Question
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 number of equal parts into which a whole is divided. When the denominators are different, it means that the fractions are representing a different number of equal parts.
For example, if you have a cake divided into 4 equal parts, each part is represented by the fraction 1/4. Now, suppose you have another cake divided into 6 equal parts, each part is represented by the fraction 1/6. These two fractions have unlike denominators because they represent a different number of equal parts. Therefore, you cannot add or subtract these fractions directly because you would be trying to combine parts that are not the same size.
On the other hand, when you have fractions with like denominators, it means that they are representing an equal number of equal parts. In this case, you can add or subtract fractions by simply adding or subtracting the numerators while keeping the denominator the same.
For example, let's say you have a pizza divided into 8 equal slices, and you eat 3 slices represented by the fraction 3/8. If later on, you eat 2 more slices, you can represent that as the fraction 2/8. Since the denominators are the same, you can add these two fractions by adding the numerators to get 3/8 + 2/8 = 5/8. This tells you that you have eaten a total of 5 out of the 8 equal slices.
In summary, you cannot add or subtract fractions with unlike denominators because they represent a different number of equal parts. However, you can add or subtract fractions with like denominators because they represent the same number of equal parts.