Fractions and percentages
Understanding fractions
A fraction can mean a division, and it can also act on a number as an operator. In this section we work with proper fractions, improper fractions and mixed numbers.
A fraction is a division
Every fraction shows the numerator divided by the denominator. So 5/6 means 5 divided by 6, and 10/4 means 10 divided by 4 = 2.5. Writing a division as a fraction is easy: '10 divided by 4' becomes 10/4.
Proper, improper and mixed
In a PROPER fraction the numerator is smaller than the denominator, so it is less than 1 whole (for example 3/4). In an IMPROPER fraction the numerator is equal to or greater than the denominator, so it is 1 whole or more (for example 6/5). An improper fraction can be written as a MIXED NUMBER: 4/3 = 1 1/3.
Using a fraction as an operator
A fraction can act on a number to find a part of it. To find 3/4 of 20, divide by the denominator, then multiply by the numerator: 20 divided by 4 = 5, then 5 times 3 = 15. So 3/4 of 20 = 15.
Worked examples
Writing a division as a fraction
- Read '10 divided by 4'.
- The first number is the numerator and the second is the denominator.
- So it is 10/4, and 10 divided by 4 = 2.5.
Answer: 10 divided by 4 = 10/4 = 2.5
Proper, improper or mixed
- Look at 6/5 and compare the numerator with the denominator.
- 6 is greater than 5, so it is an improper fraction (more than 1 whole).
- 5/5 is 1 whole, and there is 1 fifth left over.
Answer: 6/5 is an improper fraction equal to the mixed number 1 1/5.
A fraction of an amount
- To find 3/4 of 20, divide by the denominator: 20 divided by 4 = 5.
- Then multiply by the numerator: 5 times 3 = 15.
Answer: 3/4 of 20 = 15
Comparing two fractions of amounts
- Work out 3/4 of 20 = 20 divided by 4 times 3 = 15.
- Work out 4/3 of 12 = 12 divided by 3 times 4 = 16.
- Compare the results: 16 is greater than 15.
Answer: 4/3 of 12 (16) is bigger than 3/4 of 20 (15).
Where you see this in real life
- Sharing 3 cakes equally between 5 people, so each person gets 3/5 of a cake.
- Working out 3/5 of a 500 metre swim.
- Finding a fraction of an amount of money, such as 1/4 of $16.
Key words
- Numerator
- The top number of a fraction, which tells how many parts you have.
- Denominator
- The bottom number of a fraction, which tells how many equal parts the whole is split into.
- Proper fraction
- A fraction less than 1 whole, where the numerator is smaller than the denominator.
- Improper fraction
- A fraction equal to or greater than 1 whole, where the numerator is equal to or greater than the denominator.
- Mixed number
- A whole number together with a proper fraction, such as 1 1/3.
- Operator
- A fraction used to find a part of a number, such as 3/4 of 20.