Paper Together: sit a paper in a room with your friends.See how it works
This page sets out the method for using a calculator in the order you would use it, then walks through the full lesson explanation. For three complete worked examples with the slips that cost marks, see the Using a calculator topic page.
When you see a fraction line or a root, put brackets round the top, round the bottom and round anything under a root.
When you are worried about bracket mistakes, work out the numerator and denominator as two separate calculations.
A calculator does the keys you press, including a missing bracket.
Check the calculation before you trust the display.
A bracket makes the calculator do that piece first.
Without it, 2 + 3 × 4 is 14, not 20.
Division and multiplication run left to right.
Typing 20 ÷ 4 × 2 should give 10, not 20 ÷ 8.
Clear the last entry if you mistype one key.
A sensible size is a check: money should not come out as thousands by accident.
The square key applies to the number you have just entered.
3 × 2 squared is 3 × 4 if only the 2 is squared.
Write the expression, then press keys that match it.
Do not invent brackets the question did not ask for.
Match the keys to the expression, including every bracket. For (14 + 6) ÷ 4, press the bracket, then 14 + 6, then close the bracket, then divide by 4. The display goes through 20 and finishes at 5. Without the bracket, 14 + 6 ÷ 4 is 14 + 1.5 = 15.5, because division happens before addition.
A long line is still typed as one calculation. Brackets make a piece happen first. After the brackets, powers are next, then multiplication and division from the left, then addition and subtraction from the left. 3 × 5^2 is 3 × 25 = 75. It is not (3 × 5)^2.
If the display looks the wrong size, clear it and type the line again. (14 + 6) ÷ 4 should be near 20 ÷ 4 = 5. A display of 15.5 means the bracket was missed. Write the expression first, then press keys that copy it.
Method: 1. Type the expression in order, including every bracket. 2. Close each bracket before you press equals. 3. Read the display and check it matches the written calculation.
The fraction key asks for a numerator and a denominator. You type the top, move to the bottom, and the calculator treats that fraction as one number. Adding 3/8 and 1/8 on the fraction key gives 4/8, which the display may show as 0.5. That is the same value. One half of a later number is then a simple multiplication.
Typing 3 ÷ 8 + 1 ÷ 8 also gives 0.5, because each division is already a single fraction and division runs left to right. A mixed line is less safe. 1 + 3 ÷ 8 is 1.375, not (1 + 3)/8. If the 1 belongs in the numerator, the fraction key or a bracket has to put it there: (1 + 3) ÷ 8 = 0.5.
Use the fraction key whenever the question writes one quantity over another. It stops the denominator from dividing only the last number you typed. After the display shows a decimal, you can multiply or add in the usual way. 0.5 × 64 = 32.
Method: 1. Enter the numerator, move to the denominator, then enter the bottom. 2. Use the fraction key for each fraction before you add or multiply. 3. Write the display, then simplify if the question asks for a fraction.
The square key applies to the number on the display. To get 5^2, enter 5 and press square. The display shows 25. To get 3 × 5^2, square the 5 first, then multiply by 3. Squaring after the multiplication squares the 15 and shows 225, which is a different calculation.
A cube is three factors, not the number times 3. 4^3 = 4 × 4 × 4 = 64. The cube key does that in one press. A power key is for other indices: enter the base, press the power key, then enter the index. 2^5 = 2 × 2 × 2 × 2 × 2 = 32. The index is the small raised number, not a factor written beside the base.
A square root undoes a square. √(81) = 9 because 9 × 9 = 81. √(2.25) = 1.5 because 1.5 × 1.5 = 2.25. On a calculator paper, type the root of the number inside the root sign only, unless a bracket widens it. Then carry on with the rest of the line from the left.
Method: 1. Enter the base, then use the square, cube or power key. 2. For a root, enter the number and then the root key. 3. Check a square root by squaring the display.
Write the full display before you do anything else. For 19 ÷ 8 the display is 2.375. If the question asks for 2 decimal places, the decider is the third decimal digit, which is 5. Five rounds up, so 2.375 to 2 decimal places is 2.38. Truncating to 2.37 cuts the digit off and does not round.
