Welcome to learning about fractions! A fraction represents a part of a whole object. Every fraction has two main components: the numerator, which is the top number showing how many parts we have, and the denominator, which is the bottom number showing the total number of equal parts. Let's look at some examples. One half shows one part out of two equal parts. Three fourths shows three parts out of four equal parts. Two thirds shows two parts out of three equal parts.
When adding fractions with the same denominator, the process is straightforward. We keep the denominator the same and simply add the numerators together. Let's see this with an example: one fourth plus two fourths equals three fourths. Notice how we keep the denominator as four and add one plus two to get three. The visual shows how one piece plus two pieces gives us three pieces out of four total pieces.
When fractions have different denominators, we need to find a common denominator before we can add them. First, we find the least common multiple of the denominators. For one half and one third, the LCM of 2 and 3 is 6. Next, we create equivalent fractions: one half becomes three sixths, and one third becomes two sixths. Now both fractions have the same denominator and can be added together.
Now let's complete the full process of adding fractions with different denominators. We start with one half plus one third. First, we convert them to equivalent fractions with a common denominator of six: three sixths plus two sixths. Then we add the numerators: three plus two equals five. Our final answer is five sixths. The visual shows how three pieces plus two pieces gives us five pieces out of six total pieces.
Let's practice with some more challenging examples. Problem one: one fourth plus three eighths. Since the LCM of 4 and 8 is 8, we convert one fourth to two eighths, then add: two eighths plus three eighths equals five eighths. Problem two: two fifths plus one tenth. The LCM of 5 and 10 is 10, so two fifths becomes four tenths. Four tenths plus one tenth equals five tenths, which simplifies to one half. Always remember to check if your final answer can be simplified!