 # 1.09 Calculations with fractions and decimals

Lesson

### Using a calculator with fractions

Firstly, get familiar with the fraction button on your calculator. There are a couple of examples of what the button might look like below; it will just depend on the brand of your calculator. See if you can find the fraction button on your calculator. Again, how you use the fraction button when entering a calculation may vary depending on the brand of the calculator. However, the two most common methods are the following.

Say you wanted to enter $\frac{1}{2}$12. Then the common way to do it is to press the following buttons:

 $\editable{1}$1 $\editable{2}$2

The other method is that once you press the fraction key, you then scroll to the box you want using the arrow keys and then fill in the numbers. This method is less common, however some calculators (e.g. the one on the left above) will let you enter fractions this way.

### Entering mixed numbers on a calculator

You may have noticed that there are a lot of different functions in math and making all these functions fit on a calculator is a pretty tricky task! One way they do this is by using second functions, which are the ones written in tiny writing above the buttons on your calculator.

The mixed number button is one of these second functions. So how do you enter one into the calculator?

We need to use the SHIFT key, then press the fraction key like so:

 $\editable{\text{SHIFT}}$SHIFT Again the order you press these and the number keys depend on your calculator, so it's worth asking your teacher to run you through it if you're not sure.

Also, calculators tend to give their answers as decimals. However, there is another handy button you can use to convert your answer between fractions and decimals. Again you can ask your teacher to help you find it. It should look something like this:

 $\editable{\text{S }\leftrightarrow\text{D }}$S ↔D

Just a heads up – not all calculators and online devices work the same way, so it's important that your calculator is approved for use in tests and exams and that you use it often. 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!

Two useful tips!

The word 'of' in mathematics almost always indicates that you need to multiply. So $\frac{3}{5}$35 of $\frac{2}{3}$23 means you do $\frac{3}{5}\times\frac{2}{3}$35×23

A fraction can be thought of as a division. $\frac{5}{8}$58 is the same as $5\div8$5÷​8. You might find it quicker to use the $\div$÷​ key rather than the fraction button at times.

#### Practice questions

##### Question 1

Using a calculator, evaluate $4\frac{4}{11}+1\frac{4}{9}$4411+149, expressing your answer as a mixed number in its simplest form.

##### Question 2

Using a calculator, evaluate $\frac{2}{5}+\frac{2}{3}\div\frac{3}{4}$25+23÷​34.

##### Question 3

Find $\frac{2}{7}$27 of $4$4 hours.

##### Question 4

Maria is a sales assistant. She earns $\$293$$293 per week, plus a commission of \frac{2}{9}29 on anything she sells. Last week she sold \1377$$1377 of sofas.

1. Using a calculator, find Maria's commission for last week (in dollars).

2. Using a calculator, what was Maria's pay for last week (in dollars)?

### Using a calculator with decimals

The decimal point button looks like a full stop key. You enter the decimal just as it is written on the page.

For example the number $1.35$1.35, you would enter:

 $\editable{1}$1 $\editable{.}$. $\editable{3}$3 $\editable{5}$5

#### Practice questions

##### Question 5

Consider $11.59\div4.44$11.59÷​4.44

1. Estimate the answer by rounding both values to the nearest whole number.

2. Use a calculator to evaluate $11.59\div4.44$11.59÷​4.44 and write the answer below. Give your answer to two decimal places.

3. What is the difference between the estimate and the actual answer?

##### Question 6

Consider $7.38\times8.12$7.38×8.12

1. Estimate the answer by rounding both values to the nearest whole number.

2. Use a calculator to evaluate $7.38\times8.12$7.38×8.12 and write the answer below. Give the complete decimal answer.

3. What is the difference between the estimate and the actual answer?

##### Question 7

Evaluate $\frac{0.323}{0.019}$0.3230.019

### Outcomes

#### 8.B2.1

Use the properties and order of operations, and the relationships between operations, to solve problems involving rational numbers, ratios, rates, and percents, including those requiring multiple steps or multiple operations.

#### 8.B2.3

Use mental math strategies to multiply and divide whole numbers and decimal numbers up to thousandths by powers of ten, and explain the strategies used.

#### 8.B2.5

Add and subtract fractions, using appropriate strategies, in various contexts.

#### 8.B2.6

Multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers, in various contexts.