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# how is 1/2*1/2*1/2*2*2*2 equal 1

How does multiplying these end with an answer of 1. Do you make 2 in to 2 over 1.

### 3 Answers by Expert Tutors

Julian M. | Accounting, Finance, Business, Statistics and Mathematics TutorAccounting, Finance, Business, Statistic...
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1/2*1/2*1/2*2*2*2 equal 1.  So lets work the problem from let to right.  1/2*1/2 = 1/4 *1/2 = 1/8 *2= 2/8 or 1/4*2 = 2/4 or 1/2*2 = 2/2 or 1.  So just following the typical operations of mathematics from left to right you can see that by multiplying all the numbers equals 1.  You could use the commutative property and group the numbers together to see that you are really multiplying 1*1*1, however both ways in this case provide the same answer.
Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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Multiplication is commutative, which means you can change the order of the numbers. E.g., you can change your problem into:

(2*1/2)*(2*1/2)*(2*1/2)

If you have 2 halves of a pizza you have 1 pizza; so your problem becomes:

1*1*1 = 1

"Do you make 2 into 2 over 1?"

Yes, you could do that; then you'd use multiplication of fractions:

(2/1)*(1/2) = (2*1)/(1*2) = 2/2 = 1

Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
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Hi Misty;
1/2*1/2*1/2*2*2*2
If you take 1/2 and multiply it by 2, the result is 1.
(1/2)(2)
This can also be written as...
(1/2)(2/1)
Multiply the numerators together, (1)(2)...
Multiply the denominators together, (2)(1)...
2/2=1
In the equation you presented, 1/2 is presented three times and 2 is presented three times.  This is...
1*1*1=1