Franco was answering his Mathematics homework last night. But because he was in a hurry for dinner, he had misread the five items in his assignment. Instead of working out 7 1/5 ÷ 6, he calculated for 7 1/5 - 6. He was amazed to find that he had the same answer to both calculations! He then tried 5 1/3 ÷ 4 and found the same result as with 5 1/3 - 4. What do you think are the other three items in Franco's assignment? Work it out and explain your strategy. Did you spot any pattern?
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Answer:
7 1/5 ÷ 6 = 36/5 ÷ 6 = 36/5× 1/6 = 6/5 = 1 1/5
7 1/5 - 6 = 1 1/5
5 1/3 ÷ 4 = 16/3 ÷ 4 = 16/3 × 1/4 = 4/3 = 1 1/3
5 1/3 - 4 = 1 1/3
* Three other items
6 1/4 ÷ 5 = 25/4 ÷ 5 = 25/4 × 1/5 = 5/4 = 1 1/4
6 1/4 - 5 = 1 1/4
4 1/2 ÷ 3 = 9/2 ÷ 3 = 9/2 × 1/3 = 3/2 = 1 1/2
4 1/2 - 3 = 1 1/2
00
8 1/6 ÷ 7 = 49/6 ÷ 7 = 49/6 × 1/7 = 7/6 = 1 1/6
8 1/6 - 7 = 1 1/6
*Pattern
x 1/(x-2) ÷ (x-1) = x 1/(x-2) - (x-1)
example: let x=9
9 1/7 ÷ 8 = 64/7 ÷ 8 = 64/7 × 1/8 = 8/7 = 1 1/7
9 1/7 - 8 = 1 1/7