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# Math Question

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what is 6^2/2(3)+4

Guest Aug 3, 2017
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#1
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what is 6^2/2(3)+4

Power calculation before point calculation before line calculation,
then from left to right.

$$\frac{6^2}{2\times 3}+4=\frac{36}{6}+4=6+4\color{blue}=10$$

Whoever wants can also shorten de Bruch by 6.    ($$\frac{36}{6}=\frac{6}{1}$$ )

!

asinus  Aug 3, 2017
#2
+1720
+1

This is a rare example in mathematics where, I believe, parentheses is necessary in order to evaluate the expression without ambiguity. I will demonstrate why.

Strictly speaking, asinus's interpretation is incorrect. If you were to evaluate this with a calculator inputted like as is, the calculator would evaluate it as $$\frac{6^2}{2}*3+4$$. This is because the 2(3) is really multiplication, so division takes precedence since it is comes first in the expression. First it does 6^2, then it divides 6^2 by 2 because division is first from left to right, and then it multiplies that quantity by 3. Here is another example with a variable

8/2y

Using the same logic as above, this equation, in fraction form is strictly $$\frac{8}{2}y$$--not $$\frac{8}{2y}$$. Some would argue, however, that 2y is a term, so it shouldn't be separated.

How do we eliminate this ambiguity if there is no fraction button to speak of? Use parentheses!

Asinus's interpretation of $$\frac{6^2}{2*3}+4$$ will be unambiguous once you add 1 set of parentheses with $$6^2/(2(3))+4$$. Now, the only correct interpretation is $$\frac{6^2}{2*3}+4$$ because the parentheses indicate that we are dividing by the quantity of the product of 2 and 3.

The strict interpretation is $$\frac{6^2}{2}*3+4$$ should be written like $$(6^2/2)(3)+4$$. In this case, the quantity of six squared divided by two is all multiplied by three. No more ambiguity.

Okay, after all of this ranting, now I will evaluate what I believe to be, under the current rules of the order of operations, the way to evaluate the expression 6^2/2(3)+4 as $$\frac{6^2}{2}*3+4$$:

 $$\frac{6^2}{2}*3+4$$ Evaluate the numerator. $$6^2=36$$ $$\frac{36}{2}*3+4$$ Simplify the fraction by recognizing that the 36 is divisible by 2 because 36 is even. $$18*3+4$$ Do multiplication before addition. $$54+4$$ $$58$$

TheXSquaredFactor  Aug 3, 2017
#3
+7203
0

Hello  $$X^2$$

Neither of us is wrong.
Right, who puts brackets to represent the meaning of his term.
greetings :)

asinus  Aug 4, 2017
#4
+1720
0

Greetings to you, too :)

TheXSquaredFactor  Aug 5, 2017

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