Keep 2.375 in your working. A later part that says 'use your previous answer' needs the full value if the question has not told you to use the rounded one. The rounded value 2.38 is not equal to 19 ÷ 8. Only write 2.38 when that accuracy has been asked for.
Some displays are already at the accuracy you need. (48 + 12) ÷ 16 = 3.75. Asked for 2 decimal places, you leave 3.75 as it is. There is no further digit to act as a decider. Money and measurements that come out exactly, such as 7 ÷ 4 = 1.75, are written with the two decimal places the display already shows.
Method: 1. Write the full calculator display before you round. 2. Round only at the end, to the places the question asks for. 3. Keep the unrounded display in your working so a slip does not hide the method.
Some calculator questions say "Write down your full calculator display" or "Write down all the figures on your calculator display". The mark is for copying every digit, not for rounding. Press the keys, wait for the answer, then copy the whole number, such as 5.766666667. Do not shorten it to 5.77, because that throws away the mark.
If the question also says "Give your answer as a decimal", it only wants a decimal form, not a fraction. Your calculator may show a fraction by default, so use the key that changes the display to a decimal. A later part that says "Give your answer to 2 decimal places" asks for rounding, and you then round from the full display. Write the full display on the answer line first, then the rounded value.
Method: 1. Type the whole calculation in one go, using brackets where needed. 2. Copy every figure on the display. 3. If the question asks for rounding, round from that full display. 4. Check the size of the answer with a quick estimate.
Tip: Your calculator can only show about ten digits, so a recurring decimal may end in a rounded digit. That is fine to copy.
When a question writes a long expression on the top and another on the bottom, the fraction line acts like a pair of brackets. For (18.3 + 4.5)/(1.2 × 3.5) the top is 22.8 and the bottom is 4.2, so the answer is 22.8 ÷ 4.2 = 5.4285714ldots. If you type 18.3 + 4.5 ÷ 1.2 × 3.5 without brackets, the calculator divides only the 4.5 and gives a very different answer.
Either use the fraction key, or put the top in brackets, press divide, then put the bottom in brackets: (18.3 + 4.5) ÷ (1.2 × 3.5). An easy check is to work out the top and the bottom separately first, and write them down. That shows a method even if the final key sequence goes wrong, and it earns the method mark. Round at the end only, to the number of decimal places asked for.
Method: 1. Work out the top of the fraction on its own and write it down. 2. Work out the bottom of the fraction on its own and write it down. 3. Divide the top by the bottom, using brackets or the fraction key. 4. Round only at the end.
A root sign that covers a sum needs a bracket. To work out √(3.6^2 + 4.8^2) you must square each number, add the squares, and only then take the root: 12.96 + 23.04 = 36 and √(36) = 6. Taking the root of each number separately, or adding 3.6 + 4.8, gives 8.4 and is wrong. This is the form that Pythagoras' theorem uses.
For a power such as 2.5^4, use the power key, enter the index, then press equals: 39.0625. For a long calculation in stages, use the answer key to bring the exact last answer into the next line. Retyping a rounded value loses accuracy and can change the final digit. Keep full displays between stages and round only the answer you hand in.
Method: 1. Open a bracket after the root sign and close it after the last term. 2. Square or cube each part with the correct key. 3. Use the answer key for the previous result instead of retyping a rounded value. 4. Square your final answer to check it gets you back to the number under the root.
Tip: If a root answer is not close to what you expected, check that you closed the bracket in the right place.
In context questions the calculator does the arithmetic, but you must decide the calculation and the form of the answer. A car tank holds 56.4 litres and the car uses 7.3 litres every 100 km. The distance is 56.4 ÷ 7.3 × 100 = 772.6ldots km. If the question says "to the nearest kilometre", the answer is 773 km.
Write a line of working before the answer, because a wrong final digit with a clear method still gains method marks. Units matter: litres, kilometres, pounds. In money problems, a display like 19.164 must be rounded to the nearest penny, £19.16. Always read the last line of the question for the accuracy required, and finish by checking that the answer is the right size: a car cannot travel 7.7 km on a full tank.
Method: 1. Write the calculation as a line of working with the numbers from the question. 2. Type it carefully and copy the full display. 3. Round in the way the question asks: decimal places, significant figures, nearest penny or nearest whole number. 4. Write the unit and check that the size is sensible.
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