# How do you add a fraction to a decimal?

Apr 12, 2016

You need to convert them to similar format. Either both to decimal format or both to fractions.

#### Explanation:

There could be two ways of adding a fraction to a decimal.

(1) Convert fraction to the decimal format and add. If desired or required, the sum can again be converted into fraction.

(2) Convert the decimal to a fraction and then add two fractions together.

Apr 12, 2016

You need to either convert the decimal to a fraction or the fraction to a decimal.

#### Explanation:

Or at least that's the easiest way to go about adding a fraction to a decimal. For all intents and purposes (or porpoises) lets consider an example with fairly straight-forward numbers (no repeating decimals here). Lets say we wanted to add $\frac{1}{5}$ and $0.50$, that that would look like this:

1/5+0.50= ?

"Uhhhh... that doesn't look nice..."

---------------------Converting to a decimal-----------------------

To convert a decimal to a fraction all we need to do is divide the numerator (top number) by the denominator* (bottom number). Like this:

$1 \div 5 = 0.2$

Which, again, is the same as:

$\frac{1}{5} = 0.20$

We know this because $\frac{5}{5}$ equals $1$. In fact any fraction that has the same number in the numerator and the denominator equals 1 because if you divide a number by itself the quotient (result of division) is 1. We can further prove that $\frac{1}{5}$ is equal to $0.20$ by adding $0.20$ 5 times in which case we get $1$, just like this:

$0.20 + 0.20 + 0.20 + 0.20 + 0.20 = 1$

So now that we know what both numbers are in decimal form we can add the two numbers, like so:

$0.20 + 0.50 = 0.70$

---------------------Converting to a Fraction-----------------------

As I mentioned above we can also convert the decimal $\left(0.50\right)$ to a fraction. Now we may know off the top of our heads that $0.50$ equals $\frac{1}{2}$, but we might not, this is not big deal because we can always add $50$ plus $50$ to get $100$, like this:

$50 + 50 = 100$

This also means that:

$0.50 + 0.50 = 1$

Since it takes two $0.50$'s to equal $1$ this means that 1 divided by 2 (or $\frac{1}{2}$) is equal to $0.50$, in equation form:

$\frac{1}{2} = 0.50$

Now that we know that $0.50$ equals $\frac{1}{2}$, we can set up our equation which looks like this:

1/5+1/2= ?

This is a little more tricky since we can't just add the two fractions, we have to find a common denominator. The easiest way to do this is to multiply the numerator and denominator of one by the denominator of the other, like so:

$\frac{1}{5} \cdot \left(\frac{2}{2}\right) = \frac{2}{10}$

and

$\frac{1}{2} \cdot \left(\frac{5}{5}\right) = \frac{5}{10}$

Now we can add both of these fractions together like this:

$\frac{2}{10} + \frac{5}{10} = \frac{7}{10}$

If we divide any number less than ten by $10$ we get a decimal in this case if we divide $7$ by $10$ we get $0.70$ since all we're really doing is moving the decimal point one place to the left. This can be expressed as an equation:

$7 \div 10 = 0.70$

Surprise! We arrived at the same answer using two different methods!

I hope this helped!