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.
You cannot add or subtract fractions with unlike denominators because the denominators represent the total number of equal parts that make up a whole. When the denominators are different, the fractions represent different-sized parts, which cannot be directly combined.
For example, suppose you have a chocolate bar that is divided into 3 equal parts, and you want to add half of it to another chocolate bar that is divided into 4 equal parts. The first chocolate bar can be represented as 1/3 of the whole, and the second chocolate bar can be represented as 1/4 of the whole. Since the denominators (3 and 4) are different, these fractions cannot be added directly. You cannot simply add 1/3 and 1/4 to get the total amount of chocolate because the sizes of the parts are different.
On the other hand, when the fractions have like denominators, it means that they represent the same size of parts, and thus can be added or subtracted easily. For instance, if you have a pizza divided into 8 equal slices and you eat 3 slices, you can subtract this amount by using the fraction 3/8. If you eat another 2 slices, you can add the fraction 2/8. Since the denominators (8) are the same, you can directly add or subtract these fractions to find the total amount of pizza consumed.
In summary, fractions with unlike denominators cannot be added or subtracted directly because they represent different-sized parts. However, fractions with like denominators can easily be added or subtracted because they represent the same size of parts.