# Long Multiplication

You can use short multiplication if you’re multiplying one number by another that’s in your times tables (up to 12). However, if you want to multiply by a higher number, you need to use long multiplication.

• Write down the numbers one on top of the other with the smaller number on the bottom and a times sign on the left (just as you would normally), then draw three lines underneath to hold three rows of numbers.
• Multiply the top number by the last digit of the bottom number as you would normally.
• Write a zero at the end of the next answer line (to show that you’re multiplying by tens now rather than units).
• Multiply the top number by the next digit of the bottom number, starting to the left of the zero you’ve just added.
• Add the two answer lines together to get the final answer.

Notes:

• Some people write the tens they’ve carried right at the top of the sum, but that can get very confusing with three lines of answers!
• Don’t forget to add the zero to the second line of your answer. If it helps, you can try writing it down as soon as you set out the sum (and before you’ve even worked anything out).
• At 11+ level, long multiplication will generally be a three-digit number multiplied by a two-digit number, but the method will work for any two numbers, so don’t worry. If you have to multiply two three-digit numbers, say, you’ll just have to add another line to your answer.

Sample questions:

Have a go at these questions. Make sure you show your working – just as you’d have to do in an exam.

1. 216 x 43
2. 17 x 423
3. 23 x 648
4. 782 x 28
5. 127 x 92

# How to Add, Subtract, Multiply and Divide

The most important things you need to do in Maths are to add, subtract, divide and multiply. If you’re doing an entrance exam, and there’s more than one mark for a question, it generally means that you have to show your working. Even if it’s easy enough to do in your head, you still have to write down the sum on paper. That way, the examiner knows that you didn’t just guess!

Here are the basic operations:

The standard way to add numbers is the ‘column method’.

• Write down the numbers one on top of the other (however many there are), with two lines under them and a plus sign on the left.
• Add the first column of numbers on the right and put the answer between the lines.
• If the total is more than 9, ‘carry’ the tens by putting that number in small handwriting under the next space on the answer line.
• Add the next column of numbers working from the right and put the answer between the lines, adding any numbers below the line that have been carried.
• If you get to the final column of numbers and the total is more than 9, you can write both digits on the answer line.
• If you have more than two columns of numbers and the total is more than 9, you’ll have to ‘carry’ any tens again by putting that number in small handwriting under the next space on the answer line.
• You can then finish off as normal.

Notes:

• You don’t need the second line if you don’t want to use it.
• You can also choose to put the carried numbers above the top line of the sum, but that gets a bit messy if you’re doing long multiplication, so it’s best to get into the habit of using this method.

Sample questions:

Have a go at these questions. Don’t just do them in your head. That’s too easy! Make sure you show your working – just as you’d have to do in an exam.

1. 8 + 5
2. 17 + 12
3. 23 + 19
4. 77 + 88
5. 127 + 899

## Subtraction

The standard way to subtract one number from another is again the ‘column method’, but this time it’s slightly different. For a start, you can only use this method with two numbers (not three or more), and you can’t use it for negative numbers.

• Write down the two numbers one on top of the other, with the bigger one on top, the usual two lines under them and a minus sign on the left.
• Working from the right, take away the first digit in the second number from the first digit in the first and write the answer on the answer line.
• If you can’t do it because the digit on the top row is too small, you’ll have to ‘borrow’ a 10 from the digit in the next column.
• Place a 1 above and to the left of the top right-hand digit to make a new number, in this case 12.
• Cross out the digit you’re borrowing from, subtract 1 and write the new digit above and to the left of the old one.
• You can now subtract as normal, so 12 – 7 = 5 in this case.
• Working from the right, subtract the next digit in the bottom number from the next digit in the top number and put the answer between the lines.
• Repeat this step until you’ve finished the sum.
• Note that in this case you have to borrow 1 from the 2, leaving 1, and then borrow 1 from the 4, writing it next to the 1 so it makes 11. It may look like you’re borrowing 11, but you’re not. You’ve just had to write the two 1s next to each other.

If you can’t borrow from a digit because it’s a zero, just cross it out, write 9 above and to the left and borrow from the next digit to the left. If that’s a zero, too, just do the same again until you reach one that’s not zero.

