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Numbers: An introduction to subtraction
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978-1-4730-1219-6 (.epub)

978-1-4730-1987-4 (.kdl)
Introduction
Do you want to improve your ability to subtract one number from another, especially if decimals are involved, without having to rely on a calculator? This course will help you get to grips with subtraction and give you some practice in doing it.
You can start with some practice in subtracting small numbers in your head if you want to. Then we will show you how to subtract bigger numbers on paper. Finally we look at how to subtract decimal numbers.
You don’t need to complete the whole course if only certain sections are relevant to you.
Find out more about studying with The Open University by visiting our online prospectus.
After studying this course, you should be able to:
subtract one number from another
subtract using decimals
practise your subtraction skills.
<b>1 Ways of expressing subtraction</b>Another way to say ‘subtract one number from another’ is to say ‘one number minus another’. And the standard sign to show this is a minus sign, which looks like this ‘–’. The expressions ‘take away’ or ‘take from’ are also used to mean subtract or minus.So the following expressions all mean the same thing:What do I get if I subtract 2 from 3? What do I get if I take 2 from 3? What is 3 take away 2? What is 3 minus 2? What is 3 – 2?The result is 1 in all cases. <b>2 Subtracting in your head</b>To subtract one number from another without using a calculator you need to know basic subtractions up to 20. This means that you need to know, off by heart, what result you get if you subtract any number up to 10 from any bigger number up to 20. For example you have to remember that 14 minus 6 is 8, or 9 minus 5 is 4, and so on. If you are confident that you know the basic subtractions up to 20, carry on with the rest of this course. If you are unsure, or would like some practice to help you remember them, then go now to Section 9 Subtracting small numbers by following the link on the left. Then return here to continue.<b>3 Subtraction rules – order matters</b>It’s important to remember that subtraction has different rules from addition.For example, when you add up numbers, it doesn’t matter what order you add them up in. So 6 + 4 is exactly the same as 4 + 6. The result is 10 in both cases.But in subtraction, order matters. So 6 – 4 is different from 4 – 6. With the first, you start with 6, subtract 4, and are left with 2.But with the second you start with 4 and if you subtract 6, which is a bigger number, you are 2 short, or minus 2.<b>4 Subtracting on paper</b>If the numbers you want to subtract are too large for you to do the calculation in your head, you can use a calculator. Alternatively, you can do the calculation on paper.Write your starting number at the top with the number you want to subtract from it underneath. Because the order in which you subtract one number from another matters, it is important to put the correct numbers on top and bottom. Then draw a line underneath. Write the numbers so the digits form columns and they are lined up on the right-hand side, as in the examples shown below. In the calculation below left, for instance, the digit 5 in the top number is above the digit 2 in the bottom number. The far right column represents the ones (units), the next column to the left represents the tens, the next column to the left the hundreds, the next column to the left the thousands, and so on.To do the subtraction, you take each column in turn, starting from the right and moving left. You take the bottom digit from the top digit and write the result underneath the line, lined up with the digits above. If the top number in each column is bigger than the bottom number, like in the calculation above left, this is straightforward. There’s an example of this kind of straightforward subtraction in the next section.But what do you do if the number at the top of the column is smaller than the number at the bottom, like in some of the columns in the calculation on the right above? This requires an extra step. There’s an example showing what you need to do in this case later, in Section 6 Subtracting when you have to borrow.
<b>5 Example of a straightforward subtraction</b>
In the example below of a straightforward subtraction, in every column the digit at the top of the column is bigger than the digit at the bottom. Click on each step in turn to see how to carry out the calculation.
Click on ‘Now read the discussion’ to see all the individual steps at once.
Activity 1
**Discussion**
When you do any subtraction, you can check to see if your answer is correct by adding your answer to the number you subtracted. You should get the number you started with. In this example 323 + 52 gives 375.
So the answer in the above example is correct.
<b>6 Subtracting when you have to borrow</b>
If the digit at the top of any column in your subtraction is smaller than the digit at the bottom of the same column, you need to borrow (or carry) from the next column on the left.
There is an example of this below. Click on each step in turn to see how to carry out the calculation.
Click on ‘Now read the discussion’ to see all the individual steps at once.
Activity 2
**Discussion**
In this example you borrowed once. But sometimes you need to borrow in more than one column. Whichever column you are in, you do this in the same way, by borrowing 1 from the column to the left.
<b>7 Subtracting decimals by lining them up</b>Subtracting whole numbers such as 52 from 375 is fairly straightforward. Subtracting decimal numbers such as 6.892 from 223.6 uses the same process but with one extra step – you have to line the decimal points up first.Rather than arranging your two numbers so that they line up on the right-hand side, you need to line up the decimal points, regardless of how many numbers there are after the decimal point. In the example below, the top number has one number after the decimal point. It is said to have one decimal place. But the bottom number has three decimal places.In any columns that are ‘missing’ numbers after the decimal point, assume that the missing number is zero, like this.Now do the subtraction, starting on the right as usual, and borrowing from the next column where necessary. When you have finished the calculation, remember to put the decimal point into your answer below the line, in the same position as the two numbers you are subtracting.So the above subtraction when it is completed, with all its borrowings shown and with all its decimal points lined up, looks like this.<b>8 Get some practice</b>Now that you’ve learned how to do subtraction on paper, you might want to practice your new skills. To practice subtracting whole numbers, including borrowing where necessary, go to the Practice Subtracting section of the Numbers website and click on **Get sum**. Then follow the instructions. To practise subtracting decimals, go to the Adding and subtracting decimals page of the math.com website and follow the instructions. This web page gives you addition as well as subtraction problems to do, but if you want to skip the additions simply click on **New Problem** every time an addition appears. <b>9 Subtracting small numbers</b>If you want to subtract without using a calculator, you need to know off by heart what you get if you subtract any number up to 10 from any bigger number up to 20. All the possible combinations are shown in the table below.To view larger image, click HERE .Say you want to subtract 6 from 13. You look up 13 in the top row, and –6 down the leftmost column. The answer is shown where the 13 column lines up with the –6 row, so in this case the answer is 7.In other words, the top row shows the number you want to start with. The leftmost column shows the number you want to subtract from your starting number. The result of the subtraction is shown where the row and column cross.If you want to, you can use this table to practise remembering all the possible combinations. There is an interactive version of the table on the Subtract page of the Numbers website, which you might find helpful.To help you remember you can also do some practice calculations if you want. Go to the Practice sums page of the Numbers website and select **Subtraction** from the pull-down list next to **Type of sum.**Type of sum. Then follow the instructions on the page. This web page can also give you practice in addition, multiplication or division if you want. Select the appropriate option from the **Type of sum** menu.ConclusionThis free course provided an introduction to studying Maths. It took you through a series of exercises designed to develop your approach to study and learning at a distance and helped to improve your confidence as an independent learner.Keep on learning Study another free courseThere are more than **800 courses on OpenLearn** for you to choose from on a range of subjects. Find out more about all our free courses. Take your studies furtherFind out more about studying with The Open University by visiting our online prospectus. If you are new to university study, you may be interested in our Access Courses or Certificates. What’s new from OpenLearn?
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