 New Zealand
Level 6 - NCEA Level 1

Using a calculator for rational or integer calculations

Lesson

We have looked at a lot of ways of calculating with whole numbers, decimals, fractions, percentages and negative numbers using mental computation and by hand methods.

When you are faced with a computation you need to be able to look at it and identify if it is something that you can do in your head (mental computation), by hand or if you need a calculator or technological assistance.  The line you draw between what calculations you can do mentally and what you do by hand may be different to your friend or classmate, so too the line between by hand or using a calculator. Now you might think it odd but for calculations you are fluent at performing by hand, you will most likely be quicker to complete it by hand than to reach for a calculator.  Try it and see.

Not all calculators and online devices work the same way, so it's important that you use the calculator you are allowed to use in your exams or tests often.  I have seen many students struggle in a test because they borrowed a friends calculator at the last minute and they don't know how to use it!

Other things to look for on your calculator is how well it deals with the following.

Order of operations

Try the following calculation on your calculator.  Type it in exactly from left to right.

$6+3\times7$6+3×7

Some calculators will display $63$63, and others will display the correct answer of $27$27.  This is because some calculators can correctly identify that the multiplication needs to be completed before the addition of $6$6

Negative numbers

Entering in a negative number is something you need to be familiar with.   Most calculators have a $\pm$± button, and some calculators need you to press it before the number, and some after. Try this on your calculator,

$36\div\left(-3\right)$36÷​(3)

Make sure you know how to enter the negative three correctly onto your calculator.

Others

Other buttons or functions that are helpful to find how to enter are

• fractions
• exponents

Examples

Question 1

What is the output on your calculator when you enter $2.7\times10^7$2.7×107?

Question 2

We want to use a calculator to find the value of

$-692\times133$692×133

1. Before entering the calculation in to your calculator, it is useful to have an estimation in mind. Choose the correct statement:

The product of $-692$692 and $133$133 will be positive.

A

The product of $-692$692 and $133$133 will be negative.

B

The product of $-692$692 and $133$133 will be positive.

A

The product of $-692$692 and $133$133 will be negative.

B
2. Now, use your calculator to find the value of $-692\times133$692×133:

3. Which of the following expressions has the same value?

$692\times133$692×133

A

$692\times\left(-133\right)$692×(133)

B

$-692\times\left(-133\right)$692×(133)

C

$692\times133$692×133

A

$692\times\left(-133\right)$692×(133)

B

$-692\times\left(-133\right)$692×(133)

C

Question 3

We want to use a calculator to find the value of

$\left(-2492640\right)\div288$(2492640)÷​288

1. Before entering the calculation in to your calculator, it is useful to have an estimation in mind. Choose the correct statement:

If we divide $-2492640$2492640 by $288$288 our result will be positive.

A

If we divide $-2492640$2492640 by $288$288 our result will be negative.

B

If we divide $-2492640$2492640 by $288$288 our result will be positive.

A

If we divide $-2492640$2492640 by $288$288 our result will be negative.

B
2. Find the value of the division.

3. Which of the following expressions has the same value?

$2492640\div288$2492640÷​288

A

$\left(-2492640\right)\div8655$(2492640)÷​8655

B

$2492640\div\left(-288\right)$2492640÷​(288)

C

$2492640\div288$2492640÷​288

A

$\left(-2492640\right)\div8655$(2492640)÷​8655

B

$2492640\div\left(-288\right)$2492640÷​(288)

C

Outcomes

NA6-6

Generalise the properties of operations with rational numbers, including the properties of exponents

91027

Apply algebraic procedures in solving problems