want to be there in the first place.

Who's fault is it? Teachers that can not articulate or kids that don't want to be there? I will let you be the judge of that!

We will try to clear up some of the concepts here with a definition and an example. If you feel it is not articulated adequately, thats okay, because I'm not even a teacher to start with!


The numerator and denominator – These are the fancy names given to the top and bottom part of a fraction.

The denominator is the bottom part of the fraction. This number tells us how many pieces we have altogether. In this example, our cake is cut up into 4 pieces. Therefore the bottom number (the denominator) will be 4.

frac-cir-1-4
The numerator is the top part of the fraction. This bit usually tells us how many parts we want to talk about.

So, if we were to eat 1 part of that cake, then the top number will be 1.

so, if we were to write what fraction of this cake is eaten, we would write 1/4.

If we were to write what fraction of the cake is not eaten, then we would write 3/4




Basic Fractions

Writing one number as a fraction of another
To do this we need to make the units the same before we write the fraction.

For example how do we write 10 minutes as a fraction of an hour? To start with, we need to change the hour into minutes. There are 60 minutes in an hour. So, 60 minutes is our bottom number.

Then to work out the fraction, the top number is what we are looking for i.e. 10 minutes.

So, 10 minutes as a fraction of an hour is 10/60.

Try these questions

(A) write the first amount as a fraction of the second amount, the answers are at the bottom of the page:


1. 5 minutes, 1 hour

2. 20p, £3

3. 25 seconds, 4 minutes

4. 4 cm, 2m

More Fractions
We tend to get confused when math questions are wordy. But sometimes they are actually more helpful.

Example 1

Find 1/3 of 12

If you can do this question, then great! What are you doing here in the first place? Otherwise, lets explain this question in more lame terms. Another way to explain this question using an example would be:

Arifa has 12 sweets. She is sharing them equally with her 3 friends. How many do her friends get?

third of 12 equal 4 In other words we divide by 3 to get 1/3
So, they get 4 sweets



Another way to explain these kind of questions is to change the 'of' into a multiplication, then it looks like this

third times 12 we can either cross multiply or cancel/simplify the diagonal numbers such as the 3 and 12 (these will be explained further in multiplication of fractions)


Example 2

Find 2/3 of 15

To answer this type of question, there is two steps to do. The first step, we do exactly the same as above. Divide 3 into 15. This gives us 5.

The next step we multiply 2 by 5. As the top number is 2, therefore there is two lots of 5. So 2 times 5 gives us 10.



15 sweets If we try and articulate this using sweets and pictures. We divide the 15 sweets by 3 which gives us 5.

So we end up with 3 groups and in each group there is 5 sweets in them.

We then find 2 lots of these groups. 1 lot will give us 5. 2 lots will give us 10.



Try these questions (answers are at the bottom of the page):

(B) Find:

1. 1/4 of 20 marbles

2. 1/5 of an hour in minutes

3. 4/5 of 10 biscuits

4. 3/8 of 16 cans

More difficult answers
Sometimes we do not always get whole numbers as answers to theses questions. For example
Kate, Ben, Zayd and Taahirah have 7 cakes. They want to share them out equally.

How many will each person get?


To start they each take a whole cake.
There are only three cakes left. There's not enough cakes for them to have a whole one each.

Since there are 4 of them, they cut the rest of the cakes into quarters.



We end up with 12 little pieces.

Each person then gets 3 quarters

Altogether, each person gets cakes.



Answers:

(A)

1. 5/60

2. 20/300 (changing £3 into pence)

3. 25/240 (change 4 minutes into seconds, there are 60 seconds in a minute, so 6 times 4 gives the bottom number)

4. 4/200 (change meters into centimeters, 1 m is equal to 100 cm, therefore 2m = 200 cm)


(B)

1. 5 marbles

2. 12 minutes

3. 8 biscuits

4. 12 cans



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