One-quarter plus one-fifth plus one-tenth equals what?
Each of these fractions has a different denominator. When we add fractions, we need to add fractions with the same denominator. To find a common denominator, we need to find a number which is a multiple of four, five, and 10. 20 is a multiple of four, five, and 10. So we need to convert a quarters into twentieths.
To get from quarters to twentieths, we need to multiply by five. We need to do the same to the number on top, the numerator. One times five is five. One-quarter is equal to five-twentieths.
To convert fifths into twentieths, we multiplied by four. One multiplied by four is four. So one-fifth is equal to four-twentieths. And to change one-tenth into twentieths, we need to multiply the denominator and the numerator by two. One-tenth is equal to two-twentieths.
Now that the fractions have a common denominator, we can add them: five-twentieths add four-twentieths add two-twentieths. How many twentieths do we have altogether? Five-twentieths and four-twentieths makes nine-twentieths. Then we need to add another two-twentieths, which gives us a total of eleven-twentieths.
A quarter plus a fifth plus a tenth equals eleven-twentieths. A quarter, a fifth, and a tenth all have different denominators. So our first step was to find a common denominator. Then we were able to add our fractions to find the answer, eleven-twentieths.