When dividing to make a decimal: 11/5 (where did 20s come from?)

[Irishwins88]

When using a fraction solution to make a division problem into a decimal where do they get the 20/20 fraction as in this problem?

 

[Dr.Peterson]

When using a fraction solution to make a division problem into a decimal where do they get the 20/20 fraction as in this problem?View attachment 10465

It might be helpful to see more of the context. I see that this is showing a hypothetical student's solution to a problem you didn't show, not necessarily a recommended method to make a decimal; but it is valid.

Evidently the goal is to write the faction as a decimal by converting it to a fraction whose denominator is a power of 10. This is done by multiplying the denominator (and also the numerator) by 20. They could also have used 2. If the goal was to make a percentage, then 20 would be the right choice.

 

[JeffM]

When using a fraction solution to make a division problem into a decimal where do they get the 20/20 fraction as in this problem?View attachment 10465

When you multiply a number by 1, what do you get? The same number. So you can multiply any number by 1 without changing its numeric value.

\(\displaystyle 7 = 7 * 1,\) right?

Moreover, you can divide any number (except zero) by itself to get 1.

\(\displaystyle \dfrac{7}{7} = 1,\) right.

Of course, multiplying by 7 won't turn a denominator of 5 into 100, but multiplying by 20 will.

\(\displaystyle \dfrac{11}{5} = \dfrac{11}{5} * 1 = \dfrac{11}{5} * \dfrac{20}{20} = \dfrac{220}{100} = 2.2\%.\)

This method works perfectly in this case, but it does not work generally. Consequently, I would not rely on it on a test.

 

[Bob Brown MSEE]

Summary

Where do they get the 20/20 fraction?

1) They want the given to not change value when multiplied by it.
2) They want the result to have 100 as the denominator.

 

[Irishwins88]

It might be helpful to see more of the context. I see that this is showing a hypothetical student's solution to a problem you didn't show, not necessarily a recommended method to make a decimal; but it is valid.

Evidently the goal is to write the faction as a decimal by converting it to a fraction whose denominator is a power of 10. This is done by multiplying the denominator (and also the numerator) by 20. They could also have used 2. If the goal was to make a percentage, then 20 would be the right choice.

Thank you for your help. First time asking a question on a board. Not use to the protocol.

 

[Irishwins88]

It might be helpful to see more of the context. I see that this is showing a hypothetical student's solution to a problem you didn't show, not necessarily a recommended method to make a decimal; but it is valid.

Evidently the goal is to write the faction as a decimal by converting it to a fraction whose denominator is a power of 10. This is done by multiplying the denominator (and also the numerator) by 20. They could also have used 2. If the goal was to make a percentage, then 20 would be the right choice.

When you multiply a number by 1, what do you get? The same number. So you can multiply any number by 1 without changing its numeric value.

\(\displaystyle 7 = 7 * 1,\) right?

Moreover, you can divide any number (except zero) by itself to get 1.

\(\displaystyle \dfrac{7}{7} = 1,\) right.

Of course, multiplying by 7 won't turn a denominator of 5 into 100, but multiplying by 20 will.

\(\displaystyle \dfrac{11}{5} = \dfrac{11}{5} * 1 = \dfrac{11}{5} * \dfrac{20}{20} = \dfrac{220}{100} = 2.2\%.\)

This method works perfectly in this case, but it does not work generally. Consequently, I would not rely on it on a test.

Thank you for your help.

 

[Irishwins88]

1) They want the given to not change value when multiplied by it.
2) They want the result to have 100 as the denominator.

Thank you for your help.

 

[Irishwins88]

Thank you

Thank you everybody for your help. It is most appreciated.

 

[Steven G]

When you multiply a number by 1, what do you get? The same number. So you can multiply any number by 1 without changing its numeric value.

\(\displaystyle 7 = 7 * 1,\) right?

Moreover, you can divide any number (except zero) by itself to get 1.

\(\displaystyle \dfrac{7}{7} = 1,\) right.

Of course, multiplying by 7 won't turn a denominator of 5 into 100, but multiplying by 20 will.

\(\displaystyle \dfrac{11}{5} = \dfrac{11}{5} * 1 = \dfrac{11}{5} * \dfrac{20}{20} = \dfrac{220}{100} = 2.2\%.\)

This method works perfectly in this case, but it does not work generally. Consequently, I would not rely on it on a test.

Ooops! Be careful as 220/100 is 220% not 2.2%. For the original poster, any number-call it x- divided by 100 is x%. That is x/100 =x% and again, 220/100 = 220%

 

[Steven G]

When using a fraction solution to make a division problem into a decimal where do they get the 20/20 fraction as in this problem?View attachment 10465

If the denominator is 100 you should know how to do the division. 220/100 = 2.2. Personally I would have multiplied by 1 using 2/2 to get 11/5 = (11/5)*1 =(11/5)^(2/2) = 22/10 = 2.2