Difficulty: Easy
Correct Answer: 3/8
Explanation:
Introduction:
This question involves division of a fraction by a whole number. It checks whether you understand how to handle division of fractions and can reduce the result to simplest form. Such operations appear frequently in ratio, proportion, and algebra problems.
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. In general, (a/b) ÷ c = (a/b) * (1/c) = a/(b * c). After performing the multiplication, we reduce the resulting fraction if possible.
Step-by-Step Solution:
Step 1: Start with the expression: (3/4) ÷ 2.Step 2: Write 2 as a fraction: 2 = 2/1.Step 3: Division by a fraction is multiplication by its reciprocal: (3/4) ÷ (2/1) = (3/4) * (1/2).Step 4: Multiply the numerators and denominators: (3 * 1) / (4 * 2) = 3 / 8.Step 5: Check if 3/8 can be simplified. Since 3 and 8 have no common factor greater than 1, 3/8 is already in simplest form.
Verification / Alternative check:
As a decimal, 3/4 = 0.75. Dividing 0.75 by 2 gives 0.375. Converting 3/8 to decimal also gives 0.375. Since both methods produce the same decimal, this confirms that 3/8 is the correct fraction for (3/4) ÷ 2.
Why Other Options Are Wrong:
3/2 is larger than 1 and would result from multiplying 3/4 by 2, not dividing. 2/3 and 8/3 come from unrelated operations. 1/4 is 0.25 and does not match 0.375. Only 3/8 corresponds to the correct result of dividing 3/4 by 2.
Common Pitfalls:
Students sometimes mistakenly multiply by 2 instead of dividing or forget to take the reciprocal when handling fraction division. Another mistake is to divide only the numerator or only the denominator by 2 instead of using the proper method. Remember that dividing by a whole number c is equivalent to multiplying by 1/c.
Final Answer:
The value of 3/4 divided by 2 is 3/8.
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