Multiplication & Division

Mental Multiplication

Mental multiplication is one of the most important topics towards the end of primary school and in the early stages of secondary school. A good knowledge of the times tables can help you throughout your whole academic life. The easiest way to improve your mental multiplication skills is to learn the times tables by heart. This may sound like a lot of work but a bit of practise every week will allow you to master mental multiplication. Underneath, you will find the times tables from 1 x 1 to 10 x 10. Mental Division Mental division is quite important for everyday life situations. For example, if you would want to divide slices of bread between a number of people. It can be very hard to divide before you get really experienced with multiplication and division. An easy way to do simple division in your head is to think about how often you can put the amount that you want to divide something by into the amount that you want to divide. For example, if you want to divide 12 by 4. 4 goes into 12 three times so the answer is 3. Once you gain more knowledge in mathematics, simple division problems will be easy for you as you can use your number skills and experience to find the correct answer. (Written) Long Multiplication Long multiplication can be used to find answers to very difficult and complex multiplication problems. On the right, you can see an example of a multiplication problem which was solve using this method. To start off, you need to write the two numbers that you want to multiply together over each other so that the units column is aligned (usually it works if you right align the numbers). Then, multiply each digit in the bottom row by the number on the top row. In the example, we would calculate 1 x 419 first and then 2(0) x 419. Write the answers under each other underneath the line as shown in the example. Be aware that in the second part, we are actually multiplying 20 by 419. You can ignore the 0 but you must move the whole answer 1 digit to the left when filling in your answer. You can either leave the space blank or add a one as we did in the example. The last step if to add together the numbers using the long addition method. Then you have the final answer. There are two examples underneath to clarify the information above. (Written) Long Division Long division is a complex written way of solving division problems involving large numbers. It works as follows.

Setting up the Calculation

To start off, you must write the number that you want to divide by and then next to it on the right the number that you want to divide. Then put a line that goes up between the two numbers and then right above the number you want to divide as shown in the example on the right.

Solving the Problem

Start off on the left by seeing how often the left number goes into the first digit of the right number. In the example we have to see how often 20 goes into 5. The answer is 0. We put the answer above the horizontal line over the 5. Also, underneath the 5. we put a 0 to show that we could not put 20 into 5 and then add the remainder(5) underneath a horizontal line as shown in the example. Then you take down the next number, in this case 4 and put it next to the remainder so that you get a new number (54). Then we see how often 20 goes into 54. The answer is 2 (we write it above the line after the 0 from before). If you have not already realised in the past step, we also put the number that we put 20 into to get the answer (40 in this case) underneath the number we divide (54). Then we add the remainder 14 underneath. The remainder and the number above it should add up to the number you are currently dividing (54). Continue doing this procedure until there are no more numbers to take down. At the end, the answer will be written above the horizontal line. If you have divided by all the digits and you finish with a remainder, you can either write down the answer + remainder x (not very mathematical) or you continue as we have done in the example. To continue finding the answer, put a decimal point after the number you want to divide and add a few zeros (also add a decimal point above the line where the answer is written). Then perform the same procedure until there is no remainder left. Please be aware, that an answer can have infinite decimal places. If you have not found an answer using three zeros after the decimal place, you should think about stopping. Look at the two example underneath just to make sure that you have understood. Learn More Number Skills After this lesson on multiplication and division, you can go to the library and select a new topic. If you haven’t already done so, we recommend that you have look at long addition and subtraction. Please share this page if you like it or found it helpful!

Download for Offline Learning

So that you can practise the times tables offline, we have created a PDF document with the times tables. You can download this document and view or print it using your computer. The link to the file is located underneath.
Example 1 In this example, we have multiplied every digit in the bottom row by the number in the top row before adding the two products together.
Example 2 In this example, we have used long multiplication to calculate with two 3-digit numbers. The method is the same.
Example 3 In this example, we have used long multiplication to solve a multiplication problem with one 3-digit and one 4-digit number.
Example 1 In this example, we have use long division to solve a complex division problem. The answer turned out to be a full number, so we did not have to add any zeros.
Example 2 In this example, we have use long division to solve a complex division problem. Again, the answer is a whole number.
Long Multiplication Long Division Recommended
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Chapter 2.0:  Learning Outcomes Students will be able to use the times tables to solve simple multiplication problems and relate this to division problems! Students will be able to solve more complex multiplication questions using the concept of long multiplication! Students will be able to use long division to solve complex dividion questions (including with remainders and decimals)!
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