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.
Answer
(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?
Answer
(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