SOLUTION: Ned folded a set of origami animals. Of this set, 5/8 are cranes and 1/6 of the remainder are frogs. The rest are grasshoppers. What fraction of the origami figures are grasshoppe

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Question 1062673: Ned folded a set of origami animals. Of this set, 5/8 are cranes and 1/6 of the remainder are frogs. The rest are grasshoppers. What fraction of the origami figures are grasshoppers?
15/16 are grasshoppers?
Found 2 solutions by math_helper, MathTherapy:
Answer by math_helper(2461)   (Show Source): You can put this solution on YOUR website!
Fraction that are cranes = 5/8 = 5*6/48 = 30/48
Fraction that are frogs = (1/6)(3/8) = 3/48
So the fraction that are grasshoppers = (48-3-30)/48 = 15/48 = 5/16
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Check (the three fractions should add to 1):
15/48 + 3/48 + 30/48 = (15+3+30)/48 = 48/48 = 1 (ok)
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Let's put some solid numbers to it...
Say there are 48 origami animals.
If 5/8 are cranes, that means (5/8)(48) = 30 are cranes
The remainder is 48-30 = 18
1/6 of the 18 are frogs ==> (1/6)(18) = 3 are frogs
How many are grasshoppers? 48-30-3 = 15
What fraction (of the total) are grasshoppers? 15/48 (if you divide top and bottom by 3, you get 5/16)
I hope this helps!
===
I used a common denominator of 48 in the original solution. I was just solving the problem as I typed and I recognized 48 would work as a common denominator (from the calculation of the frogs fraction). The LEAST common denominator (LCD) that would work is 16. Normally you would want to use the LCD cause it often saves you from having to reduce fractions at the end (like I did to arrive at 5/16).

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

Ned folded a set of origami animals. Of this set, 5/8 are cranes and 1/6 of the remainder are frogs. The rest are grasshoppers. What fraction of the origami figures are grasshoppers?
15/16 are grasshoppers?
No, that's incorrect!

Cranes: , so  represents non-cranes.

Frogs: 

Grasshoppers:  

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