Refresh Your Basic Maths Addition and Subtraction Skills
If you can do whole number addition and subtraction well, you have some of the tools to do well in a numeracy test. When you can add up and take away whole numbers, you’ve also got a really solid foundation for the rest of the maths you may need in real life. The most common examples of everyday maths are adding up your shopping bill and working out change.
You add things whenever you end up with a specific amount more than you started with – for instance, if you earn some money, or pack more weight into your suitcase, or combine two groups of people.
Obviously, if you have a calculator, all you need to worry about is making sure you enter the sum correctly.
On the other hand, if you’re in a non-calculator (mental arithmetic) test, you need to know how to add up quickly on paper. Here’s what you need to do:
Line up the numbers you want to add so their ends are in line.
Add up the right-most column.
If your total is less than ten, write the total under the column. If the total is ten or more, write the second digit under the column and put the first digit under the next column to the left.
In the middle column of the first example, 7 + 6 = 13, you write a 3 under the 7 and 6 and a 1 below the next column to the right.
Go to the next column to the left and add up the numbers – and add any numbers you’ve written below this column.
In the left-hand column of the first example, 4 + 3 = 7, there’s a 1 below the column as well, so you write down 8.
Repeat Steps 3 and 4 until you run out of numbers.
You subtract or take away whenever you end up with a specific amount less than you started with – for example, if you spend money, or pour away some drink, or remove some people from a group.
As with most things in maths, several ways exist to do take-away sums and get the right answer. Here, you review how to take away the traditional way using the column method, and then an alternative, the do the same thing method, which some people find easier.
If either of the numbers in the sum is negative, you have to use a different method. See "Addition and subtraction of negative numbers."
Here’s how the column method works:
If the second number is bigger than the first, swap them around and write a big minus sign somewhere you won’t miss it. Your answer is going to be less than zero, or a negative number.
(Luckily, this is quite rare in numeracy tests.)
Write down your numbers with the bigger one above the smaller one. If they’re different lengths, make sure they’re right-justified – that they end in the same column. Underline the lower number. Give yourself plenty of space!
Starting from the left, compare the lower digit with the upper one.
If the lower digit is bigger, then you’ve got a problem. You need to borrow one from the next column to the left.
Reduce the upper number of the next column by one and write a little one above and to the left of the upper number – for instance, in the right-hand column, 3 has become 13.
Now take away the lower number from the upper number and write the answer below the underline in that column.
Repeat steps 2 to 4 until you run out of digits.
If you didn’t write down a big minus sign in Step 1, your answer is the number beneath the underline. If you did write down a big minus sign, put a minus in front of the number beneath the underline and that’s your answer.
What happens if you want to borrow from a zero? You can’t really reduce nothing by one! In that case, what you have to do is borrow one from the next column to the left, turning the zero into a ten, so you can borrow one from it.
Here's how the do the same thing method works:
Write down the sum.
First, you want to make the second number into a multiple of 10.
Look at its last digit and work out how many you need to add to make it end in 0. Add this number on to both numbers and write down the new sum. If you had 435 – 79, you’d add 1 to both numbers to get 436 – 80.
If you can do the sum easily, do the sum.
If not, you make the second number into a multiple of 100. Look at the last two digits and see what you need to add to make it end in 00. Add this number onto both numbers and write down the new sum. In this example, you’d add 20 to both numbers and get 456 – 100 (which gives you 356).
If your sum still isn’t easy, keep going – make the second number into a multiple of 1,000, then 10,000, then 100,000 and so on until you can easily take away the second number. (You’d be really unlucky to need to do this!)
Addition and subtraction of negative numbers
You may have to deal with small negative numbers in a numeracy test. They’re not hard if you take a deep breath and think about them carefully!
To add or take away from a negative number, think about the first number as your original temperature, and then getting warmer or colder by the second. To work out –12 + 5, imagine it being –12ºC and getting 5ºC warmer: you’d end up at –7ºC. To work out –8 – 3, imagine a temperature of –8ºC getting 3ºC colder: you’d end up at –11ºC.
Finding the difference between two negative numbers is also easy: it’s the same as the difference between the two numbers ignoring the minus signs. The difference between –3 and –7 is 4, the same as the difference between 3 and 7.
The easy way to find the difference between a positive and a negative number is to drop the minus sign and add the numbers together. The difference between 5 and –5 is the same as 5 + 5 = 10.
Lastly, taking a bigger number away from a smaller number is something you can do using the recipes for taking away from earlier: you do the sum the wrong way around (for example, if you had to do 15 – 20, you’d work out 20 – 15), and then put a minus sign in front of your answer. For that question, the answer is –5.