Simple division of fractions

[itsulfaaa]

Hi there just struggling to understand the logic of the method.

If we divide 3 by 1/2, and the calculation is 3 x 2/1 = 6/1 = 6. Why do we not times 3 by 1 aswell as 3x2? I ask because this would be the case with a question like 1/2 ÷ 2/3.

Thanks

 

[Deleted member 4993]

Hi there just struggling to understand the logic of the method.

If we divide 3 by 1/2, and the calculation is 3 x 2/1 = 6/1 = 6. Why do we not times 3 by 1 aswell as 3x2? I ask because this would be the case with a question like 1/2 ÷ 2/3.

Thanks

1/2 [divided by] 2/3

= 1/2 [multiplied by] 3/2

= (1*3) [divided by] (2*2) = 3/4
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In the problem, you posted:

3 [divided by] 1/2

= 3/1 [divided by] 1/2

= 3/1 [multiplied by] 2/1

= (3*2) [divided by] (2*1) = 6/2 = 3

 

[itsulfaaa]

Thank you for the reply.

I see 3 is the same as 3/1 and only the second fraction is flipped over. Therefore

3 divided by 1/2 =
3/1 × 2/1 = 6/1 = 6

As 3÷0.5=6.

 

[Steven G]

If you times both the numerator and denominator by 3, then clearly in the end you can divide the numerator and denominator by 3. This would mean that multiply by 3 has no impact on the answer which can't be true.

Note that if 3(2/1) = 6/3 = 2/1 then we getting back 2/1 in the end means that multiply 2/1 by 3 did not change the value. If multiplying 2/1 did not change its value than you must have multiplied by 1 not 3. After all, 3/3 is 1. When you multiply the numerator and denominator by 3 you are really multiplying by 3/3 or 1.