One-half plus one-fifth equals what?
These fractions have different denominators. And we know that, to add two fractions together, we need them to have a common denominator. What’s a multiple of two but also a multiple of five? What about 10? Let’s convert both fractions into 10ths.
To convert a number of halves into 10ths, we need to multiply two by five. To make sure that our new fraction has exactly the same value as one-half, we need to do the same to the top number, the numerator, as we did to the bottom, to the denominator. We multiplied the denominator by five. So we also need to multiply the numerator by five. One times five equals five. And so one-half equals five-tenths.
Now, let’s convert one-fifth into 10ths. To get from fifths to 10ths, the denominator has doubled. So to make sure we make a fraction that’s equal to one-fifth, we need to double the numerator too. One times two equals two. One-fifth equals two-tenths. By converting both fractions into 10ths, we can now add them. Five-tenths plus two-tenths equals how many 10ths? Well, five plus two equals seven. So five-tenths plus two-tenths equals seven-tenths. Another way we could write the answer is as a decimal. Seven in the tenths place is 0.7.
A common mistake when we’re adding fractions is to think that we need to add the numerators and then add the denominators. In other words, we add all the numbers that we can see. But what we needed to do was to make sure that we were adding the same type of fraction. And that way, we could keep the denominator the same and just add the numerators.
So the first thing we did was to find a common denominator. 10 is a multiple of two. And it’s also a multiple of five. So we could change halves into 10ths and fifths into 10ths easily. A number of 10ths plus another number of 10ths equals a total number of 10ths. And we found the answer by adding five plus two.
One-half plus one-fifth equals seven-tenths or 0.7.