c) $\frac{2}{3}-\frac{1}{2}$
Answer (1)
Find a common denominator: The least common denominator of 3 and 2 is 6.
Rewrite the fractions with the common denominator: 3 2 = 6 4 and 2 1 = 6 3 .
Subtract the fractions: 6 4 − 6 3 = 6 1 .
The final answer is 6 1 .
Explanation
Understanding the Problem We are asked to evaluate the expression 3 2 − 2 1 . Both terms are fractions, and we need to find a common denominator to subtract them.
Finding a Common Denominator The least common denominator (LCD) of 3 and 2 is 6. We rewrite both fractions with the common denominator 6: 3 2 = 3 × 2 2 × 2 = 6 4 2 1 = 2 × 3 1 × 3 = 6 3
Subtracting the Fractions Now, we subtract the fractions: 6 4 − 6 3 = 6 4 − 3 = 6 1
Final Answer The result of the subtraction is 6 1 .
Examples
Fractions are a fundamental part of everyday life. For example, if you are baking a cake and the recipe calls for 3 2 cup of flour, but you only have a 2 1 cup measuring cup, you need to know how much more flour to add. This problem demonstrates how to subtract fractions to find the difference, which in this case is 6 1 cup of flour.
