Fractions, Decimals and Percentages

Simplifying Fractions

How to Find a Fraction of an Amount

Comparing and Ordering Fractions

Fractions

Equivalent Fractions

Mixed and Improper Fractions

How to Find a Fraction of a Amount?

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

This method works for any question.

Step 1.

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.

Step 2.

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

Comparing and Ordering Fractions

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.

Comparing

In this case the two fractions are equal.

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Mixed and Improper Fractions

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

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Remember: the denominator never changes

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

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Improper to Mixed Fractions

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Mixed to Improper Fractions

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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.

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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.

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Equivalent Fractions

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

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Ex.

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

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

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

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

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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.

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Simplifying Fractions

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

Ex.

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.

Rounding

Multiplying by 10, 100 and 1,000

Place Value

Decimals

Dividing by 10, 100 and 1,000

SWM with Decimals

Place Value

Hundreds

Tens

Units

Decimal

Tenths

Hundredths

Thousandths

and so on...

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.

Rounding

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.

Key Rule:

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.

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.

35.61 x 100 =...

Two zeros, two places along..

Dividing

The answer to this question would be 3561!

35.61 divided by 10 =...

A. 3.561

1 zero, 1 place...

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