Difficulty: Easy
Correct Answer: 3/8
Explanation:
Introduction / Context: This question checks your understanding of how to divide a fraction by a whole number. Such operations are fundamental in arithmetic and appear frequently in word problems involving sharing or scaling quantities.
Given Data / Assumptions:
Concept / Approach: Dividing a fraction by a whole number is equivalent to multiplying the fraction by the reciprocal of that whole number. The reciprocal of 2 is 1/2. Therefore 3/4 ÷ 2 can be written as 3/4 × 1/2. We then multiply numerators and denominators and simplify the result if possible.
Step-by-Step Solution: Step 1: Write the division as multiplication by the reciprocal: 3/4 ÷ 2 = 3/4 × 1/2. Step 2: Multiply the numerators: 3 × 1 = 3. Step 3: Multiply the denominators: 4 × 2 = 8. Step 4: The resulting fraction is 3/8. Step 5: Check for further simplification. Since 3 and 8 have no common factor greater than 1, 3/8 is already in simplest form.
Verification / Alternative check: We can also reason with decimals. 3/4 equals 0.75. Now divide 0.75 by 2. The result is 0.375, which we know is the decimal representation of 3/8. This confirms that 3/4 ÷ 2 equals 3/8. Both fraction based and decimal based methods lead to the same answer.
Why Other Options Are Wrong: 3/2 is larger than 1, but dividing 3/4 by 2 must give a fraction smaller than 3/4, not larger. 2/3 is about 0.6667, which is less than 3/4 but not equal to 3/4 ÷ 2. 8/3 is greater than 2 and is far from the expected reduced fraction.
Common Pitfalls: A common mistake is to divide only the numerator or only the denominator by 2 instead of using the reciprocal method. Another error is to treat 3/4 ÷ 2 as 2 ÷ 3/4, which inverts the operation. Always remember that dividing by a number is the same as multiplying by its reciprocal and then simplify carefully.
Final Answer: The fraction 3/4 divided by 2 equals 3/8.
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