 Adding Fractions with Unlike Denominators Although we are focusing on addition, remember that whenever you add, subtract, or compare fractions, the denominators must be the same. When working with different denominators, you must change them to a common denominator before solving the problem. In this lesson, we will be going through fraction concepts, fraction terms, adding fractions with like denominators, and finally, adding fractions with unlike denominators. Fraction Concepts A common fraction has two components, the top number and the bottom number. The top number is the number of pieces we are talking about. These pieces are shaded, eaten, taken away, etc. The bottom number is the number of pieces in the whole object. A common fraction can be read three ways. This fraction can be read as two-fourths, two divided by four, or two out of four. Fraction Terms Numerator The top of a fraction, the number of parts being talked about. Denominator The bottom of a fraction, the number of parts in the whole object. Common Denominator A number that can be divided by the denominators of two or more fractions. For example, with two-thirds and three-fourths. Twelve is able to be divided by the denominators three and four. Improper Fraction A fraction that looks incorrect or upside down because the numerator is larger than the denominator. Mixed Number A combination of whole number and a fraction. Adding Fractions with Like Denominators When adding fractions with the same denominator, you only add the numerator. The denominator remains the same. Why do denominators remain the same? Three-fifths plus one-fifth is similar to saying three oranges plus one orange. You are adding like things. Adding Fractions with Unlike Denominators There are three steps for adding fractions with unlike denominators. First, find a common denominator. Second, rename the fractions so that they have the same denominator. Third, add the like fractions. Step Number One Finding a Common Denominator A common denominator is found by listing the multiples of the original denominators. For the fractions of one-fourth and two-sixth, we list the multiples of four and six because they are the denominators. All of the circle numbers are common denominators. Always choose the smallest number. Step Number Two Rename the fractions so they have a common denominator. In the previous example, we used the denominators of four and six to find the least common denominator of twelve. Now we take the answer of twelve and change the original fractions. What do we have to do to four to increase it to twelve? We multiply it by three. If you multiply the bottom of the fraction by three, you must do the same to the top. What about the six? What do we have to do to the six to get twelve? We multiply it by two. Remember, whatever you do to the bottom, you must do to the top. So we have now successfully converted our original fractions of one-fourth and two-sixths into fractions we can add together because they have a common denominator. Step Number Three Add the like fractions. Now we can do three-twelfths plus four-twelfths to get a final answer of seven-twelfths. Now that we know the steps to add unlike fractions, let's practice them. First, we'll work on finding the least common denominator in some practice problems shown below. Pause the video here and try to find the least common denominator for each of the problems. Click Play once you are ready to move on. Here are the least common denominators for each set. Why choose the smallest common denominator? Just as replacing the divot in Gulf is proper Gulf etiquette, presenting a fractional math answer in lowest terms is proper Math etiquette. Consider these two answers. It is quite easy to see that four and twelve can be reduced by four. However, the larger the numbers, the more difficult reducing it will be. Previously, we found common denominators for the numbers four and nine with a final answer of thirty-six. Below, use these fractions and rename them to a denominator of thirty-six. Pause the video here and click Play once you think you know the answers. The correct answers are shown here. You have completed this learning object, adding fractions with unlike denominators.