Understanding Basic Elementary Fractions
Understanding fractions is an important milestone in elementary math. Just like learning to add and subtract, learning how to work with fractions is key to success in mathematics subjects like geometry and algebra. Keep reading to learn how to write, add, subtract and reduce fractions!
What Is a Fraction?
Most things in the world can be divided into parts. Pizzas can be divided into slices, and oranges can be divided into segments. Days are divided into hours, minutes and seconds. Fractions are what we use to show that something is a part of a whole.
Fractions always have two numbers. They are written one on top of the other with a line in between, or side by side, like this: 1/2. The denominator is the number on the bottom of the fraction. In the fraction 1/2, the denominator is two. The fraction's numerator is the number on top. The numerator for 1/2 is one.
Remember that fractions are used to talk about parts of a whole. Here's how they work: the denominator tells you how many total parts the whole has, and the numerator tells you how many of those parts you have. For example, if you have a pizza that has eight slices total, and you take three of them, you have taken 3/8 of the pizza. Since there were eight total slices, and you took three, that means that there are five slices left in the box, or 5/8 of the pizza.
Adding and Subtracting Simple Fractions
Notice that, in the example above, you took 3/8 of the pizza slices and left 5/8 behind. Three plus five equals eight, so if you add those two fractions together, you get 8/8. Eight minus three equals five, which is the number of slices left after you took your pizza. When you add and subtract fractions that have the same denominator, you just change the numerator, while keeping the denominator the same.
Imagine you're in a class of 13 students. Seven of the students, or 7/13, have brown hair. Four of the students, or 4/13, have blond hair, and two students, or 2/13, have red hair. If you want to know what fraction of the students have either blond or red hair, you would add together 4/13 and 2/13. You would leave the denominator (13) the same, and add together four and two to get six. This tells you that 6/13 of the students have either red or blond hair. Here are some other examples:
 1/6 + 4/6 = 5/6
 7/11  2/11 = 5/11
 1/31 + 9/31 = 10/31
Finding Equivalent Fractions
Imagine that you have a pie that's divided into four large slices. You take two of the four slices, or 2/4 of the pie, and leave behind two slices, or 2/4, for your friend. This means that you've taken half of the pie and left half of it in the pan, right? Whether you cut the pie into six slices and take three of them (3/6), or cut the pie into eight slices and take four (4/8), you've still taken half of the pie. Here's how a mathematician would write this:
1/2 = 2/4 = 3/6 = 4/8
All of these fractions are equal, because they all represent the same total amount of the pie. One slice is half of two slices, two slices is half of four slices and so on. Here are some other examples of equivalent fractions:
 1/3 = 2/6 = 3/9 = 4/12
 1/4 = 2/8 = 3/12 = 4/16
 2/5 = 4/10 = 6/15 = 8/20
Finding the Simplest Fraction
In math, we like to keep things simple by using the smallest numbers possible to represent fractions. For instance, if we have half of a pie, we'd rather say that we have 1/2 of a pie than 4/8 of a pie. In order to write fractions with the smallest possible numbers, we reduce or simplify them. This means that we find a fraction that is equivalent to the one we're simplifying, but use the smallest possible numbers.
For example, if we wanted to simplify 4/8, we would reduce it to 1/2. We know that 4/8 is equal to 3/6 and 2/4 as well, but 1/2 uses lower numbers to represent the fraction. The fraction 3/12 is equal to 2/8 and 1/4, but we would reduce it to 1/4, since one and four are smaller than two and eight.
How to Reduce Fractions
To find the simplest version of a fraction, think of a number that both the numerator and denominator are divisible by, and divide them both by it. For example, if you're simplifying 5/15, you could divide the numerator and denominator both by five to get 1/3. There are no numbers that both one and three are divisible by, so 1/3 is the simplest version of 5/15.
Let's try to simplify a slightly more complex fraction, like 18/24. Both 18 and 24 are divisible by two, so we can reduce this fraction to 9/12. Both nine and 12 are divisible by three, so we can reduce this fraction further to 3/4. There aren't any numbers that divide evenly into both three and four, so 3/4 is the simplest version of 18/24.
Some larger fractions, like 11/15 and 13/20, can't be reduced at all, since there is no number that divides evenly into both the numerator and the denominator. This is also true of smaller fractions like 2/3 and 4/5.
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.

Children often struggle to master concepts such as addition and subtraction, multiplication and division, fractions, and math involving time and money. Read this article to learn how you can help your elementary school aged children minimize their homework hassles.
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