If the bottoms of the fraction (the denominators) are the same, you simply add or subtract the tops (numerators). Do not add or subtract the denominators. For example: If the denominators are not the same, we need to make them the same. We can multiply or divide (not add or subtract) to do this. Remember, whatever we do to the bottom of a fraction we also do to the top. Like this: Here we multiply the first fraction by 2 top and bottom to make the denominators 10 on both fractions.

Sometimes we have to change both fractions to find a common denominator, like this: We can’t make 3 into 7 or 7 into 3, so we turn them both into 21. We multiply the first fraction by 7 and the second by 3.

## Multiplying and Dividing Fractions

To multiply fractions, just multiply the tops and multiply the bottoms. Like this: To divide fractions, we need to flip the second one upside down then multiply. Like this: Sometimes the word ‘of’ is used instead of ‘x’.

## Simplifying Fractions

Questions often ask you to ‘give your answer in the simplest form’. That means you need to know how to simplify fractions to get the final mark.

Simplifying fractions just means finding a number that goes into both the top and bottom of the fraction and dividing by it. Keep repeating until you can’t go any further. For example: Here we divide top and bottom by 2 first and then by 7. We can’t go any further.

## Improper Fractions and Mixed Numbers

To turn a mixed number into an improper (top heavy) fraction, multiply the denominator by the whole number and add the top of the fraction. Like this: Turning an improper fraction into a mixed number is the opposite process. Divide the top by the bottom to get the whole number and use the remainder as the top of the fraction part of the answer: When adding or subtracting mixed numbers, you can either turn both numbers into improper fractions before you start or you can do the whole numbers and the fractions separately and combine the results. I like to do whole numbers and fractions separately whan adding but prefer to convert to improper fractions first when subtracting.

When multiplying or dividing mixed numbers, you must turn them into improper fractions first.

1. Maths
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3. National 5 Maths
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5. National 5 Fractions
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7. National 5 Fractions Revision