# Repeated operations

Repeated operations refers to problems where the same operation is applied many times.

The choice of order in using the numbers can make a significant difference to the difficulty of the calculation.

Repeated operations also assist students to apply the properties of the operations.

For example, suppose that you need to add up a list of grocery items so you can check if you have enough money. You could associate the items in the order you look at them in your trolley:

$14 +$9 + $7 +$11 + $6 However, to make the calculation easier, you could associate the amounts in a different order, noting that:$11 + $9 =$20 and $14 +$6 = $20. With subtraction you might have a problem where amounts are sequentially taken away, such as spending different amounts in different shops.$64 – $9 –$13 – $7 could be carried out in the order it occurs or you could recognise that –$13 – $7 is the same as –($13 + \$7) using the properties of inverse operations.

Repeated multiplication and division help students to identify factors and multiples in numbers; essential knowledge for understanding equivalent fractions.

For example, simplifying $$\frac{24}{36}$$ is made easier by repeated division of both numerator and denominator:

$$\frac {24}{36} = \frac {12}{18} =\frac {6}{9} =\frac {2}{3}$$