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3.9 Using a calculator
A calculator is a handy tool that can help you to calculate quickly and accurately, provided that you know how to press the correct keys.
Also, you need the right attitude when using a calculator.
Calculations like 9 + 3, 5 × 6, 30 + 7 and 200 + 300 can be done faster mentally than with a calculator. You should not use a calculator for such calculations.
Learning calculator language
The calculator cannot think for you. It only does what you tell it to do.
So you must learn how to talk calculator language, so that the calculator can understand you!
If you want to use the calculator to solve a word problem, you must first translate from English into the language of arithmetic, and then into calculator language.
Calculator language is written as a keystroke sequence using the different kinds of keys on the calculator.
There are many different kinds of calculators. Some are called simple calculators and some scientific calculators.
here we work only with a very simple calculator.
Display Clear key(s)
equals key Operations keys Number (digit) keys
English language Words
Arithmetic language Calculation plan
Calculator language Keystroke sequence I have 3 bags with
4 sweets each and another 5 sweets
3 × 4 + 5
3 × 4
+ 5 =
We do simple basic operations on the calculator like this:
Calculation plan Calculator keystroke sequence 6 + 2
6 − 2 6 × 2 6 ÷ 2
It is very important to understand that you must always use the
= key to tell the calculator to now do the operations that you typed.
Note that we are using small numbers here only to explain, and so that we can easily check the calculator mentally. But we should only use the calculator when calculating with large numbers.
1. Use your calculator to calculate these. Check by estimating the answers.
(a) 11 × 21 (b) 150 ÷ 6
(c) 212 − 103 (d) 136 + 48
(e) 23 × 52 (f) 1 728 − 619
2. (a) What is the biggest number that can be typed on your calculator?
Press 123456789 and see what happens. Can you type 100 000 000?
(b) What is the biggest number that the calculator can show or display? Press 99999999 + 2 = and see what happens.
6 6 6 6
+
−
×
÷ 2 2 2 2
=
=
=
=
3. Calculate using your calculator. How will you check that the answers are correct?
(a) 123 456 + 234 567 (b) 1 234 567 + 7 654 321 (c) 97 531 − 57 975 (d) 7 654 321 − 779 348 (e) 7 557 − 5 975 + 7 979 (f) 879 715 + 54 021 − 176 534 Correcting mistakes
What if you make mistakes?
It is very easy to press wrong keys by accident, and then to get wrong answers, for example:
• You may press the wrong operation:
For example, you may press + instead of − .
• You may press the wrong number:
For example, you may press 32 instead of 23.
Instead of then having to redo everything, you can learn shortcuts to correct different kinds of mistakes.
4. How do we correct the mistake of keying the wrong operation, for example pressing + instead of − , except to start over again?
Do the following keystroke sequences on your calculator. Look at the display after every keystroke and try to explain how your calculator works. Try to predict the display before pressing each key.
(a) (b)
(c) (d)
(e) (f)
Describe a method to correct an incorrect operation entry on your calculator.
it is a good habit to keep your eyes on the display, so that you can immediately see when you make a typing error.
7 + × 3 =
7 + − 3 =
7 + + 3 =
7 × + 3 =
7 − + 3 =
7 − × 3 =
5. Your calculator will have a C (clear) key and maybe also an AC (all clear) key. Different calculators use these keys
differently. On most calculators the C key clears only the last entry, and on some calculators pressing the C key twice deletes everything.
Find out how the correction (clear) key on your calculator works by typing these key sequences. Try to predict what the calculator will display after each keystroke.
(a) 2 + 3 C 5 =
(b) 2 + 3 C C 2 + 5 =
(c) 2 + 3 AC 2 + 5 =
(d) 2 × 3 C 5 =
(e) 2 × 3 AC 2 × 5 =
6. Suppose you want to calculate 15 + 28 − 12 + 46, but make the following mistakes. In each case type the given keystroke sequence, including the mistake. Then correct the mistake and complete the calculation. If you really make mistakes, correct them too!
(a) 15 + 29 (b) 15 + 28 + (c) 15 + 28 − 21
(d) 15 + 28 − 12 − 56
7. If you discover that you typed a wrong operation only after you entered the next number, the mistake cannot be corrected in any of the above ways.
Ben has a bright idea: He wanted to calculate 35 + 89, but typed 35 − 79.
