Friday, March 8, 2013

Rearranging terms and simplifying an expression.


I am behind schedule and hope to get back to baseball tomorrow.  This is a challenging arithmetic problem.

Simplifying the expression below:

What is Y=(1/3) x ((6/7)+(9/21)) / ((19/42)((1/3)+(5/9))

The numerator is

N=(1/3) x (27/21)

The denominator is

D= (19/42) x (8/9)


Y= (1/3) x (27/21) /  (19/42)  x  (8/9)

Dividing by a number is the same as multiplying by its reciprocal.

See the hint in the link below:


Using this fact we invert the denominator and multiply all terms.  We get.

Y=(1/3) x (27/21) x (42/19) x (9/8)

We rearrange terms because multiplication is both associative and commutative.  This is discussed in the link below:



So rearrange and observe

3=9/3

2=42/21

Y=1 x 3 x 2 x 27/ 19 x 8

2/8 =1/4

Y=3 x 27 / 19 x 4

Y = 81/76

This is in simplest form.

In decimal form this is 1.0658.

I really want to get back to baseball tomorrow. 

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