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
- Using the same idea, 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