He corrects it like this: 35 − 79 + 79 + 89 = Explain why his method is correct.
Checking your work: estimate
It is very easy to press wrong keys by accident, and then to get wrong answers. You should develop the habit of always checking calculator answers.
8. Use your calculator to calculate 723 + 489.
How do you know if the answer is correct?
Mary just types without thinking and did not see that she typed the × and not the + key. She got the answer 353 547. Mary thought the answer was correct because she thinks the calculator is always right.
But Cyndi always first estimates the answer before she starts typing on the calculator. See if you understand her reasoning:
723 + 489 is more than 700 + 400 = 1 100 723 + 489 is less than 800 + 500 = 1 300
So the answer must be between 1 100 and 1 300.
Only then Cyndi typed on the calculator: 723 × 489 = and just like Mary got the answer 353 547. But Cyndi immediately knew that the answer was wrong and that she must have made a mistake. Then she did it correctly and got 1 212. She was satisfied that the answer seemed reasonable because it is between 1 100 and 1 300. Do you agree?
9. In each case, first estimate the answer like Cyndi did. Then calculate the answer using your calculator, and decide if your answer seems about right.
(a) 3 456 + 4 567 (b) 34 567 + 45 678
(c) 34 × 56 (d) 678 × 234
(e) 123 456 + 257 257 (f) 34 527 + 426 426 Using the calculator to check the calculator
Because it is so easy to make mistakes, it is important that you check your calculator answers.
It usually is not a good idea to check a calculation by just repeating it, because you often make the same mistake again. It is better to check by using a different method the second time.
One way to check is to do the calculation in a different order.
10. Do the following calculations on your calculator in the given order and draw a conclusion.
(a) (1) 483 + 159 – 286 (2) 483 − 286 + 159 (b) (1) 276 + 288 + 951 (2) 276 + 951 + 288 (c) (1) 776 − 288 − 259
(2) 776 − 259 − 288
Two different keystroke sequences that give the same answer are called equivalent sequences.
You can check calculator results using the rearrangement principle:
if you repeat the calculation with a different (but equivalent) keystroke sequence, you will get the same answer.
11. Use your calculator to calculate each of the following. Check the result by using the rearrangement principle.
(a) 15 432 + 8 786 + 3 286 (b) 15 432 − 8 786 + 3 286 (c) 15 432 + 8 786 − 3 286 (d) 15 432 − 8 786 − 3 286 (e) 15 432 + 76 894 + 32 861 (f) 15 432 + 76 894 − 32 861 Checking our work: inverses
12. Use your calculator to calculate each of the following. Draw a conclusion.
(a) 432 + 878 − 878 (b) 5 432 − 786 + 786
(c) 1 234 + 878 − 878 (d) 54 321 − 12 786 + 12 786 (e) 1 234 + 878 − 878 − 1 234 (f) 12 786 − 12 786 + 6 787
Calculator results can be checked by applying inverse operations to the result, in reverse order. You must then get the original input number as answer.
Sipho must calculate 2 345 + 3 214 − 2 255.
He uses this keystroke sequence:
2 345 + 3 214 − 2 255 = and gets 3 304.
To check, he continues with 3 304 + 2 255 − 3 214 = and gets 2 345, and knows that the answer 3 304 must be right. Why?
13. Use your calculator to calculate each of the following.
Check the result by using inverse operations.
(a) 437 + 878 (b) 837 − 378
(c) 1 234 + 878 − 978 (d) 54 321 − 12 786 + 896 (e) 67 897 + 87 834 − 35 978 (f) 54 321 + 12 786 + 49 786
Brackets
14. How can we do 2 × 4 × (5 + 6) on a calculator?
If you have a calculator with brackets, you can use the bracket keys to do calculations on the calculator just as they are written. If your calculator does not have brackets, you will have to make a plan!
Jane says that we must do the operation in brackets first:
5 + 6 = × 2 × 4 = → 88
Do you agree that the answer is 88? Check on your calculator.
15. Calculate the following using your calculator.
(a) 15 432 − (8 786 + 3 286) (b) 15 432 − (8 786 − 3 286) (c) 15 432 + (8 786 + 3 286) (d) 15 432 + (8 786 − 3 286) (e) (786 + 289) × 2 + 3 456 (f) 6 789 − (5 789 − 3 276)