Pplease provide me the solution in step by step:
- Thread starter deep1521
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Otis
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- Apr 22, 2015
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Hi deep1521. When we work with fractions of a whole, it's important to remember that all the fractions add up to 1. Here's a worked example.
2/5 of a group is men, 1/3 is women, and the rest is 8 children. How many people are in the group?
Right away, we know that (2/5 + 1/3) of the group is adults. Let's simplify that. First, we change to common denominators:
2/5 + 1/3 = 5/15 + 6/15
Now we can add them:
(5 + 6)/15 = 11/15
11/15 of the group is adults. Therefore, the whole group must be 15/15 (remember, the number 1 represents the whole group). What fraction of the group is children, if the adults is 11/15? We find the difference.
15/15 - 11/15 = (15 - 11)/15 = 4/15
We see that 8 children is 4/15 of the group.
Lastly, 4/15 of what number is 8? We divide 8 by 4/15, to find out.
8 ÷ 4/15 = 8 × 15/4 = 2 × 15 = 30
There are 30 people in the group.
Let's check that answer.
The men: 2/5 × 30 = 12
The women: 1/3 × 30 = 10
The children: 8
12 + 10 + 8 = 30
It checks. Now, if you understand the example, then please try your exercise the same way. If you get stuck, then show us your work and we'll go from there. (Feel free to ask any questions about the example above, also.)
PS: Please read the forum guidelines, when you have time. Thanks!
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2/5 of a group is men, 1/3 is women, and the rest is 8 children. How many people are in the group?
Right away, we know that (2/5 + 1/3) of the group is adults. Let's simplify that. First, we change to common denominators:
2/5 + 1/3 = 5/15 + 6/15
Now we can add them:
(5 + 6)/15 = 11/15
11/15 of the group is adults. Therefore, the whole group must be 15/15 (remember, the number 1 represents the whole group). What fraction of the group is children, if the adults is 11/15? We find the difference.
15/15 - 11/15 = (15 - 11)/15 = 4/15
We see that 8 children is 4/15 of the group.
Lastly, 4/15 of what number is 8? We divide 8 by 4/15, to find out.
8 ÷ 4/15 = 8 × 15/4 = 2 × 15 = 30
There are 30 people in the group.
Let's check that answer.
The men: 2/5 × 30 = 12
The women: 1/3 × 30 = 10
The children: 8
12 + 10 + 8 = 30
It checks. Now, if you understand the example, then please try your exercise the same way. If you get stuck, then show us your work and we'll go from there. (Feel free to ask any questions about the example above, also.)
PS: Please read the forum guidelines, when you have time. Thanks!
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