Question

How do you evaluate `\frac { 1} { 4} + \frac { 3} { 2} + 5\frac { 1} { 3}`?

Answer 1

`85/12` or `7 1/12`

Explanation:

1. Convert `5 1/3` into an improper fraction. Multiply 5 by 3, then add 1 to get the numerator. 3 remains the denominator.

`5 1/3 = 16/3`

2. We need to get a least common denominator (LCD) for all three fractions.

Multiples of 4: 4, 8, 12...
Multiples of 3: 3, 6, 9, 12...
Multiples of 2: 2, 4, 6, 8, 10, 12...

The smallest number that can be divided by 4, 2, and 3 is 12.

3. Multiply each fraction in the expression by a equivalent form of 1 so that each has a denominator of 12.

`(1/4)(3/3) + (3/2)(6/6) + (16/3)(4/4)`
`= (3/12) + (18/12) + (64/12)`

4. Add the fractions. Remember, when adding fractions, only add the numerators together and keep the denominators the same.

`= 85/12`

Since `(85/12)` is in simplest form, you could keep your answer as an improper fraction . You could also convert it into a mixed fraction, which would be `7 1/12`. (12 goes into 85 seven times, with a remainder of 1.)