Question

How do you solve `4 1/6 = 3\frac { 1} { 3} c`?

Answer 1

See a solution process below:

Explanation:

First, convert the two mixed numbers to improper fractions:

`4 1/6 = 3 1/3c`

`4 + 1/6 = (3 + 1/3)c`

`[6/6 xx 4] + 1/6 = ([3/3 xx 3] + 1/3)c`

`24/6 + 1/6 = (9/3 + 1/3)c`

`25/6 = 10/3c`

Next, multiply each side of the equation by `color(red)(3)/color(blue)(10)` to solve for `c` while keeping the equation balanced:

`color(red)(3)/color(blue)(10) xx 25/6 = color(red)(3)/color(blue)(10) xx 10/3c`

`color(red)(3)/color(blue)(5 xx 2) xx (5 xx 5)/(3 xx 2) = cancel(color(red)(3))/cancel(color(blue)(10)) xx color(blue)(cancel(color(black)(10)))/color(red)(cancel(color(black)(3)))c`

`cancel(color(red)(3))/color(blue)(color(black)(cancel(color(blue)(5))) xx 2) xx (color(blue)(cancel(color(black)(5))) xx 5)/(color(red)(cancel(color(black)(3))) xx 2) = c`

`5/(2 xx 2) = c`

`5/4 = c`

`c = 5/4`

We can now convert this solution into a mixed number:

`c = (4 + 1)/4`

`c = 4/4 + 1/4`

`c = 1 + 1/4`

`c = 1 1/4`