# 6.1.11 Using the Calculator for Fractions

You can use the calculator to carry out calculations involving fractions. In the following exploration, you will learn how to use the calculator:

- To convert fractions to decimal numbers.
- To reduce fractions.
- To convert improper fractions to mixed numbers.
- To convert decimal numbers to fractions.

The calculator can be accessed on the left-hand side bar under Toolkit.

A fraction is one number divided by another, so to input a fraction on the calculator, use the division key: .

## Converting Fractions to Decimal Numbers

To enter the fraction one-half, the calculator sequence is .

Or, you can type on your keyboard, if you prefer.

Enter one-half, then click on the equals sign (or Enter on your keyboard). In the top window, you should see the fraction, followed by the decimal equivalent.

Try entering the following fractions and see what happens. Remember to clear each one by clicking the button before you enter the next fraction.

### Calculator Activity: Entering Fractions

(a)

#### Discussion

Enter the numerator (top), then the division sign, then the denominator (bottom), and finally the equals sign. When you reach the mixed number in part (e), enter it as 2 whole units plus the fraction part.

#### Answer

(b)

#### Answer

We say that is a repeating decimal, but it is shown on the calculator rounded to 14 decimal places. Why is the final digit 7 rather than 6? If you were asked to round this to 2 decimal places, what would your answer be?

Think before you read on.

Let’s round the displayed number. Remember from Unit 2, that when you are rounding a number, you look at the first digit that you want to cut off. If this digit is 5 or more, then round up the previous digit, which becomes the final digit in your answer. So, , when written as a decimal rounded to 2 decimal places, is 0.67.

(c)

#### Answer

can be reduced, so the calculator shows first, then the reduced form, , and finally, the decimal equivalent.

(d)

#### Answer

is an improper fraction. The calculator shows it as a mixed number before converting it to a rounded decimal.

(e)

#### Answer

means 2 with an extra added on, so enter it like this on the calculator:

## Converting Decimals to Fractions

The calculator can help you write a terminating decimal as a fraction too. Enter the decimal 0.4375 into the calculator, then click on . In the top screen you should see:

### Calculator Activity: Converting Decimals to Fractions

Use the calculator to convert the following decimal numbers to fractions:

(a) 0.65

#### Discussion

Clear the previous calculation from the calculator, enter the decimal number and click on the equals sign.

#### Answer

(a)

(b) 7.36

#### Answer

(b)

The number is greater than 1, so the calculator displays it first as an improper fraction, then as a mixed number.

(c) 0.986

#### Answer

(c)

The calculator has its limitations. When the fractional equivalent of a decimal has a large denominator, the calculator gives an approximation. The sign ≈ means “is approximately equal to.”

rounded to 6 decimal places, so the fraction approximation for 0.986 given by the calculator is quite close to the exact answer. If you need an exact answer, you will need to work it out for yourself by remembering that 0.986 is the same as , and then reducing that fraction as far as possible.

## To recap:

- To enter a fraction, enter the numerator, the division sign and then the denominator.
- To enter a mixed number, enter the whole number, then the plus sign, then the fraction as described above.
- To reduce a fraction, enter the fraction and click on the equals sign.
- To convert:
- a fraction to a decimal number,or
- an improper fraction to a mixed number, or
- a decimal number to a fraction,

If you feel that you need extra practice in converting fractions from one form to another, try making up some of your own examples and then check your answers on the calculator.

6.1.10 Practice with Fractions