Kara’s class had 9 bottles of glue. They used about 2/3
of each of 4 of the bottles and about 3/4
of another bottle. Then they found 2 and 1/2
more bottles of glue. How many full bottles of glue does the class have now?
Looks to me like just 4+2 = 6 since the others had all been used some.
I assume that the author of this poorly worded question simply wanted
us to add up all those partially fill bottles, apparently topping them up
So we have:
4(2/3) + 3/4 + 2 + 1/2
= (32 + 12 + 24 + 6)/12
= 74/12
= 6 1/6 bottles
hmmm. I think that you have to subtract the bottles used, and then add in the new ones:
9 - 2/3 * 4 - 3/4 + 2 1/2 = 8 1/12
To find the number of full bottles of glue the class has now, we need to add up the amounts used and the amount found.
First, let's calculate the amount used from the 4 bottles. Since they used about 2/3 of each bottle, we can calculate the total amount used as follows:
Total amount used from 4 bottles = (2/3) * 4 = 8/3
Next, let's calculate the amount used from the remaining bottle. They used about 3/4 of that bottle, so:
Amount used from the remaining bottle = (3/4) * 1 = 3/4
Now, let's add up the amount used from the 4 bottles and the remaining bottle:
Total amount used = Total amount used from 4 bottles + Amount used from the remaining bottle
= 8/3 + 3/4
To add these fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12. So let's rewrite the fractions with a denominator of 12:
Total amount used = (8/3) * (4/4) + (3/4) * (3/3)
= 32/12 + 9/12
= 41/12
Now, let's add the amount of glue they found, which is 2 and 1/2. To add the mixed number to a fraction, we need to convert the mixed number to an improper fraction:
2 and 1/2 = (2 * 2 + 1) / 2 = 5/2
Finally, let's add the total amount used to the amount found:
Total amount of glue the class has now = Total amount used + Amount found
= 41/12 + 5/2
= (41/12) + (30/12)
Now, we can add these fractions with the same denominator:
Total amount of glue the class has now = (41/12) + (30/12)
= 71/12
Therefore, the class has 71/12 full bottles of glue now.