# 6.1.10 Practice with Fractions

## Activity: Mixed Numbers and Improper Fractions

(a) Change the following mixed numbers into improper fractions.

• (i)
• (ii)
• (iii) ### Discussion

If you are having trouble with this, did you try using a picture? To get started, look at the extra example offered in the example at the end of the last screen, or watch the pencast that is located in the same place. (a)

• (i) Using our “pizza math,” the calculation would look like this: So, as there are four quarters in each whole, three wholes will give quarters. The one extra quarter makes 13 overall.

Thus, .

• (ii) We could use the following shortcut to solve this one:

• (iii) There are eight eighths in each whole, so seven wholes will give 56 eighths. The extra three eighths makes 59 overall, so the fraction is . Hence, .

(b) Change the following improper fractions into mixed numbers.

• (i)
• (ii)
• (iii) ### Discussion

Have you thought about drawing pizzas that contain five slices each? What about performing long division? (b)

• (i) Since , 20 fifths will make up 4 wholes. This leaves an extra 3 fifths, so the fraction is . Thus, .

• (ii) Let’s try using long division: Since , 14 sevenths will make up two wholes. This leaves one seventh over, so the fraction is . Hence, .

• (iii) Since , 16 quarters will make up four wholes. This leaves one quarter over, so the fraction is . Consequently, .

6.1.9 Improper Fractions

6.1.11 Using the Calculator for Fractions