6.3.2 Multiplying Mixed Numbers and Fractions on the Calculator

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

In this exploration, you will learn how to multiply fractions on the calculator.

When you used the calculator to add fractions, you didn’t have to think too hard about entering them correctly, because the calculator follows the correct order of operations. It prioritizes division over addition, and the fractions are automatically entered as you intend.

More care is needed for multiplication of fractions, because division and multiplication have equal priority where order of operations is applied.

To be sure that the calculator is performing the calculation that you want it to, it is best to insert parentheses around each fraction.

So, to multiply three divided by four multiplication two divided by five, you must enter the calculation as open three divided by four close multiplication open two divided by five close on your calculator.

The proper key sequence is:

The calculator should show:

Note how the calculator automatically converts six divided by 20 into three divided by 10 before it displays the answer as a fraction and a decimal.

Activity symbol Activity: Multiplying Fractions

Try the next examples for yourself.

(a) two divided by three multiplication six divided by 11

Hint symbol

Discussion

(a) Remember to put parentheses around the fractions.

Solution symbol

Answer

By hand: equation left hand side two divided by three sub one multiplication six squared divided by 11 equals right hand side four divided by 11

Using the calculator:

(b) 10 divided by 27

Hint symbol

Discussion

To do the calculation without the calculator, you need to change the mixed number into an improper fraction. You can enter the fraction as a mixed number on the calculator.

Solution symbol

Answer

By hand: equation sequence 10 divided by 27 equals nine super one divided by five sub one multiplication 10 squared divided by 27 sub three equals two divided by three

Using the calculator, you can enter the mixed number as a sum. You need parentheses around the whole of open one plus four divided by five close to show that you are multiplying all of this by 10 divided by 27.

(Here, the top window of the calculator only displays the first eight of the 14 decimal places. The entire rounded output is shown in the window below.)

To recap:

  • The calculator follows orders of operations. It calculates results in parentheses first, then exponents, then multiplication and division, and lastly addition and subtraction.
  • When multiplying fractions on the calculator, enclose each fraction or mixed number in its own set of parentheses.

6.3.1 Multiplying Mixed Numbers and Fractions

6.3.3 Banking with Fractions