So far in this activity, the four arithmetic operations have been written as , –, and . However, in scientific calculations, division is more usually written as a fraction (see Section 3.1 for more about fractions). Twelve divided by three could equally accurately be written as or
Or, to give a slightly more complicated example, could equally accurately be written as or as
Note that the bracket, used to indicate that the addition should be done before the division in this case, has been omitted from the final statement of this expression. This is because the horizontal line used to indicate division acts as an ‘invisible bracket’, i.e.
Other mathematical symbols can act as ‘invisible brackets’. The most commonly used one is the square root sign . Finding the square root of a number is the opposite of finding the square. So, since (said as ‘three squared’) is 9, (said as ‘the square root of 9’) is 3 (strictly, the square root of 9 could also be the negative number -3, but this activity will only consider positive square roots). If you are asked to calculate , the fact that the upper line of the square root sign extends to include the whole of the addition means that the addition should be done first, i.e. Note that this is rather different from , in which the square root sign only extends over the 9, so
Provided the meaning is clear without it, the multiplication sign is also sometimes omitted from calculations. So could be written as and could be written as
Question 1.5
Evaluate (i.e. calculate the value of) the following, with or without your calculator:
