6.3.3 Banking with Fractions

Activity symbol Activity: Banking with Fractions

In the New Policy Institute survey introduced before, three divided by five of the 210 young people had bank accounts. Of these, one divided by three had overdraft protection and approximately two divided by five had checkbooks.

(a) How many of the people surveyed had overdraft protection?

Hint symbol

Discussion

How many people from the group had a bank account? The word “of” often translates into multiplication and a whole number can be written as a fraction by placing it over 1. What fraction of those with bank accounts have overdraft protection?

Solution symbol

Answer

(a) Let’s use our new knowledge of fraction multiplication. three divided by five of 210 translates to equation sequence three divided by five multiplication 210 equals three divided by five multiplication 210 divided by one equals three multiplication 210 super 42 divided by five sub one multiplication one equals three multiplication 42 divided by one multiplication one equals 126 divided by one equals 126.

So, we know that 126 people have bank accounts. One third of this group have overdraft protection, so equation sequence one divided by three multiplication 126 divided by one equals one multiplication 126 super 42 divided by three sub one multiplication one equals one multiplication 42 divided by one multiplication one equals 42 divided by one equals 42.

Therefore, 42 of the people surveyed have overdraft protection.

(b) How many survey participants had checkbooks?

Hint symbol

Discussion

What fraction of the group with bank accounts also have checkbooks?

Solution symbol

Answer

(b) We already know how many people have bank accounts: 126. We then need to find two divided by five of this group.

We can calculate that equation sequence two divided by five multiplication 126 divided by one equals two multiplication 126 divided by five multiplication one equals 252 divided by five equals 50.4 people.

This fraction, it turns out, is an approximation. You need to interpret the results of your calculation carefully, particularly if it involves fractions of a person!

So, about 50 people have checkbooks.

In the previous activity, you might have approached the problem differently. Perhaps you found what one-fifth of the group was first by using division, and then used this portion to find three of those sets. Once you had this value, which indeed is 126 people, you could have then found the number of people with overdraft protection and checkbooks as done above.

Both approaches are valid and will give you the correct answers. Choose whichever method is easier for you.

6.3.2 Multiplying Mixed Numbers and Fractions on the Calculator

6.4 Introduction to Dividing Fractions