Directed Numbers

NZ Level 5

Use a calculator to evaluate expressions with directed numbers

Lesson

A calculator is a mathematician's tool. Just like a hammer is for a builder, and a paintbrush is for a painter. Anyone can use a hammer or paintbrush, but the builder and the painter know how to use their tools really well to make the jobs they have to do as easy as possible.

As apprentice mathematicians, we all need to know how to use our calculators efficiently and correctly.

Most calculators have a special button to make negative numbers, here are some examples on some common calculator types.

To enter the calculation $-351\times996$−351×996 on a calculator.

Some calculators would need you to enter the negative sign before you enter the negative number calculation like this:

Some calculators would need you to enter the negative sign after you enter the negative number calculation like this:

Try this calculation on your calculator: the correct answer is $-349596$−349596.

Which way do you need to enter the negative on your calculator to get the correct answer?

But what if the negative number is not at the beginning of the calculation?

Well, here is another one we will try out.

We want to use a calculator to find the value of:

$-6.3\times9\times\left(-14.08\right)$−6.3×9×(−14.08)

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

The product of two negatives and a positive could be positive or negative.

AThe product of two negatives and a positive is a positive.

BThe product of two negatives and a positive is a negative.

CThe product of two negatives and a positive could be positive or negative.

AThe product of two negatives and a positive is a positive.

BThe product of two negatives and a positive is a negative.

CNow, use your calculator to find the value of:

$-6.3\times9\times\left(-14.08\right)$−6.3×9×(−14.08)

Which of the following expressions also have the same value as the product in the previous part? Select all of the correct answers.

$6.3\times\left(-9\right)\times14.08$6.3×(−9)×14.08

A$6.3\times9\times14.08$6.3×9×14.08

B$-14.08\times9\times\left(-6.3\right)$−14.08×9×(−6.3)

C$-6.3\times9\times14.08$−6.3×9×14.08

D$6.3\times\left(-9\right)\times14.08$6.3×(−9)×14.08

A$6.3\times9\times14.08$6.3×9×14.08

B$-14.08\times9\times\left(-6.3\right)$−14.08×9×(−6.3)

C$-6.3\times9\times14.08$−6.3×9×14.08

D

$9989-\left(-9885\right)$9989−(−9885)

Some calculators will need you to enter the negative number in brackets, whilst some will need you to enter the calculation as you see it from left to right. Try these two methods, and see what your calculator does. You want the correct answer of course, and in this question it is 19874.

Method 1:

Method 2: Some calculators (particularly older ones) need you to use brackets when the negatives are within the calculation.

The associated Mathspace exercise will really test out your calculator skills with negative numbers. Use your calculator and check your answers with Mathspace. It's as much about learning how to read the mathematical questions as it is learning how to use your tool the best!

We want to use a calculator to find the value of:

$\frac{26-64}{-58+53}$26−64−58+53

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

The answer will be

*negative*as we are dividing a*positive*number by a*negative*number.AThe answer will be

*positive*as we are dividing a*negative*number by a*negative*number.BThe answer will be

*negative*as we are dividing a*negative*number by a*positive*number.CThe answer will be

*positive*as we are dividing a*positive*number by a*negative*number.DThe answer will be

*negative*as we are dividing a*positive*number by a*negative*number.AThe answer will be

*positive*as we are dividing a*negative*number by a*negative*number.BThe answer will be

*negative*as we are dividing a*negative*number by a*positive*number.CThe answer will be

*positive*as we are dividing a*positive*number by a*negative*number.DNow, use your calculator to find the value of $\frac{26-64}{-58+53}$26−64−58+53, giving your answer as an exact decimal.

Which of the following expressions has the same value? Choose all correct answers

$\frac{26+64}{-58-53}$26+64−58−53

A$\frac{64-26}{58-53}$64−2658−53

B$\frac{64-26}{53-58}$64−2653−58

C$\frac{-26+64}{-53+58}$−26+64−53+58

D$\frac{26+64}{-58-53}$26+64−58−53

A$\frac{64-26}{58-53}$64−2658−53

B$\frac{64-26}{53-58}$64−2653−58

C$\frac{-26+64}{-53+58}$−26+64−53+58

D

Understand operations on fractions, decimals, percentages, and integers