Explain why you cannot add or subtract fractions with unlike denominations while you can add or subtract fractions with like denominations. Include one or more real world examples in your explanation
You cannot add or subtract fractions with unlike denominations because the denominators represent the number of equal parts the whole is divided into. When the denominators are different, it means the wholes are divided into different numbers of equal parts, which makes it impossible to add or subtract them directly.
For example, imagine you have a cake divided into 4 equal parts and another cake divided into 5 equal parts. Adding or subtracting these fractions would be like trying to combine 4 slices of cake with 5 slices of cake. Since the sizes of the slices are different, it is not possible to directly add or subtract them.
On the other hand, when the fractions have like denominators, it means the wholes are divided into the same number of equal parts. In this case, adding or subtracting the fractions is possible because you are essentially combining or taking away the same-sized pieces.
For instance, let's say you have a pizza divided into 8 slices and another pizza also divided into 8 slices. You can now add or subtract these fractions because the slices are of the same size. Adding 3/8 of the first pizza with 4/8 of the second pizza would give you 7/8 of a whole pizza.
In conclusion, fractions with unlike denominators cannot be added or subtracted directly because they represent divisions of different wholes, whereas fractions with like denominators represent divisions of the same-sized wholes, allowing for direct addition or subtraction.