Add fractions, what fraction of the hour remained

Question

Four students were scheduled to give book reports in 1 hour. After the first report, 2/3 hour remained. The next two reports took 1/6 hour and 1/4 hour. What fraction of the hour remained?

Answer 1

When adding fractions you need a common denominator so lets look at what "fractions" we are dealing with:

2/3 1/6 and 1/4.

HOWEVER the first sentence says "2/3 of an hour was left" which means only 1/3 was used. So our real fractions that were used are:

1/3 1/6 and 1/4

 

So 3 and 6 can both go into 6 but 4 cannot so we cannot use 6 as our common denominator. Since 6 was the largest number we need to search for a larger number that is a common denominator for ALL of the current denominators.

One way to do this is by multiplying the denominators by each other.

 

In this case 6x4= 24 Can 3 go into 24? Yes it can, 8 times

So we can use 24 as our common denominator. So next step we fix the fractions so they all have 24 as their denominator:

1/3 since 3 goes into 24 8 times we times both sides of the fraction by 8:

1x8= 8

3x8= 24

so the new fraction is 8/24

 

our next fraction is 1/6. 6 goes into 24 4 times so we times each side of the fraction by 4:

1x4=4

6x4= 24

so our new fraction is: 4/24

 

Our last fraction is 1/4 4 goes into 24 6 times so we times each side of the fraction by 6:

1x6=6

4x6=24

so our new fraction is 6/24

 

If you were to simplify each of these new fractions you would end up with our original fractions of 1/3 1/6 and 1/4

Now that we have the same denominator we can add all the fractions together:

8/24 +4/24 +6/24

the denominator will stay the same (24) so we just add the top:

8+4+6= 18

So our added total is 18/24 we can now simplify this: think of numbers that can go into both 18 and 24. 2 can, but so can 3, and so can 6. Since 6 is higher lets use that one:

18/6= 3

24/6=4

so our new fraction is 3/4, so our answer is 3/4 of an hour was used

BUT, the question asks how much of an hour was LEFT.

so we need to take how much was used and subtract it from a full hour.

 

We know that 3/4 of an hour was used, we can represent 1 full hour by the fraction 4/4. Because 4/4=1, I chose 4 because that matches our denominator in 3/4.

Now we subtract 4/4-3/4. Our denominator stays the same and we subtract the top values: 4-3=1

so 1/4 of an hour is left.

 

Answer 2

If 2/3 remained then 1/3 was used. So if you add what has been used you have: 1/3 + 1/6 + 1/4 and then subtract the answer from 1. Get a common denominator which would be 12 so: 4/12 + 2/12 + 3/12 = 9/12 1 - 9/12 + 3/12 or 1/4 is left