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## Question

primary 5 | Maths
| Fractions

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Hi pls help my kid thanks

Notice a pattern?

-1/2 is cancelled out by + 1/2

-1/3 is cancelled out by + 1/3

-1/4 is cancelled out by + 1/4

And so on.

The only terms left are 1/1 and -1/10

So,

1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + 1/4 - 1/5 +.... + 1/8 - 1/9 + 1/9 - 1/10

= 1/1 - 1/10

= 10/10 - 1/10

= 9/10

### See 1 Answer

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After all the cancellations, the surviving terms are 1/1 and -1/10, and of course 1/1 - 1/10 = 9/10.

This method is also known as the method of differences.