How do you simplify `2/5+1/2`?

To add two fractions they must be over a common denominator, which for this problem is `10`.

To put each fraction over a common denominator we must multiply each fraction by the appropriate form of `1`:

`2/5 + 1/2 => (2/2 xx 2/5) + (5/5 xx 1/2) => 4/10 + 5/10`

We can now add the numerators of the two fractions over the common denominator:

`4/10 + 5/10 => (4 + 5)/10 => 9/10`

You need a 'common denominator': the number at the bottom of each fraction must be the same. To get that, we can multiply a fraction by `x/x`, where `x` is any number, since `x/x=1`.

Since our denominators are 2 and 5, we need a common denominator that both of those will divide into equally. I'm going to choose 10. It's true that 20 or 100 or 1 000 000 would also work, but we usually try to use the 'least common denominator' or 'lowest common denominator' (both are abbreviated as LCD).

To get `2/5` to have 10 as the denominator, I will multiply it by `2/2`, and get `4/10`. (we've really just multiplied it by 1, since `2/2 = 1`)

To get `1/2` to have 10 as the denominator, I will multiply it by `5/5`, and get `5/10`.

Now we can add the two fractions: `4/10 + 5/10 = 9/10`.

We can't simplify that any further, so `9/10` is our answer.

Start by finding the least common multiple of 5 and 2, the denominators. Their lcm is 10. Now we have to make the denominators both 10.

`2/5*2/2`

Since 2/2 is one, you aren't really changing the fraction. Either way, we end up with

`4/10` as our first fraction. Now for the second one, we make its denominator 10 as well, by multiplying by 5/5. Since 5/5=1, the fraction isn't changing.

`1/2*5/5`

The final fraction is 5/10. Now that the denominators are the same, simply add the numerators and simplify the fraction.

`(5+4)/10` => `9/10`

However, the greatest common multiple of 9 and 10 is 1, so the fraction can't be simplified and `9/10` is the final answer.