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 into which the whole is divided, and in the case of unlike denominators, the total number of equal parts is different.
For example, let's consider a real-world scenario where you have two pizzas. One pizza is divided into 8 equal slices, while the other pizza is divided into 12 equal slices. The denominator of the fraction represents the total number of equal slices in each pizza. If you try to add or subtract these fractions, it would be like trying to add or subtract pieces from both pizzas at the same time, which is not possible because the total number of slices in each pizza is different.
On the other hand, when you have fractions with like denominators, it means the whole is divided into the same number of equal parts. In this case, the denominators represent the same number of equal parts in the whole, which allows you to add or subtract the fractions.
For example, let's say you have two cakes, both divided into 6 equal pieces. In this scenario, the denominator of the fraction represents the total number of equal pieces in each cake. If you have 2/6 of one cake and 3/6 of the other cake, you can add them together to get 5/6 of cake in total. Since both cakes are divided into the same number of equal pieces, you can easily add or subtract the fractions.