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

##### 3 Answers

See a solution process below:

#### Explanation:

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

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

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

Choose 10 as the 'common denominator', so:

#### Explanation:

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

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

To get

Now we can add the two fractions:

We can't simplify that any further, so

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.

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

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

However, the greatest common multiple of 9 and 10 is 1, so the fraction can't be simplified and