Question

Of all the people going, 5/8 are children and 3/8 are adults. How much moreis 5/8 than 3/8?Explain your answer using equations, diagrams, and words.

Answer 1

Given, the fraction of children, C=5/8.

The fraction of adults, A=3/8.

Therefore 5/8 is more than 3/8 is given by,

`\begin{gathered} \text{Percent}=(C-A)/(A)*100 \\ =((5)/(8)-(3)/(8))/((3)/(8))*100 \\ =((5-3)/(8))/((3)/(8))*100 \\ =(2)/(3)*100 \\ =66.67 \end{gathered}`

Therefore, 5/8 is more than 3/8 by 66.67%.

In each of the figures, there are 8 boxes. In the first figure showing the fraction of children, two boxes are shaded more than the figure for adults. In the second figure for the fraction of adults, only 3 boxed are shaded.

So, the % by which 5/8 is more than 3/8 can be found as

`\begin{gathered} \text{percentage}=\frac{Number\text{ of extra shaded boxes in first figure}}{\text{Number of shaded boxes in second figure}}*100 \\ =(2)/(3)*100=66.67 \end{gathered}`

5/8 is 5 parts of 8. 3/8 is 3 parts of 8. So, if the total number of people is 8, five people are children and three people are adults.

So, number of children is 2 more than the number of adults, whose number is 3.

Therefore, the fraction for number of children more than the adults with respect to the number of adults is 2/3. In percentage,

`\text{percentage}=(2)/(3)*100=66.67`

So, 5/8 is more than 3/8 by 66.67%.