# 6.1.5 Equivalent Fractions

## Activity: Equivalent Fractions

This activity may require you to work out some of the solutions on paper. It is recommended that you use your math notebook to keep track of your work.

(a) Use your knowledge of equivalent fractions to fill in the missing numbers.

• (i)
• (ii) ### Discussion

The denominator of the fraction on the left is 3. What do you have to multiply it by to get 18? Remember that if you multiply the denominator by a particular number, you must do the same to the numerator. (a)

(i) The 3 is multiplied by 6 to reach 18, so this is the number that is used to multiply the numerator and the denominator. The missing number is 12. (ii) Similarly, since , multiply the numerator and the denominator by four.

The missing number is 16. (b) Which of the following three fractions are equivalent to each other?

• (i)
• (ii)
• (iii) ### Discussion

Did you check to see if multiplying the numerator, 7, by any numbers gave the numerator of another of the given fractions? If so, try multiplying the denominator, 8, by the same number and see what denominator is yielded. (b) Multiplying the numerator and the denominator of the first fraction by five gives Only the two fractions labelled (i) and (ii) are equivalent.

You cannot create from by multiplying numerator and denominator by the same number.

If you multiply by 7 top and bottom, which is to multiply it by , you get , which isn’t , and if you multiply by 8 top and bottom (that is, multiply it by ) you get , which isn’t , either.

(c) Reduce (cancel) the following fractions into their lowest terms.

• (i)
• (ii)
• (iii)
• (iv) ### Discussion

Look at each fraction individually. What number can divide evenly into both the numerator and the denominator of each? Remember, there could be more than one option. (c)

• (i) Dividing the top and the bottom by 2 gives .

• (ii) Dividing the top and the bottom by 10 (or by 5 and then by 2) gives .

• (iii) Dividing the top and the bottom by 9 and then by 3 gives .

• Dividing the top and the bottom by 4 and then 3 gives: .

(Of course it does not matter which number you divide by first, and there are even more choices than the ones shown. Reducing is a process.)

If you find it difficult to spot the numbers to divide by, try to work systematically by trying 2, 3, 5, … in turn. You can check these results by using your calculator, as you will see shortly. Does the notation of reducing a fraction used in part (c) of this activity look new to you? Click the “View document” link for an explanation.

View document [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)]

6.1.6 Fractions of a Group