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.
6th grade simple explanation
You cannot add or subtract fractions with unlike denominators because the denominators represent how many equal parts a whole is divided into. If the denominators are different, it means the wholes are divided into different numbers of equal parts. For example, if you have 1/4 of a pizza and 1/2 of a pizza, you cannot directly add them together because they have different denominators. It's like trying to add apples and oranges.
On the other hand, you can add or subtract fractions with like denominators because they represent the same number of equal parts. For example, if you have 1/4 of a pizza and you add 2/4 of a pizza, you can easily add them together to get 3/4 of a pizza. This is because both fractions have the same denominator of 4, which means they represent the same size of equal parts.
In everyday life, adding or subtracting fractions with like denominators is similar to combining or separating quantities that are divided into the same number of equal parts. For instance, if you have 2/3 of a bag of candies and your friend gives you 1/3 of a bag of candies, you can add them together to have a total of 3/3 (which is equal to a whole bag) of candies.