Different denominators Show When the denominators are unequal, we have to find a common denominator before we can add or subtract the fractions. To find a common denominator, we need to find the least common multiple (LCM) of the denominators. Then we can use the LCM as our common denominator. In fact, we call that the “least common denominator,” because it’s the smallest common denominator we can use. Consider the fractions ???3/5??? and ???1/3???. The LCM of ???5??? and ???3??? is ???15???, so the least common denominator will be ???15???. Since ???15=3\cdot5???, we have to multiply ???5??? (the denominator of ???3/5???) by ???3??? to get the common denominator of ???15???. And we have to multiply ???3??? (the denominator of ???1/3???) by ???5??? to get the common denominator ???15???. We aren't allowed to change the value of either of the fractions, so we have to multiply the numerator of each fraction by the same number that we multiplied by its denominator. So we have to multiply the numerator and denominator of ???3/5??? by ???3???, and we have to multiply the numerator and denominator of ???1/3??? by ???5???. What is Common Denominator?A fraction has two parts – a numerator and a denominator. Any arithmetic operation such as addition or subtraction involving two or more fractions is possible if the denominators of both fractions are the same. This is known as the common denominator. One can add or subtract fractions only when they have a common denominator. (see example below) A common denominator is a number with which both denominators share at least one factor other than 1. Fractions without a Common DenominatorWe can obtain common denominators by multiplying both numerator (top) and denominator (bottom) by the same amount. For example, consider the addition of two fractions that do not have the same denominator: Addition of 2⁄5 and 1⁄2 . First, multiply 2⁄5 by 2⁄2 to get 4⁄10 . Now multiply the second fraction 1⁄2 by 5⁄5 to get 5⁄10 . The new fractions have a common denominator 10. Add the two fractions 4⁄10 + 5⁄10 to get 9⁄10 . Fun Fact Download Article Download Article Adding fractions with unlike denominators may look tricky, but once you make the denominators the same, addition is a snap. If you're working with improper fractions where the numerators are larger than the denominators, make the denominators the same. Then add the numerators. If you're adding mixed numbers, turn them into improper fractions and make each fraction equivalent. This will make it easy to add the fractions together. Practice Problems
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About This ArticleArticle SummaryX To add fractions with unlike denominators, start by finding the least common multiple for the denominators. Then, divide the least common multiple by the denominator in each fraction. Take the number you get for each fraction and multiply it by the numerator and denominator of that fraction, which will make both denominators equal to the least common multiple. Finally, add the numerators together and leave the denominator as is to get your answer. To learn how to simplify your answer, keep reading! Did this summary help you? Thanks to all authors for creating a page that has been read 866,649 times. Did this article help you?How do you make the denominators of a fraction the same?We can obtain common denominators by multiplying both numerator (top) and denominator (bottom) by the same amount. For example, consider the addition of two fractions that do not have the same denominator: Addition of 2⁄5 and 1⁄2 . First, multiply 2⁄5 by 2⁄2 to get 4⁄10 .
Why do you make denominators the same when adding fractions?If you're adding two fractions with a common denominator, you can combine them together by adding the numerators together (the top numbers). The denominator will always stay the same because the size of the equal pieces does not change when you combine the two fractions together.
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