Fractions, explained
A fraction is a part of something shared out equally. The bottom number says how many equal parts there are, and the top number says how many of them you have. The pages below start with what a fraction means and end with dividing one fraction by another.
-
What is a fraction?
Equal parts of a whole. The bottom says how many parts, the top how many you have.
-
Comparing fractions
Which is bigger? Same bottom, same top, or make the bottoms the same.
-
Equivalent fractions
The same amount with different numbers, like 1/2 = 2/4 = 4/8.
-
Adding fractions
Same bottom number, add the tops. Different ones, make them match first.
-
Subtracting fractions
Same bottom number, take away the tops. Different ones, make them match first.
-
Multiplying fractions
Multiply the tops, then multiply the bottoms.
-
Dividing fractions
Keep the first, change ÷ to ×, flip the second, then multiply.
Questions people ask
In what order are fractions usually learned?
First what a fraction means, then comparing them and finding equal ones. Adding and taking away come next, and they need equal fractions to work. Multiplying and dividing come last.
Why do so many children find fractions hard?
Because a bigger number can mean a smaller piece. 1/8 is smaller than 1/4, even though 8 is bigger than 4. A picture of the pieces fixes that better than any rule.
More explained
-
Divisibility rules
Tell whether a number divides exactly by 2 to 13, without doing the division.
-
Factors and primes
What a prime is, how to break a number into primes, and the HCF and LCM.
-
Written methods
Long addition, subtraction, multiplication and division, decimals included.
-
Number facts
Adding and taking away small numbers, the times tables and division facts.
-
Shapes and space
Naming flat shapes and solids, counting sides, corners, faces and edges, and angles.