The key to solve this problem is using ratios and proportions.
Ratio is the relationship between two numbers, defined as the quotient of one number for the other. So: The ratio between two numbers a and b is the fraction a/b and it is read a to b. This reason can also be written a : b.
Given two reasons a/b and c/d we say that they are in proportion if a/b = c/d. The terms a and d are called extremes while b and c are the means. In every proportion the product of the extremes is equal to the product of the means: a.d = b.c
A student uses the ratio of 4 oranges to 6 fluid ounces of juice to find the numbers of oranges needed to make 24 fluid ounces of juice.
The ratio of 4 oranges to 6 fluid ounces of juice is 4/6.
The ratio of x oranges to 24 fluid ounces of juice is x/24
Writing the proportion
4/6 = x/24
Clear x to obtain the oranges needed
x = (4)(24)/6 = 96/6 = 16
Then, the proportion is:
[tex]\frac{4}{6} = \frac{16}{24}[/tex]
The error in the student's work was that they reversed the reason, 24/16 instead of 16/24.
