A guide to fractions, decimals and percentages. Everything you need to know.

Fractions, Decimals and Percentages

When comparing and ordering fractions the key rule is to make sure that all of the numbers that you are comparing have the same denominator. 

You have to find the lowest common denominator (LCD)- in this case it is 12 which is a factor of both 6 and 3.

Then you change them all into that denominator, remembering that what you do to the denominator you do to the numerator.

To get from four sixths to eight twelfths you have to time both the numerator and the denominator by two. 

In this  case the two fractions are equal. 

We know that 0.36 has the same value as                   and we also know that 1% is the same as                    . This means that when we convert 0.36 to a percentage we have the answer 36%. 

Step 1. Pretend that the decimal point isn’t there so that we are left with only 45. 

Key Rule, always remember to divide by the denominator and multiply by the numerator

In this question the denominator of two thirds is three, so you have to divide the number 45 by 3 which gives you the answer 15. 

Next, you have to times the number 15 by 2 which is the numerator. This will give you the answer 30. 

An equivalent fraction is more than one fraction that are worth the same amount. 

This pizza is split in half and one of those halves have been eaten. 

This pizza is cut into quarters and this time two of the quarters have been eaten. 

This pizza is cut into eighths and this time four slices have been eaten. 

All these fractions are equivalent as in the picture you can see that they have the same amount eaten. 

To find a equivalent fraction you have to times both the numerator and the denominator by the same number. From one half to two fourths you multiplied both the numbers by 2. 

Even though one of these numbers has 4 digits and the other has 3 digits, you still have to line up the sum with the Decimals directly on top of each other. 

Subtraction also not that different, if it’s with a decimal or not. You also need to remember to put the decimal back in your answer, however apart from that everything is still the same process. 

Just like every other standard written method, the only thing you have to remember is to put your decimal place back in. 

SWM division is actually exactly the same as SWM division with a decimal. The only rule is that you have to remember to put your decimal back in your answer. 

When simplifying fractions you are aiming to find the simplest form of a fraction, using the smallest possible numbers. 

Step 1. Firstly, you have to look at both the numerator and the denominator and find the highest common factor between them. The highest common factor between 48 and 72 is 8. 

Step 2. After finding the highest common factor, you have to divide both the numerator and the denominator by that number. In this case we would divide both 48 by 8 and 72 by 8 which leaves us with 6 and 9. 

If you are unsure of what to divide them by, you can just divide by two if both the numbers are even. 

Step 3. Sometimes you can carry on dividing three or more times until you can divide no more. However in this case six ninths is the simplest form.  

You will know you have reached the simplest form when both numbers are prime numbers. 

Notice how after the decimal you add “ths” to the word to make it different. 

After the decimal place the numbers carry on however you miss out the units column and go straight onto the tenths. 

When rounding, the key rule is look at the number one column to the right. If the number is four or below you round it down, if it if five or above you round it up. 

Say you were asked to round 568.4 to the nearest whole number. Firstly, you would look to the column to the right which is the tenths column. As you can see the number in the tenths column is 4 which is rounded down. Therefore, 568.4 rounded to the nearest whole number is 568.

If you were asked to round a number to the nearest one decimal place you would still follow the same process, and look next door at the hundredths column. 

Find your place, Look next door, 4 or less, Just ignore, 5 or greater, Add one more

The answer for this question would be 568.5 because it is rounded up. 

In a mixed fraction the whole number shows how many wholes there are and the fraction shows the amount left over. 

In a improper fraction the numerator is always larger than the denominator. 

When converting a improper fraction to a mixed number you divide the numerator by the denominator which is in this case, 37 divided by 5. The answer is the whole number and the remainder would be the leftover fraction. 

When converting a mixed number to a improper fraction you have to times the denominator of the fraction (which is in this question 4) by the whole number (5), which in this case is 20. Then, you have to add on the remaining numerator (which is 1). In this question the answer would be 21 fifths. 

Multiplying and Dividing by 10, 100 and 1,000

When multiplying decimals you have to move everything however many zeros in the number you are multiplying by to the right. Do not move the decimal! The number of zeros in the number you are multiplying by- 10, 100 or 1,000- is however many zeros there are in your answer. 

The answer to this question would be 3561!

In dividing it is very similar however this time you are moving everything to the left. 

When converting percentages to fractions, all you have to to remember is that 1% is exactly the same as 

Step 1. The first thing you have to do is divide the number by 10 to find 10%. (70 divided by 10 = 7) Step 2. Once you have found 10% you have to find 40%, to do that you must times 10% by 7. (5 x 7 = 35) Now you know what 70% of 50 is... 35!

Step 1. Divide the number by 100, so that you now know what 1% is. (30 divided by 100 = 0.3) Step 2. Times whatever 1% is by the percentage which is in this case, 25. (0.3 x 25= 7.5) Now you know what’s 25% of 30-...7.5.

Here are two different yet simple ways that you can find a percentage of an amount very easily. 

Step 1. The first step is to make the denominator of the number 100. You can do that by multiplying it. You must remember that whatever you do to the bottom you do to the top. For example if you multiplied 25 by 4 to make it a hundred you must also multiply the numerator by 4. 

Step 1. Firstly you have to find 10% of 50, and to do that you must divide the number by 10. 

Step 2. Once you have found 10% (which in this case is 5) you have to times it so that it is the correct percentage ( in this case you have to multiply 5 by 4 to make it 40%). 

Step 3. Now you know what the amount is you can add on the amount to your previous price. So, £50 + £20= £70. 

Step 1. Find 10%, But this time halve it and find 5% as well. 

Step 2. Multiply the 10% by 4 to get 40% and add on the additional 5% to make it 45%. 

Step 3. Now you know what 45% is, add it on to the previous price to get the new price. 

Step 1. Much like finding a percentage increase you divide the number by 10, to find 10%. (70 divided by 10 = 7) Step 2. To find 20% you have to times the 10% by 2, to give you 20%. (7 x 2 = 14) Step 3. Now you must subtract your answer from the original price. (£70- £14 = £56)

Step 1. You still have to find 10% but this time you have to halve it to find 5% as well. Step 2. Multiply 10% by the right number to get the correct percentage and then you can add the extra 5%. Step 3. Now you know what 35% of £80 is you must subtract it from the original price.

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