McGraw Hill Glencoe Algebra 2, 2012
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McGraw Hill Glencoe Algebra 2, 2012 View details
1. Expressions and Formulas
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Exercise 44 Page 9

What does the definition of a$b$c mean?

1/11

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We are given the following definition. a$b$c=- a-b-c/c-b-a This means, that for any given a, b, and c, the value of the expression on the left-hand side is the same as the value of the expression on the right-hand side. To find -2$( -4)$ 5, we can substitute a= -2, b= -4, and c= 5 in the expression on the right-hand side and evaluate the result.

a$b$c=- a-b-c/c-b-a
-2$( -4)$ 5=-( -2)-( -4)- 5/5-( -4)-( -2)
-2$(-4)$5=2-(-4)-5/5-(-4)-(-2)
-2$(-4)$5=2+4-5/5+4+2
-2$(-4)$5=1/11

Extra

Alternative interpretation
Before we discuss an alternative way of interpreting the question, let's look at a familiar example. What is - 3^2?

  • Is it -(3^2)=-9? The negative of three squared?
  • Is it (- 3)^2=9? The square of negative three?

The agreed order of operations tells us, that it is -9.

Back to our question. How do we interpret the leading negative in -2$(-4)$5?

  • Is it -(2$(-4)$5)?
  • Is it (-2)$(-4)$5?

Since this is a newly introduced operation, there is no agreement to apply. In our solution above, we substituted a=-2, b=-4 and c=5 to find -2$(-4)$5. This assumes that we used the second interpretation. Let's see the result using the first interpretation. In this case we need to substitute a=2, b=-4 and c=5.

-(2$(-4)$5)=--2-(-4)-5/5-(-4)-2
-(2$(-4)$5)=--2+4-5/5+4-2
-(2$(-4)$5)=--3/7
-(2$(-4)$5)=-(-3)/7
-(2$(-4)$5)=3/7