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

Jun 11, 2017

See a solution process below:

#### Explanation:

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 $1$:

$\frac{2}{5} + \frac{1}{2} \implies \left(\frac{2}{2} \times \frac{2}{5}\right) + \left(\frac{5}{5} \times \frac{1}{2}\right) \implies \frac{4}{10} + \frac{5}{10}$

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

$\frac{4}{10} + \frac{5}{10} \implies \frac{4 + 5}{10} \implies \frac{9}{10}$

Jun 11, 2017

Choose 10 as the 'common denominator', so:

$\left(\frac{2}{5} \times \frac{2}{2}\right) + \left(\frac{1}{2} \times \frac{5}{5}\right) = \frac{4}{10} + \frac{5}{10} = \frac{9}{10}$

#### 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 $\frac{x}{x}$, where $x$ is any number, since $\frac{x}{x} = 1$.

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 $\frac{2}{5}$ to have 10 as the denominator, I will multiply it by $\frac{2}{2}$, and get $\frac{4}{10}$. (we've really just multiplied it by 1, since $\frac{2}{2} = 1$)

To get $\frac{1}{2}$ to have 10 as the denominator, I will multiply it by $\frac{5}{5}$, and get $\frac{5}{10}$.

Now we can add the two fractions: $\frac{4}{10} + \frac{5}{10} = \frac{9}{10}$.

We can't simplify that any further, so $\frac{9}{10}$ is our answer.

Jun 11, 2017

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.

$\frac{2}{5} \cdot \frac{2}{2}$

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

$\frac{4}{10}$ 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.

$\frac{1}{2} \cdot \frac{5}{5}$

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

$\frac{5 + 4}{10}$ => $\frac{9}{10}$

However, the greatest common multiple of 9 and 10 is 1, so the fraction can't be simplified and $\frac{9}{10}$ is the final answer.