Adding Fractions for 5th Grade Students
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!
Adding Fractions in 5th Grade
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.
Practice Adding Fractions
Here are a few problems to help you practice adding fractions. For each problem, you'll have to find equivalent fractions with common denominators first, and then add those together to get your answer.
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.
Other Articles You May Be Interested In

Fractions can be a confusing topic for some students. Read on to learn how you can help your children better understand the uses of fractions.

Support for children learning to read comes in many forms, such as books, tutors and educational DVDs. More and more applications for mobile devices, also known as apps, are adding to this field by providing interactive and adaptive reading tools. This list includes ten apps that can help your child develop reading skills in fun...
We Found 7 Tutors You Might Be Interested In
Huntington Learning
 What Huntington Learning offers:
 Online and incenter tutoring
 One on one tutoring
 Every Huntington tutor is certified and trained extensively on the most effective teaching methods
K12
 What K12 offers:
 Online tutoring
 Has a strong and effective partnership with public and private schools
 AdvancEDaccredited corporation meeting the highest standards of educational management
Kaplan Kids
 What Kaplan Kids offers:
 Online tutoring
 Customized learning plans
 RealTime Progress Reports track your child's progress
Kumon
 What Kumon offers:
 Incenter tutoring
 Individualized programs for your child
 Helps your child develop the skills and study habits needed to improve their academic performance
Sylvan Learning
 What Sylvan Learning offers:
 Online and incenter tutoring
 Sylvan tutors are certified teachers who provide personalized instruction
 Regular assessment and progress reports
Tutor Doctor
 What Tutor Doctor offers:
 InHome tutoring
 One on one attention by the tutor
 Develops personlized programs by working with your child's existing homework
TutorVista
 What TutorVista offers:
 Online tutoring
 Student works oneonone with a professional tutor
 Using the virtual whiteboard workspace to share problems, solutions and explanations