 In 5th grade, you'll learn to perform number operations with fractions, like adding, subtracting and multiplying. Mastering these skills is important for succeeding in math class, so read on to learn how to add fractions! Remember that fractions represent parts of a whole. You can add together parts of a whole, just like you can add together integers. The difference is that, with fractions, you have to relate the parts you've added together to a common denominator, which is the whole that they came from. Sometimes fractions already have a common denominator, but other times you have to do a bit of work to find one.

### Adding Fractions with a Common Denominator

The denominator is the number on the bottom of the fraction, or on the right side if the fraction is written like this: 3/4. In that example, four is the denominator. The numerator is the number that's at the top, or on the left side. In the fraction 3/4, the numerator is three.

If fractions have a common denominator, this means that their denominators are the same. For example, 1/5 and 3/5 have a common denominator, five. To add fractions that have a common denominator, just add the numerators together, and keep the denominators the same. If you add 1/5 and 3/5, you'll get 4/5, since one plus three equals four. Here are some other examples:

• 2/7 + 3/7 = 5/7
• 1/3 + 2/3 = 3/3
• 5/9 + 2/9 = 7/9

### Adding Fractions with Different Denominators

When you add two fractions with different denominators, like 2/3 and 1/2, you have to find equivalent fractions that have the same denominators. Then, add together the numerators of those fractions. To do that, follow these steps:

1. List the multiples of each of the denominators. For example, some multiples of three are six, nine and 12, and some multiples of two are four, six and eight.
2. Identify the least common multiple of the two denominators. This is the lowest number that's a multiple of both. If the denominators are three and two, then six is the lowest number that's a multiple of both of them.
3. Determine what number you must multiply the denominator of each fraction by to get the least common multiple. In the example with 1/2 and 2/3, we already determined that for three and two, six is the least common multiple. For 2/3, you must multiply three by two (3 x 2) to get six, and for 1/2, you need to multiply two by three (2 x 3) to get six.
4. For each fraction, multiply both the numerator and the denominator by the number that you uncovered in the previous step. For instance, multiply both the numerator and the denominator of 2/3 by two, which gives you 4/6. Then, you'd also multiply both the numerator and the denominator of 1/2 by three, so the fraction 1/2 becomes 3/6. Both 4/6 and 3/6 are equivalent to the original fractions, and now they have a common denominator.
5. Add together the numerators of the new fractions, and keep the denominators the same. If you add the fractions 4/6 and 3/6, you get 7/6, because 4 + 3 = 7.

Tip: If a fraction's numerator is larger than its denominator, like it is with 7/6, it's called an improper fraction. This means that it is greater than one. Sometimes your teacher will ask you to convert improper fractions into mixed fractions, but that's for another lesson! For now, we'll leave 7/6 as it is.

#### Problem One

Shannon has used up 1/3 of her backyard for a flower garden, and she has a swimming pool that takes up another 1/4 of her yard. How much of her backyard do the swimming pool and the flower garden take up together?

#### Solution One

1. First, find equivalent fractions for 1/3 and 1/4 with common denominators. To do this, list the multiples of the denominators, three and four, until you find the least common multiple. The first few multiples of three are six, nine and 12, and the first few multiples of four are eight, 12 and 16. The least common multiple of three and four is 12, so that will be the new common denominator.
2. Now, you need to convert 1/3 and 1/4 so their denominators are both 12. To do this, multiply the numerator and denominator of each fraction by the same number, so that the denominator of each one is 12. For 1/3, you multiply one and three by four to get 4/12, and for 1/4, you multiply one and four by three to get 3/12.
3. Last, you add the numerators of 4/12 and 3/12 together to get 7/12.

#### Problem Two

At football practice, Jaden ran 3/7 of a mile on Saturday and 4/5 of a mile on Sunday. How many miles did he run altogether? Write your answer as an improper fraction.

#### Solution Two

1. First, find the least common multiple of the denominators, five and seven. Multiples of seven include 14, 21, 28 and 35. The multiples of five include ten, 15, 20, 25, 30 and 35, so the least common multiple of five and seven is 35.
2. Multiply both three and seven by five (3/7 x 5/5) to get 15/35. Now, we want to change the denominator of 4/5, so we multiply four and five by seven (4/5 x 7/7). This gives us 28/35.
3. Last, add together the numerators (28 + 15) to get 43. Our answer is 43/35 miles.
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