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Question

Jon spent 1/3 of his study time doing math homework and 2/7 preparing for a history exam. What fraction of his study time remains

Answer 1

You should do your own homework! Still, I will give the answer
1-1/3-2/7 = 8/21

Answer 2

If x is his total study time, and he lost 1/3 of it, then he should have x - (1/3)x remaining. ("of" means "multiply".) Additionally, he lost another 2/7 of his total time, so he actually has x - (1/3)x - (2/7)x. Find a common denominator to subtract these fractions. You've got a 3 and a 7 in the denominators, so go with 21.

(21/21)x - (7/21)x - (6/21)x =
(21 - 7 - 6)x/21 =
(8/21)x

So he has 8/21 of his study time left.

Another way to think of this is that the fraction representing his whole study time is 1/1, or just "1" (one whole). So take 1 - 7/21 - 6/21 and you get 8/21.

Answer 3

Well, the remaining study time is given by 1 - (1/3) - (2/7). Any time you subtract a fraction from a whole, you subtract it from one. (Kind of like if I take 1/3 and 2/7 of your 1 pizza.)

So we have 1 - 1/3 - 2/7. The next step is to get common denominators for them since we can't easily subtract them in this form. The most direct way to find a common denominator is to multiply the two denominators together. (The result MUST be divisible by both 3 and 7).

3 * 7 is 21. Now let's convert those fractions into something divided by 21.

1/3 * (7/7) = 7/21. (I can multiply 7/7 to 1/3 and still not change it because 7/7 is 1, and any number multiplied by 1 is itself.)

Likewise with 2/7:
(2/7) * (3/3) = 6/21.

With 1, we multiply (21/21) and get ... 21/21. :-)

So now we have 21/21 - 6/21 - 7/21. Since they have like denominators now, we can subtract and get 8/21.

Hope that helped!!
UMRmathmajor

Answer 4

We need to find a common denominator in order to add these fractions. I always multiply the Denominators it's easier for me. 3 * 7 is 21 so I'm going to use 21 as my common denominator.

(1/3) 3 goes into 21, 7 times and 7 times 1 is 7...So 1/3 = 7/21
(2/7) 7 goes into 21, 3 times and 3 times 2 is 6...So 2/7 = 6/21

Now we can add these fractions by adding the numerators across and carrying our denominator over.

7/21 + 6/21 = 13/21

Now that's how much time Jon has used. To find out how much he has left, we'll take 13/21 from 1 or 21/21. (I use 21/21 because we need a common denominator in order to subtract)

21/21 - 13/21 = 8/21. That's how much of his study time Jon has left.

If you can, I know a lot of the kids I teach prefer to use decimals rather than fractions. So if you want go ahead and divide 1 by 3, and 2 by 7 add your answers together and subtract from 1. Just beware, your answers aren't going to be as accurate because 1/3 is 0.3 repeating.

Hope this helped, Good Luck with your Math.

Answer 5

1/3+2/7=7/21+ 6/21=13/21 study time used.
7/7-13/21=21/21-13/21= 8/21 study time remaining.
(7/7 is the total study time)

Answer 6

First figure your lowest comon denominator--- 3 x 7 = 21

1/3 = 7/21. 2/7 = 6/21

7/21 + 6/21 = 13/21.

1 = 21/21. 21/21 - 13/21 = 8/21 remaining.

Answer 7

1/3 +2/7= 13/21
21-13= 8
8/21 remains

Answer 8

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Answer 9

8/21 of his time remains.