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simplifying a particular fraction: "Henry can write 5 pages of his novel in 3 hours."

NewAge500

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Joined
Aug 16, 2017
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3
simplifying a particular fraction: "Henry can write 5 pages of his novel in 3 hours."

Hello and takes for taking time to help me with this problem. This is from Khan Academy.

I was asked to find the rate of this problem:

Henry can write 5 pages of his novel in 3 hours

At this rate, how many pages can Henry write in 8 hours?

I know the formula to working the problem but what makes me pause is the answer I get 13.33 (its abbreviated). When I typed it in the answer box it was wrong because it wasn't in fraction form which is written as 13 1/3.

and that's where I'm stuck, 1/3 written as a decimal is 0.33 so I get why the 13 1/3 but 0.33 written as a fraction is 33/100 and it cant be simplified any further.

My question is...how do i get 1/3, I understand why the fraction form after researching it but I don't understand the formula of how it got there.

I hope my explanation of my problem was helpful I really didn't know how to word it.

Thanks in Advance for the help.


 

mmm4444bot

Super Moderator
Staff member
Joined
Oct 6, 2005
Messages
10,139
Henry can write 5 pages of his novel in 3 hours

At this rate, how many pages can Henry write in 8 hours?

I know the formula to working the problem but what makes me pause is the answer I get 13.33 (its abbreviated). When I typed it in the answer box it was wrong because it wasn't in fraction form which is written as 13 1/3.
When you wrote that your answer 13.33 is abbreviated, I'm guessing you meant truncated or rounded, instead.

In other words, your answer was actually 13.33333333… (the 3s continue forever).

When I work this exercise, I get 40/3 for the answer. That's an improper fraction. Changing this improper fraction to a mixed number (i.e. dividing 40 by 3) yields 13 and 1/3.

(Maybe you used a calculator, at some point, instead of doing it by hand.)

Can you show your work?
:cool:


… 1/3 written as a decimal is 0.33 …
No, 1/3 is not the same as 0.33

If we divide 1 by 3, we get a repeating decimal:

1/3 = 0.33
333333… (the 3s continue forever).

We cannot simply chop off (i.e., truncate) all of
those infinite 3s from the number because -- if we do -- then the number no longer equals 1/3.

Again, I'm not sure what you did, but if you see 0.3333333333 as a result on a calculator, it means 1/3.
 

stapel

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Staff member
Joined
Feb 4, 2004
Messages
15,937
Henry can write 5 pages of his novel in 3 hours. At this rate, how many pages can Henry write in 8 hours?

I know the formula to working the problem but what makes me pause is the answer I get 13.33 (its abbreviated). When I typed it in the answer box it was wrong because it wasn't in fraction form which is written as 13 1/3.

and that's where I'm stuck, 1/3 written as a decimal is 0.33 so I get why the 13 1/3 but 0.33 written as a fraction is 33/100 and it cant be simplified any further.

My question is...how do i get 1/3, I understand why the fraction form after researching it but I don't understand the formula of how it got there.
To learn how to convert between mixed numbers (like "thirteen and one-third") and improper fractions (like "forty thirds"), try some online lessons, such as are listed here. In essence, it comes down to doing the long division, knowing when to quit, and knowing how to handle the remainder. ;)
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
3,174
Hello and takes for taking time to help me with this problem. This is from Khan Academy.

I was asked to find the rate of this problem:

Henry can write 5 pages of his novel in 3 hours

At this rate, how many pages can Henry write in 8 hours?

I know the formula to working the problem but what makes me pause is the answer I get 13.33 (its abbreviated). When I typed it in the answer box it was wrong because it wasn't in fraction form which is written as 13 1/3.

and that's where I'm stuck, 1/3 written as a decimal is 0.33 so I get why the 13 1/3 but 0.33 written as a fraction is 33/100 and it cant be simplified any further.

My question is...how do i get 1/3, I understand why the fraction form after researching it but I don't understand the formula of how it got there.

I hope my explanation of my problem was helpful I really didn't know how to word it.

Thanks in Advance for the help.


I am guessing you did something like this.

\(\displaystyle 8 * \dfrac{5}{3} = \dfrac{40}{3} \approx 13.33.\)

That is, I think you recognize that \(\displaystyle 13.33 \ne \dfrac{40}{3}.\)

In fact there is NO decimal expansion that equals 40/3. I think you are asking how they got what they got:

\(\displaystyle \dfrac{40}{3} = \dfrac{39 + 1}{3} = \dfrac{39}{3} + \dfrac{1}{3} =\)

\(\displaystyle \dfrac{3 * 13}{3 * 1} + \dfrac{1}{3} = 13 + \dfrac{1}{3}.\)

Does this help?
 
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