6.1.10 Practice with Fractions

Activity symbol Activity: Mixed Numbers and Improper Fractions

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

  • (i)
  • (ii)
  • (iii)
Hint symbol


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.

Solution symbol



  • (i) Using our “pizza math,” the calculation would look like this:

    The figure shows three circles (representing pizzas) each divided into four quarters, together with a quarter circle. There are thirteen quarters all together.

    So, as there are four quarters in each whole, three wholes will give three multiplication four equals 12 quarters. The one extra quarter makes 13 overall.

    Thus, equals 13 divided by four.

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

    equals open whole multiplication denominator close plus numerator divided by denominator equals equation sequence open two multiplication five close plus four divided by five equals 10 plus four divided by five equals 14 divided by five
  • (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 59 divided by eight. Hence, equals 59 divided by eight.

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

  • (i) 23 divided by five
  • (ii) 15 divided by seven
  • (iii) 17 divided by four
Hint symbol


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

Solution symbol



  • (i) Since four multiplication five equals 20, 20 fifths will make up 4 wholes. This leaves an extra 3 fifths, so the fraction is . Thus, 23 divided by five equals.

  • (ii) Let’s try using long division:

    Since two multiplication seven equals 14, 14 sevenths will make up two wholes. This leaves one seventh over, so the fraction is . Hence, 15 divided by seven equals.

  • (iii) Since four multiplication four equals 16, 16 quarters will make up four wholes. This leaves one quarter over, so the fraction is . Consequently, 17 divided by four equals.

6.1.9 Improper Fractions

6.1.11 Using the Calculator for Fractions