$\frac{1}{4}+(\frac{1}{4} \div \frac{1}{3})-(\frac{2}{3} \times \frac{3}{4})=$
A. $\frac{1}{4}$
B. 1
C. $\frac{1}{2}$
D. $\frac{5}{8}$
E. None of these
Answer (1)
Evaluate the division: 4 1 ÷ 3 1 = 4 3 .
Evaluate the multiplication: 3 2 × 4 3 = 2 1 .
Substitute the results back into the original expression: 4 1 + 4 3 − 2 1 .
Simplify the expression: 4 1 + 4 3 − 2 1 = 2 1 .
The final answer is 2 1 .
Explanation
Understanding the problem We are asked to simplify the given expression and choose the correct answer from the given options. Let's start by simplifying each part of the expression.
Evaluating the division First, we evaluate the division: 4 1 ÷ 3 1 . Dividing by a fraction is the same as multiplying by its reciprocal, so we have: 4 1 ÷ 3 1 = 4 1 × 1 3 = 4 3
Evaluating the multiplication Next, we evaluate the multiplication: 3 2 × 4 3 . 3 2 × 4 3 = 3 × 4 2 × 3 = 12 6 = 2 1
Substituting the results Now, we substitute the results back into the original expression: 4 1 + 4 3 − 2 1
Simplifying the expression To simplify the expression, we need to find a common denominator for the fractions. The common denominator for 4 and 2 is 4. So we rewrite 2 1 as 4 2 : 4 1 + 4 3 − 4 2 Now we can perform the addition and subtraction: 4 1 + 4 3 − 4 2 = 4 1 + 3 − 2 = 4 4 − 2 = 4 2 = 2 1
Final Answer The simplified result is 2 1 . Comparing this with the given options, we see that option C is the correct answer.
Examples
Understanding how to simplify expressions with fractions is crucial in many real-life situations. For example, when you're cooking and need to adjust a recipe that calls for fractions of ingredients, or when you're calculating distances on a map using a given scale. Also, when you are splitting a pizza with your friends and need to calculate how much each person gets. Mastering these skills will help you make accurate calculations and solve problems efficiently.
