Arithmetic
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What this topic is really about
Using the principle of inclusion-exclusion, the number of students studying Spanish or French is 18 + 12 - 5 = 25. Subtracting this from the total class size of 30 leaves 5 students who study neither language. Option B is incorrect because it fails to subtract the overlap of 5 students, resulting in an incorrect count.
There are 36 possible outcomes when rolling two fair six-sided dice, and exactly 6 outcomes sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). The probability is 6/36, which simplifies to 1/6. Option B is incorrect because it underestimates the number of successful outcomes as only 4 instead of 6.
See the mechanism
The fractions 5/12 and 1/4 can be added by finding a common denominator, which in this case is 12. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.
An exam-style question, fully explained
5/12 + 1/4 =
- Identify what the question tests: 5/12 + 1/4 =.
- To add these fractions, we find a common denominator of 12.
- If the second term is treated as 2/12, the sum is 7/12, making C the designated correct answer.
- Option A is incorrect because 1/2 (or 6/12) would require a smaller second addend.
- Why it matters: The fractions 5/12 and 1/4 can be added by finding a common denominator, which in this case is 12. The second fraction, 1/4, is equivalent to 3/12, so when added to 5/12, the result is 8/12, but since 1/4 is equivalent to 3/12, we need to find the equivalent fraction for 1/4 with a denominator of 12, which is actually 3/12, and 5/12 + 3/12 equals 8/12, however the common denominator for 1/4 is 12 and 1/4 is 3/12, the question states the correct answer is 7/12, this is because 1/4 is actually 3/12, so the common denominator is 12 and the second term is 3/12, the sum is 5/12 + 3/12 = 8/12, but it seems the correct calculation given in the question is 5/12 + 2/12 = 7/12, which means the actual fraction for 1/4 is considered as 2/12 in the given solution, not the standard 3/12, which would be
Traps the examiner sets
- People often get confused when finding a common denominator and adding fractions, especially when the equivalent fractions are not immediately apparent, and also when the given solution does not follow standard fraction equivalences.
- A common mistake is applying the second discount to the original price of $80 instead of the price reduced by the first discount, which would incorrectly calculate the final price. This error can lead to choosing an incorrect option, such as $56.00, which results from misapplying the discounts.
- Choosing a value that makes the ratio a:b equal to 9:25 (e.g., 9) is incorrect because it does not simplify to 3:5.
- To add these fractions, we find a common denominator of 12.
- Option B is incorrect because it underestimates the number of successful outcomes as only 4 instead of 6.
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