How do you add a fraction to a decimal? | Socratic (2024)

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 #1/5# and #0.50#, that that would look like this:

#1/5+0.50= ?#

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

**Courtesy of: http://www.hakaproducts.com/voice-of-the-customer-lost-in-space/**

---------------------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:

#1div5=0.2#

Which, again, is the same as:

#1/5=0.20#

We know this because #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 #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 #(0.50)# to a fraction. Now we may know off the top of our heads that #0.50# equals #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 #1/2#) is equal to #0.50#, in equation form:

#1/2= 0.50#

Now that we know that #0.50# equals #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:

#1/5*(2/2)=2/10#

and

#1/2*(5/5)=5/10#

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

#2/10+5/10=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:

#7div10=0.70#

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

I hope this helped!