Question

How do you evaluate `1/3+1/2+2/3`?

Answer 1

`color(maroon)(=> 9/6 = 1 1/2`

Explanation:

`1/3 + 1/2 + 2/3`

As there is no common factor between 2 & 3, 2*3 = 6 is the L C M.

`=> (1/3) * (2/2) + (1/2)* (3/3) + (2/3)*(2/2)` as 6 is the L C M of 2 & 3.

`=> (2/6) + (3/6) + (4/6)`

`=> (2 + 3 + 4) / 6`

`=> 9/6`

`=> 1 (cancel(3)^color(red)(1) / cancel(6)^color(red)(2))= 1 1/2`

Answer 2

See a solution process below:

Explanation:

To add fractions they must be over a common denominator.

To change the denominator without changing the value of the fraction we can multiply each fraction by a form of `1`

`1/3 = 2/2 xx 1/3 = (2 xx 1)/(2 xx 3) = 2/6`

`1/2 = 3/3 xx 1/2 = (3 xx 1)/(3 xx 2) = 3/6`

`2/3 = 2/2 xx 2/3 = (2 xx 2)/(2 xx 3) = 4/6`

We can now rewrite the problem and add the fractions as:

`2/6 + 3/6 + 4/6 = (2 + 3 + 4)/6 = 9/6`

We can reduce the fraction as:

`9/6 = (3 xx 3)/(3 xx 2) = (color(red)(cancel(color(black)(3))) xx 3)/(color(red)(cancel(color(black)(3))) xx 2) = 3/2`

If necessary, we can convert this improper fraction into a mixed number:

`3/2 = (2 + 1)/2 = 2/2 + 1/2 = 1 + 1/2 = 1 1/2`

Answer 3

`3/2`

Explanation:

Recall that to add fractions, we must have like denominators. We can start off by adding the fractions with the denominator of `3` to get

`3/3+1/2=1 1/2`, or `1.5`.

A more systematic way would be to get a common denominator of `6`, since this is the LCD of the fractions.

To get a denominator of `6`, we can multiply the first by `2/2`, the second by `3/3`, and the third by `2/2`. We now have

`2/6+3/6+4/6`

Adding the numerators, we get

`9/6`, or `3/2`, or `1 1/2`, or `1.5`.

Hope this helps!

Answer 4

`3/2`

Explanation:

`1/3+1/2+2/3`

`=\frac{1\cdot 2+1\cdot 3+2\cdot 2}{6}`

`=\frac{2+3+4}{6}`

`=\frac{9}{6}`

`=\frac{3\cdot 3}{3\cdot 2}`

`=3/2`