Challenge Level

Firstly here's the Excel file: Fraction Multiplication (simple) . Right-click, "Save Target As", and select where you want the file to be saved.

There's another version of this file called Fraction Multiplication (extra) which shows more of the stages in the justification. However, I prefer the simpler version, it feels less cluttered.

Question: What's 2/5 of . . . 1/3, 2/3, 3/4, 3/5, or 4/5?

Here's what I say and do if I'm using Fraction Multiplication (extra); with the simple version, what I say will be much the same.

- Set the spinners to get 2/5 of 1/3
- Show 1/3 at the top of the board or screen
- Next look at 1/5 of 1/3 and observe that this is the same as 1/15
- Show 2/5 of 1/3 - obviously 2/15
- Change the spinner to get 2/5 of 2/3, and discuss how this answer can be worked out almost instantly from the first one.
- 2/5 of 2/3 would be . . . 2/15 from the first third, then another 2/15 from the second . . . in other words: 4/15
- Move on to think about 2/5 of 3/4
- Using fifths of quarters means we will be counting up twentieths
- 1/5 of 1/4 is 1/20
- 1/5 of each of the three quarters (1/5 of 3/4 ) is 1/20 three times: 3/20
- So another 1/5 (that's two fifths of 3/4 in all) makes another 3/20 , or 6/20 in all. * Sometimes, as in this case, the result can be expressed more simply: 3/10 instead of 6/20