explain why you cannot add or subtract fractions unlike denominators while you can add or subtract fractions with like denominators. Include one or more real-world example in your explanation
You cannot add or subtract fractions with unlike denominators because the denominators represent the total number of equal parts a whole is divided into. When the denominators are different, it means the wholes being represented are divided into different numbers of parts, making it impossible to compare or combine them directly.
For example, let's consider baking a cake. If you have one cake recipe that requires the batter to be divided into 4 equal parts (denominator of 4), and another recipe that divides the batter into 6 equal parts (denominator of 6), you cannot directly add or subtract these fractions. They represent different divisions of the batter, so you need to find a common denominator (a common number of equal parts for both recipes) before performing any addition or subtraction.
However, if you are dealing with fractions that have the same denominator (like denominators), it means they represent parts of the same whole, divided uniformly. In this case, you can add or subtract these fractions because the denominators indicate that they represent the same kind of parts. For instance, if you have a pizza divided into 8 equal slices and you eat 3 of them, you can subtract that from the total number of slices.