6.2.1 Adding and Subtracting Fractions with the Calculator

In the following exploration you’ll learn how to use the calculator to add and subtract fractions.

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

Let’s try adding some fractions on the calculator.

Enter one divided by five plus two divided by five, then click , or press Enter on your keyboard. You should see the following:

So, adding one-fifth and two-fifths gives three-fifths, which should make sense.

Notebook symbolCalculator Activity: Adding and Subtracting Fractions

Try the following additions and subtractions on the calculator.

(a) three divided by eight plus six divided by eight

Hint symbol


Remember to clear the previous calculation before you start by clicking . Then, enter each calculation exactly as it is written. With complicated calculations like these, it is important to watch the top screen to make sure that the calculator is doing what you want it to do.

Solution symbol


(a) Both fractions in this calculation are eighths, so you can add them directly, giving nine divided by eight. Because the result is bigger than 1, it is given as a mixed number and then as a decimal number.

(b) nine divided by 10 minus seven divided by 10

Solution symbol


(b) You can subtract fractions, too. Both fractions are tenths, so subtracting

seven divided by 10 from nine divided by 10 gives two divided by 10, which reduces to one divided by five by dividing both the numerator and the denominator by 2.

(c) one divided by three plus five divided by 24

Solution symbol


(c) This time the fractions have different denominators. The calculator has converted to twenty-fourths by multiplying top and bottom by 8.

This gives equation left hand side eight divided by 24 plus five divided by 24 equals right hand side 13 divided by 24

The decimal form has been rounded here, so is not exact. For this reason, mathematicians often prefer to leave numbers as exact fractions rather than expressing them as rounded decimals.

(d) sum with, 3 , summands one divided by two plus one divided by three plus one divided by four

Solution symbol


(d) The calculator has converted all the fractions to twelfths, because twelve is the smallest number that 2, 3, and 4 all divide into evenly. The sum sum with, 3 , summands one divided by two plus one divided by three plus one divided by four is written as sum with, 3 , summands six divided by 12 plus four divided by 12 plus three divided by 12. Now the fractions can be added, because they are all have the same denominator, giving the answer 13 divided by 12, or .

(e) one divided by nine minus two divided by three plus one divided by two

Solution symbol


(e) This time, all the fractions are written as eighteenths, because 18 is the smallest number that 9, 3, and 2 divide evenly into. So, equation left hand side one divided by nine minus two divided by three plus one divided by two equals right hand side two divided by 18 minus 12 divided by 18 plus nine divided by 18. The calculation in the numerator is equation left hand side two minus 12 plus nine equals right hand side one minus. (You learned how to work with negative numbers in Unit 2.)

So, the answer is 118 minus

Notice here that there is only room on the top screen for the calculator to display the first 8 decimal places of the decimal answer, but the answer correct to 14 decimal places is shown in the screen below.

6.2 Adding and Subtracting Fractions

6.2.2 Mixed Numbers on the Calculator