![]() ![]() Summary: In order to add or subtract fractions, they must have like denominators. How much more pie did Spencer eat than Carly?Īnalysis: This problem is asking us to subtract fractions with unlike denominators: How many miles did he run altogether?Īnalysis: This problem is asking us to add fractions with unlike denominators:Įxample 6: At a pie-eating contest, Spencer got through three-fourths of a pie before time was called Carly finished just one-half of a pie. Let's look at some word problems.Įxample 5: A member of the school track team ran two-thirds mile on Monday, and one-fifth mile on Tuesday. Make equivalent fractions using the LCD.įor step 2, remember that the numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions.Procedure: To add or subtract fractions with unlike denominators: The following procedure summarizes the steps we used in examples 1 through 4: The LCD of 10 and 15 is 30.Īnalysis: The denominators are not the same. Let's look at some more examples.Īnalysis: The denominators are not the same. In example 2, we had an improper fraction, so it was necessary to simplify the result. Solution: Make equivalent fractionswith the new denominator: Let's look at some examples.Īnaysis: The denominators are not the same. Remember that the LCD is simply the least common multiple of the denominators. ![]() However, for the remainder of this lesson, we will use the LCD method. You can use either method, whichever you prefer. Least common denominator (LCD) - leads to having less slices of pizza.Common denominators - leads to having more slices of pizza.We have presented two methods for adding (and subtracting) fractions with unlike denominators: This is shown below.Īs you can see, using a common denominator instead of the LCD can lead to unnecessary simplifying of the result (like having more slices of pizza). We could have used a common denominator, such as 24, to solve this problem. In example 1, note that the numerator and the denominator of a fraction must be multiplied by the same nonzero whole number in order to have equivalent fractions. Solution: Make equivalent fractions with the new denominator: The least common denominator (LCD) of 4 and 6 is 12. We will use equivalent fractions to help us, as shown in the examples below. It is not always practical to draw circles to solve these problems. Now we can use 6 as our least common denominator.Īs you can see, the least common denominator lets you add (or subtract) fractions using the least number of slices. List the least common multiple of 3 and 6: Lets' find the LCD of one-third and one-sixth. ![]() It is the least common multiple of the denominators. Method 2: We can rename these fractions using their least common denominator(LCD), which is the smallest number that is evenly divisible by all the denominators. However, for most chefs, making 18 slices is too much work! Let's try using another method that involves less slices. In the problem above, we found a common denominator by multiplying the denominators of the original fractions. So instead of having 3 or 6 slices of pizza, we will make both of them have 18 slices. We can find a common denominator by multiplying the denominators together: 3 x 6 = 18. Solution: We need to make the denominators the same. But we cannot add these fractions since their denominators are not the same! How much pizza was left over altogether?Īnalysis: This problem is asking us to add two one-third and one-sixth together. At the end of the day, there was a third of one pizza, and a sixth of another pizza left over. Problem: A pizza restaurant had two equally-sized pizzas, each sliced into equal parts. ![]()
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