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 total number of equal parts that make up the whole. When the denominators are different, the total number of equal parts in each fraction is not the same, making it impossible to directly combine or compare them.
To add or subtract fractions with like denominators, you simply combine or subtract the numerators while keeping the denominator the same. This is possible because the fractions have the same number of equal parts defined by the denominator. For example, if you have two pizzas, each divided into 8 equal slices, and you want to find the total number of slices you have, you can add them together by adding the numerators (number of slices) and keeping the denominator (total equal parts) the same. So, 3/8 + 4/8 = 7/8, meaning you have a total of 7 out of the 8 slices.
On the other hand, when the fractions have unlike denominators, the total number of equal parts is different for each fraction. It's like trying to compare the number of slices from two different-sized pizzas. For instance, if you have a pizza divided into 8 slices (8 equal parts) and another pizza divided into 6 slices (6 equal parts), you cannot directly add them together because the total number of slices is not the same. The fractions 3/8 and 4/6 cannot be added or subtracted without first finding a common denominator.