Notes:

• You don’t need the second line if you don’t want to use it.
• If the answer to the sum in the last column on the left is zero, you don’t need to write it down, so your answer should be 17, say, not 017.
• You don’t need to put commas in numbers that are more than 1,000.
• You could cross out the numbers from top left to bottom right instead, but that leaves less room to write any little numbers above and to the left (where they have to go), so it’s best to get into the habit of using this method.

Sample questions:

Have a go at these questions. Don’t just do them in your head. That’s too easy! Make sure you show your working – just as you’d have to do in an exam.

1. 8 – 5
2. 17 – 12
3. 43 – 19
4. 770 – 681
5. 107 – 89

## Multiplication (or short multiplication)

This is short multiplication, which is meant for multiplying one number by another that’s in your times tables (up to 12). If you want to multiply by a higher number, you need to use long multiplication.

• Write down the numbers one on top of the other with the single-digit number on the bottom, two lines underneath and a times sign on the left.
• Multiply the last digit of the top number by the bottom number and put the answer between the lines.
• If the total is more than 9, ‘carry’ the tens by putting that number in small handwriting under the next space on the answer line.
• Working from the right, multiply the next digit of the top number by the bottom number, adding any number below the answer line.
• As with addition, if you get to the final column of numbers and the total is more than 9, you can write both digits on the answer line.

Notes:

• You don’t need the second line if you don’t want to use it.
• You can also choose to put the carried numbers above the top line of the sum, but that gets a bit messy if you’re doing long multiplication, so it’s best to get into the habit of using this method.
• If you’re multiplying one or more numbers with a decimal point, take the decimal point(s) out first then multiply the numbers and put the decimal point in afterwards. You just need to make sure that the number of decimal places is the same as the total number of decimal places in the original numbers, eg 2.5 x 1.1 = 25 x 11 Ã· 100 = 275 Ã· 100 = 2.75.

Sample questions:

Have a go at these questions. Don’t just do them in your head. That’s too easy! Make sure you show your working – just as you’d have to do in an exam.

1. 21 x 3
2. 17 x 4
3. 23 x 6
4. 77 x 8
5. 127 x 9

## Division (or short division, or the ‘bus stop’ method)

This is short division, which is meant for dividing one number by another that’s in your times tables (up to 12). If you want to divide by a higher number, you need to use long division (see my article here). It’s called the ‘bus stop’ method because the two lines look a bit like the area where a bus pulls in at a bus stop.

• Write down the number you’re dividing (the ‘dividend’), draw the ‘bus stop’ shape around it so that all the digits are covered and then write the number you’re dividing by (the ‘divisor’) on the left.
• Try to divide the first digit of the dividend by the divisor. If it goes in exactly, write the answer on the answer line above the first digit of the dividend.
• If it goes in, but there’s a remainder, write the answer on the answer line above the first digit of the dividend and then write the remainder above and to the left of the next digit in the dividend.
• If it doesn’t go, then make a number out of the first two digits of the dividend and divide that number by the divisor, adding any remainder above and to the left of the next digit. Just make sure you don’t write a zero on the answer line – the only time you should do that is if the answer is a decimal, eg 0.375.
• Repeat this process for each of the remaining digits, using any remainders to make a new number with the next digit.
• If you divide one number by another in the middle of the dividend and it doesn’t go, then just put a zero on the answer line and combine the digit with the next one.

Notes:

• If you have a remainder at the end of the sum, you can either show it as a remainder or you can put a decimal point above and below the line, add a zero to the dividend and carry on until you have no remainder left.
• If the remainder keeps going, it’s likely to repeat the same digits over and over again. This is called a ‘recurring decimal’. Once you spot the pattern, you can stop doing the sum. Just put a dot over the digit that’s repeating or – if there’s more than one – put a dot over the first and last digit in the pattern.
• If your handwriting is a bit messy, make sure you make the numbers quite large with a bit of space between them so that you can fit everything in!

Sample questions:

Have a go at these questions. Don’t just do them in your head. That’s too easy! Make sure you show your working – just as you’d have to do in an exam.

1. 36 Ã· 3
2. 172 Ã· 4
3. 222 Ã· 6
4. 816 Ã· 8
5. 126 Ã· 9