Given mn denotes 2m+n , evaluate a) 35 b.) 2(35
The Correct Answer and Explanation is:
Given Operation:
The symbol * is defined as:
m * n = 2m + n
Part (a)
Evaluate 3 * 5
Using the definition:
m = 3, n = 5
m * n = 2m + n = 2(3) + 5 = 6 + 5 = 11
So, 3 * 5 = 11
Part (b)
Evaluate 2 * (3 * 5)
We already found from part (a) that:
3 * 5 = 11
Now, substitute into the expression:
2 * (3 * 5) = 2 * 11
Again, apply the same operation definition:
m = 2, n = 11
m * n = 2m + n = 2(2) + 11 = 4 + 11 = 15
So, 2 * (3 * 5) = 15
Final Answers:
a) 3 * 5 = 11
b) 2 * (3 * 5) = 15
Explanation:
This problem involves an operation defined differently from regular multiplication. In mathematics, operations can be redefined with special rules. Here, the symbol * means we take twice the first number and add the second number. Understanding such definitions is important because the same symbols may carry different meanings in different contexts.
For part (a), we substitute the given numbers directly and apply the rule step by step. In part (b), the expression is nested, meaning we have to solve the inner operation first. This follows the common order of operations principle where expressions inside parentheses are evaluated before applying the outer operation.
This type of custom operation question is common in algebra and logic tests to check if the learner reads instructions carefully and follows definitions precisely. It is also a good exercise in substituting values and simplifying expressions systematically.
