Written Methods for the Four Operations

Written methods are ways of setting out addition, subtraction, multiplication and division on paper, so that you can work out exact answers without a calculator.

On Paper 1, where calculators are not allowed, you are often asked to "Work out" a calculation such as a three-digit number times a two-digit number, for 2 or 3 marks. Later in the paper you may have to multiply two decimals, or divide by a decimal, for 3 marks.

You also use these methods inside longer problems about money, change, packs and remainders. Marks are given for a correct method, so set your working out clearly in columns.

Every digit sits in a column: thousands, hundreds, tens and ones. After the decimal point come tenths, then hundredths.

To add or subtract, write the numbers so that ones are under ones and tens are under tens. With decimals, line up the decimal points. You may fill a gap with a zero: 7.4 = 7.40

Start with the column on the right. When a column adds up to 10 or more, carry the extra ten into the next column. When a column has too little to take away from, exchange one from the column to its left.

To multiply by a two-digit number such as 37, split it into tens and ones: 37 = 30 + 7. Multiply by each part, then add the two answers.

Multiplying by 30 is multiplying by 3 and then by 10. So on the second row, write a 0 in the ones column first, then multiply by 3.

Before you start, round each number to make an estimate. If your answer is far from the estimate, look for a slip.

Ignore the decimal points and multiply the whole numbers. Then count the decimal places in the question. The answer has the same total number of decimal places.

For example, for 0.3 \times 0.2, work out 3 \times 2 = 6. The question has 2 decimal places, so 0.3 \times 0.2 = 0.06

Check the size with an estimate: 4.1 \times 2.9 must be close to 4 \times 3 = 12

Short division, the bus stop method, starts on the left. Divide each digit in turn. If there is a remainder, carry it to the next digit: 3 hundreds left over become 30 tens.

With a decimal, put the decimal point in the answer directly above the decimal point in the number: 93.6 \div 6 = 15.6

A remainder at the end is not a digit of the answer. Write a 0 after the decimal point and keep dividing: 9 \div 4 = 2.25

To divide by a decimal, multiply both numbers by 10, or by 100, until you are dividing by a whole number. The answer stays the same: 2.8 \div 0.4 = 28 \div 4 = 7

In a word problem, decide what each step finds. Add to find a total, subtract to find a difference or the change, multiply for equal groups, and divide to share or to find how many groups.

Any remainder must make sense in the story. 150 people travel in minibuses that hold 16 people each. 150 \div 16 = 9 remainder 6, so 9 minibuses would leave 6 people behind. You need 10 minibuses.

Now suppose each cake needs 16 g of butter and there is 150 g. You can make only 9 cakes, because the 6 g left over is not enough for another one.

Finish by answering the question that was asked, with units. Write money with two decimal places: £3.50, not £3.5.

• Forgetting the 0 on the tens row. When you multiply by the tens digit, write a 0 in the ones column first.
• Multiplying tens by tens and ones by ones only. Every part of one number must be multiplied by every part of the other.
• Putting the decimal point in the wrong place. Count the decimal places in the question, then check the size with an estimate.
• Writing a remainder as a digit. In short division, carry each remainder on to the next digit; never write it into the answer.
• Changing only one number when dividing by a decimal. Multiply both numbers by the same 10 or 100, and do not divide the answer again afterwards.
• Rounding a remainder the wrong way. Ask what the remainder means: people left over need one more bus, but butter left over does not make another cake.