Answer:
A proportion equation is something like:
[tex]\frac{A}{B} = \frac{x}{C}[/tex]
Where A, B, and C are known numbers, and we want to find the value of x.
Now we want two cases where in one of the numerators we have a mixed number, where a mixed number is something like:
1 and 1/3
which actually should be written as:
1 + 1/3
1) a random problem can be:
[tex]\frac{1 + 1/3}{4} = \frac{x}{5}[/tex]
We can see that the numerator on the left is a mixed number.
First, let's rewrite the numerator then:
1 + 1/3
we need to have the same denominator in both numbers, so we can multiply and divide by 3 the number 1:
(3/3)*1 + 1/3
3/3 + 1/3 = 4/3
now we can rewrite our equation as:
[tex]\frac{4/3}{4} = \frac{x}{5}[/tex]
now we can solve this:
[tex]\frac{4/3}{4} = \frac{4}{3*4} = \frac{x}{5} \\\\\frac{1}{3} = \frac{x}{5}[/tex]
now we can multiply both sides by 5 to get:
[tex]\frac{5}{3} = x[/tex]
Now let's look at another example, this time we will have the variable x in the denominator:
[tex]\frac{7}{12} = \frac{3 + 4/7}{x}[/tex]
We can see that we have a mixed number in one numerator.
Let's rewrite that number as a fraction:
3 + 4/7
let's multiply and divide the 3 by 7.
(7/7)*3 + 4/7
21/7 + 4/7
25/7
Then we can rewrite our equation as
[tex]\frac{7}{12} = \frac{25/7}{x}[/tex]
Now we can multiply both sides by x to get:
[tex]\frac{7}{12}*x = \frac{25}{7}[/tex]
Now we need to multiply both sides by (12/7) to get:
[tex]x = \frac{25}{7}*\frac{12}{7} = 300/49[/tex]
