Arithmetic is the study of numbers, their properties, and certain operations on numbers. Massey University's Maths First website contains detailed information about arithmetic.
Additional interactive content is included below.
Order of operations
There is an accepted priority of mathematical operations that must be followed. Most calculators have this order built in. This priority is not left to right as it is in written expression in English. See order of operations for more.
3 is a common factor of 9 and 15 as 3 divides into both without any left over. To reduce fractions we need to identify a common factor (CF).
Any division can be reinterpreted as a multiplication. The calculation 72 ÷ 9 can be thought of as 9 times a number equals 72. See dividing fractions for more.
An improper fraction has the numerator greater than the denominator. In order to multiply or divide mixed numbers, you must convert the mixed numbers into improper fractions. See mixed numbers and improper fractions for more.
Adding fractions with different denominators
In order to add fractions with different denomimators you must first find the lowest common denominator (LCD). See adding fractions for more.
References and further reading
Dunning, B. (1991). Critical mathematics for business studies. Palmerston North, New Zealand: Massey University. [Massey Library link]