### I am having hard time to understand why a-b = -(b-a)

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I just memorize it but I don't quite understand why.

Community: Riverside High School 9th Grade Math

### 2 Answers

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Using the the distributive property,

$-\left(b-a\right)=-1\times\left(b-a\right)=-b+a=a-b$−(`b`−`a`)=−1×(`b`−`a`)=−`b`+`a`=`a`−`b`

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Intuitively speaking, a-b is the difference between a and b. Whereas b-a is the difference between b and a. They are just opposite of each other and therefore the minus sign.

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