Part a) Work out two-fifths of 400. There is a second part to this question that we will look at later.
There are lots of methods for working out fractions of quantities. We will look at two methods here. Firstly, we will look at the method of dividing by the bottom and then multiplying the answer by the top. In this question, we’ll divide 400 by five and then multiply our answer by two.
We could do the first calculation using the bus stop method. However, you might notice that 40 divided by five is equal to eight. This means that 400 divided by five is equal to 80. We’ve worked out that one-fifth of 400 is 80. To work out two-fifths, we need to multiply 80 by two. Eight multiplied by two is equal to 16. Therefore, 80 multiplied by two is equal to 160. Two-fifths of 400 equals 160.
Before looking at our second method, we can look at this pictorially. The rectangle has been split into five equal pieces. Therefore, each piece is worth one-fifth. As our total in this case was 400, each fifth will be worth 80 as 80 multiplied by five equals 400. We wanted to calculate two-fifths. This is 80 multiplied by two or 80 plus 80. Either way, we can see that two-fifths of 400 is equal to 160.
An alternative method to calculate two-fifths of 400 is to use the fact that the word “of” in mathematics means multiply. We need to calculate two-fifths multiplied by 400. Two-fifths can be rewritten as two multiplied by one-fifth. We can now calculate one-fifth of 400, which we already know is 80. Therefore, we need to multiply two by 80. Once again, this gives us an answer of 160. Two-fifths of 400 equals 160.
The second part of our question says the following. b) Work out 32.4 minus 33.3 divided by three.
In order to answer this question, we need to remember our order of operations, sometimes known as BIDMAS. The B stands for brackets, the I for indices or powers, the D for division, M for multiplication, A for addition, and S for subtraction. If we consider our question 32.4 minus 33.3 divided by three, we have no brackets or indices. We do have a division sign. Therefore, the first calculation we need to work out is 33.3 divided by three.
This can be done using the bus stop method. Three divided by three is equal to one. The three in the units column divided by three is also equal to one. We need to remember to keep our decimal point in the same place. And the three in the tenths column divided by three is also equal to one. 33.3 divided by three is equal to 11.1. This leaves us with 32.4 minus 11.1.
A common mistake here is to try and subtract 32.4 from 11.1. It is important that we keep the numbers underneath each other in the calculation. We need to subtract 11.1 from 32.4. Once again, we must make sure that the decimal point remains in the same place. Four minus one is equal to three. Two minus one is equal to one. And finally, three minus one is equal to two. This means that 32.4 minus 11.1 is equal to 21.3.
The answer to the calculation 32.4 minus 33.3 divided by three is 21.3.