Fractions



Fractions

A fraction is simply another way of writing a division.

e.g. [pic]

If you are asked to write a fraction as a decimal number then all you need to do is perform the division, either on a calculator or using short division.

e.g. Write [pic] as a decimal. [pic]= 7 ÷ 20 = 0.35

The top part of a fraction is called the numerator while the bottom part is called the denominator.

Equivalent fractions are fractions which although they look different, they have the same value e.g. [pic]

Equivalent fractions are very important as they are used to simplify/cancel down fractions into their simplest forms as well as being vital when adding/subtracting expressions involving fractions.

The golden rule of equivalent fractions is ‘do the same to the top and bottom’; in other words if you multiply the top (numerator) by 3 then you have to multiply the bottom (denominator) by 3 etc.

e.g. Change [pic] into 60th s. We need to multiply 12 by 5 to make it into 60 so we need to multiply the numerator by 5 too.

[pic]

When simplifying fractions we need to find the largest whole number (integer) which will divide exactly into both the numerator and the denominator (the highest common factor of the numerator and the denominator – see notes on factors)

e.g. Simplify [pic]

The Highest Common Factor (HCF) of 32 and 48 is ……..16 so we need to divide top and bottom by 16:

[pic]

If you don’t spot the highest common factor it will take a little longer but you should still get the same answer. Below is what happens if you saw that 4 was a common factor, then 2 and then 2 again

[pic] (same answer)

Mixed numbers are made up of whole numbers and fractions e.g [pic]

We can change a mixed number into a ‘top-heavy’ or ‘improper’ fraction (and vice versa). In the case of the ‘top-heavy’/’improper’ fraction the numerator will be bigger than the denominator.

e.g. Express [pic] as a top-heavy fraction.

Each of the 3 units (‘whole ones’) is made up of 5 fifths, so the 3 units are the same as 15 fifths (3x5) but we also have another 2 fifths so altogether we have 17 (15+2)

fifths.

so [pic]

We can also change from a top-heavy fraction to a mixed number by reversing the process.

Addition and subtraction of fractions

If you wish to add or subtract fractions then they must have the same bottoms (denominators). All we need to do is find a ‘common denominator’ i.e. a number which both the denominators will divide exactly into to, and then use equivalent fractions.

e.g. [pic] Find a common denominator – in this case ……35

[pic]

e.g. [pic]

[pic] change both mixed numbers into top-heavy fractions

[pic] common denominator of 15 using equivalent fractions

[pic] change from top-heavy fraction to mixed number

so [pic]

Multiplication of fractions

This is really straight-forward. Everything needs to be written as a fraction, so if you have a mixed number you need to write it as a top-heavy fraction, and if you have a whole number (integer) then write it as a fraction e.g. 7 = [pic]

All you need to do find your answer (the product) is to multiply the numerators together and then multiply the denominators together.

The denominators do not have to be the same.

Examples

[pic]

Division of fractions

This is very similar to multiplication as it uses the fact that division is the inverse of multiplication.

Follow the same procedure as for multiplication except for instead of dividing, ‘flip’ the divisor (the fraction you are dividing by – or if you prefer the fraction after the ÷) and then multiply.

Examples

[pic]

Fractions on a calculator

Most scientific calculators have a fraction button which usually is similar in appearance to [pic].

See your maths teacher if you are unsure of how to use it.

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