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. plz help and thank you.
You cannot add or subtract fractions with unlike denominators because the denominators represent different-sized parts or divisions in a whole. When the denominators are different, it means that the fractions represent different-sized pieces, making it impossible to directly combine or compare them. It is like trying to add apples and oranges together - you can't because they are different fruits.
On the other hand, when fractions have like denominators, it means that they represent the same-sized parts or divisions in a whole. This allows for easy comparison and combination. Adding or subtracting fractions with like denominators is akin to adding or subtracting similar objects. For example, if you have three slices of pizza and then someone gives you two more slices, you can easily see that you now have a total of five slices of pizza.
Real-world example: Let's say you are organizing a bake sale and want to determine how many cakes you need to bake. You know that each cake can be divided into 8 equal slices. On Monday, you sold 3 slices of cake, and on Tuesday, you sold 2 slices. You can easily calculate the total number of slices sold by adding the fractions: 3/8 + 2/8 = 5/8. This means that you sold a total of 5 out of 8 slices of cake so far.
Real-world example: Suppose you are planning a trip with your friends and need to calculate the amount of money each person will contribute. You have $10, and your friend contributes $7.50. To determine the total amount of money, you can add the fractions: $10 + $7.50 = $17.50. Here, the like denominators (both are in dollars) allow you to directly combine the amounts.