Explain why you cannot add or subtract fractions with unlike denominators while you can add or subtract fractions with like denominators. Include one or more real-world examples in your explanation.(2 points
You cannot add or subtract fractions with unlike denominators because the denominators represent the number of equal parts that make up a whole. When the denominators are different, it means that the parts being referred to in each fraction are not the same size or shape. Therefore, it is not possible to directly compare or combine them.
For example, let's say you have a pizza that is divided into 8 equal slices. If you have 3 slices out of the 8, you can represent it as 3/8. Now, let's imagine you also have a cake that is divided into 12 equal slices, and you have 4 out of the 12 slices. This can be represented as 4/12.
Since the pizza and cake have different denominators (8 and 12 respectively), you cannot just add or subtract the fractions directly. However, you can find a common denominator to enable adding or subtracting. In this case, the lowest common denominator for 8 and 12 is 24. So, you would need to convert both fractions to have a denominator of 24 before adding or subtracting (e.g., 3/8 becomes 9/24 and 4/12 becomes 8/24). Only then can you perform the addition or subtraction.
On the other hand, if you have fractions with like denominators, it means the parts being referred to are the same size or shape. In such cases, it is possible to directly compare or combine them. For instance, if you have two pizzas with 8 slices each, and you have 3 slices from one and 2 slices from the other, you can simply add their numerators while keeping the denominator same to get 5/8.
Hence, fractions with like denominators can be added or subtracted directly, while fractions with unlike denominators require a common denominator to perform these operations.