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Fractions are everywhere.

You might use them when you cook or when you share items with friends and family, even if you don’t realize it. In this video, we’ll explore how to add three or more fractions with unlike denominators.

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Fractions with the Same Denominator

Suppose that you share a pie with a friend. You eat 1/4 of the pie, and your friend eats 3/4 of the pie.

How much of the pie did you both eat all together? In this situation, each fraction has the same denominator, which is the bottom number of a fraction. You can also think of the denominator as the ‘name’ of the fraction. If fractions have the same denominator (name), then we can simply add the numerators together and keep that ‘name.


commondenom


In this image, you ate one of the four pieces of pie, or ¼. Your friend ate three out of the four pieces of the pie, or ¾. In total, you and your friend ate four out of the four pieces of the pie, or 4/4.

Notice that we kept the denominators the same. You and your friend ate from the same pie, and that pie was cut into 4 pieces. You did not change the original number of pie pieces (4) and so the denominator stayed the same.Now, imagine sharing a pie with two of your friends, not just one.

Let’s say you had 1/4 of the pie, another friend had 1/4 of the pie, and another friend had 2/4 of the pie. Since the denominators are the same, we will add the numerators together and keep the denominator.1/4 + 1/4 + 2/4 = (1 + 1 + 2) = 4/4, where both numerator and denominator are 4.

Fractions with Different Denominators

Let’s take the same example of sharing a pie, but this time you eat 1/4 of the pie, while your friend eats 1/2. Since the denominators of the fractions are different, we cannot add them. We need to rewrite each fraction so that the denominators are the same.

How many 2s go into 4? Well, 2 x 2 = 4. We can use this information to help us change our fractions, like so:

fraction1


Here, we multiplied the denominator by 2 to get to 4, so we need to multiply the numerator by 2. Now that the denominators are the same, we can add the numerators and keep the denominator.So, 1/4 + 1/2 = 1/4 + (2/4) = 3/4.

You and your friend ate 3/4 of the pie all together.

Adding Three or More Fractions

We can use multiplication to convert fractions with different denominators, by finding least common denominator (LCD) also known as least common multiple. For example:

lcm3numbers

The LCM of 2, 3, and 4 is 12 because it is the smallest number our list of multiples have in common. The next step is to multiply each denominator by a number that will give us 12, and then multiply each numerator by that number.

converting

Now that all our fractions have the same denominator, we can add the numerators and keep the denominator.

6/12 + 4/12 + 3/12 = 13/12.

Lesson Summary

When adding three or more fractions that do not have the same denominator, or bottom number, first make a list of multiples for each denominator. Then find the least common denominator, or least common multiple. This will be your new denominator. Next, rewrite the original fractions so they reflect the new denominator, making sure to multiply the numerator by the least common multiple.

Once all fractions have the same denominator, add the numerators and keep the denominator the same. If needed, simplify the fraction.

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