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