Operations mistake

Algebra Level 2

Vikram has been working with Order of Operations all day, and has a strong sense that

( − a ) + b = b − a , (-a) + b = b - a,

but doesn't know why. How many of the 11 × 11 11 \times 11 ordered pairs of integers ( a , b ) (a, b) , where a a and b b are integers from 0 to 10 (inclusive) , are there, such that

( − a ) + b = b − a ? (-a) + b = b-a?


The answer is 121.

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Arron Kau by Arron Kau

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2 solutions

It is always true that (-a)+b = b-a so you can use any numbers. but the question told you that it must be integers from 0 to 10 to be paired. There is 11 integers from 0 to 10. So you will have 11x11=121 pair of integers.

Sorry if my english is bad.

7 Helpful 0 Interesting 0 Brilliant 1 Confused

great yongyutha !

your english is good.

sourabh jain - 5 years, 11 months ago

Prove that it is true?

Surya Subbarao - 5 years, 3 months ago
Bryan Chin
Jul 17, 2015

(-a) + b is just a different way of writing b - a, so b - a = b - a, therefore it does not matter which number you choose for a and b. So as it says that you have to choose 1 of 11 integers from 0 to 10 for both a and b, you have 11x11 which is 121.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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