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 into which a whole is divided. When the denominators are not the same, the fractions are representing different sized parts, making it impossible to combine or compare them directly.
In real-world terms, let's consider an example:
Imagine you have a recipe that requires 1/4 cup of flour and 1/2 cup of sugar. If you try to add these fractions together, you cannot directly combine them because the denominators (4 and 2) are different. It is not possible to determine how many cups of a mixture you would have by simply adding 1/4 and 1/2.
On the other hand, when fractions have like denominators, it means they represent the same-sized parts. This makes it possible to directly combine or compare them.
For instance, think about a piece of land that is divided equally between two people. If one person owns 1/2 of the land and the other person owns 1/4 of the same land, you can add these fractions together because they have like denominators. The resulting fraction, 3/4, indicates that the two individuals collectively own 3/4 of the entire land.
By having like denominators, fractions have a common unit of measurement, making it feasible to perform addition and subtraction operations.