"Explain the process of adding fractions with like denominators and provide examples of solving such problems."
Adding fractions with like denominators is a relatively simple process. When the denominators (the numbers on the bottom) of the fractions are the same, you can simply add the numerators (the numbers on the top) and keep the same denominator. Here's how you can do it step by step:
1. Write down the two fractions you want to add. Make sure they have the same denominator. For example, let's take the fractions 3/5 and 2/5, where the denominators are both 5.
2. Add the numerators of the fractions. In our example, 3 + 2 = 5.
3. Keep the same denominator. In our example, since the denominators are already the same, we will keep the denominator as 5.
4. Write down the sum of the numerators over the common denominator. In our example, the sum is 5 and the denominator is 5. So the answer is 5/5.
5. Simplify the fraction, if possible. In this case, 5/5 can be simplified because both the numerator and denominator are divisible by 5. Dividing both by 5 gives us 1/1.
Therefore, 3/5 + 2/5 = 1/1 or simply 1.
Here's another example:
Let's add 1/3 and 2/3:
1. The fractions have the same denominator, which is 3.
2. Add the numerators: 1 + 2 = 3.
3. Keep the denominator as 3.
4. The sum of the numerators over the denominator is 3/3.
5. This fraction can be simplified since both the numerator and denominator are divisible by 3. Dividing both by 3 gives us 1/1 or simply 1.
Therefore, 1/3 + 2/3 = 1.