Basic Fractions

What is a fraction?

A fraction is part of a whole
A fraction is written as where a and b are whole numbers (integers)

The number on the top, a, is called the numerator
The number on the bottom, b, is called the denominator

means split something into b parts and take a of them

means split something into 2 parts and take 1 of these parts
means split the something into 3 parts and take 2 of these parts
means split something into 5 parts and take 4 of these parts

How do I find equivalent fractions?

“Splitting something into 2 parts and taking 1 of these parts” gives the same overall amount as “splitting something into 4 parts and taking 2 of these parts”
- is the same as $\frac{2}{4}$ is the same as , or , or etc
Equivalent fractions are two fractions that represent the same amount (they are different ways of writing the same thing)
To make equivalent fractions, multiply the top and bottom of a fraction by the same amount
- is equivalent to and and …etc
- For each fraction, there are an infinite number of equivalent fractions
To cancel a fraction down to its “simplest” equivalent form, divide the top and bottom of a fraction by the biggest whole number that goes into both (“common factor”)

How do I find a fraction of an amount?

Method 1: divide by the denominator and multiply by the numerator
- To find of an amount, divide it by 2
- To find of an amount, divide it by 3
- To find > of an amount, divide it by 5 then multiply it by 2
  - of 60: do 60 ÷ 5 = 12, then 12 × 2 = 24
Method 2 (if you know how to change fractions into decimals): change the fraction into a decimal, then multiply
- To find of an amount, multiply the amount by 0.25
- To find of an amount, multiply the amount by 0.9
Method 3 (if you know how to multiply fractions): write both numbers as fractions and multiply two fractions together
- To find of 60, work out
- To find of , work out

Mixed Numbers & Top Heavy Fractions

What are mixed numbers & top heavy fractions?

A mixed number has a whole number (integer) part and a fraction part
eg. has the whole number 3 and the fraction , meaning “three and three quarters”
A top heavy fraction – also called an improper fraction – is one with the top (numerator) bigger than the bottom (denominator)
eg. means “fifteen quarters”

Turning mixed numbers into top heavy fractions

Multiply the whole number by the denominator (big × bottom)
Add that value to the numerator
Write the “new” numerator over the same denominator as before

Turning top heavy fractions into mixed numbers

Divide the top by the bottom (to get a whole number and a remainder)
The whole number is the big number
The fraction part is the remainder over the denominator

Exam Tip

Top heavy fractions are also called “improper” fractions

Worked example

Calculate an estimate for $fraction numerator 17.3 cross times 3.81 over denominator 11.5 end fraction.$ State, with a reason, whether the estimate is an overestimate or an underestimate.

Round each number to 1 significant figure.

17.3 → 20
3.81 → 4
11.5 → 10

Perform the calculation with the rounded numbers.

$fraction numerator 20 cross times 4 over denominator 10 end fraction equals 80 over 10 equals 8$

An estimate is 8.
This is an overestimate as the numerator was rounded up and the denominator was rounded down.