# FOLLOWING RULES

Date of the Problem
April 25, 2022

Define the relation M @ N as M @ N = M2 + 2M/N. What is the value of 9 @ 4? Express your answer as a common fraction.

Substituting 9 for M and 4 for N in the given relation, we get 9 @ 4 = 92 + 2 × 9 ÷ 4 = 81 + 18/4 = 324/4 + 18/4 = 171/2.

Define the relation A # B as A # B = (A2 – B2 + AB)/(2B). What is the value of 5 # 4? Express your answer as a common fraction.

Substituting 5 for A and 4 for B in the given relation, we get (52 – 42 + 5 × 4)/(2 × 4) = (25 – 16 + 20)/8 = 29/8.

Using the two relations defined above, what is the value of (4 @ 2) # 10?

We’ll start with the relation in parentheses first. So, substituting 4 for M and 2 for N in the relation provided in problem 1, we get 4 @ 2 = 42 + 2 × 4 ÷ 2 = 16 + 8/2 = 20. Now, we can substitute 20 for A and 10 for B in the relation provided in problem 2 to get 20 # 10 = (202 – 102 + 20 × 10)/(2 × 10) = (400 – 100 + 200)/20 = 500/20 = 25.

Page 1 of the linked PDF contains PROBLEMS & SOLUTIONS.

Page 2 contains ONLY PROBLEMS. ♦

Math topic
CCSS (Common Core State Standard)
Difficulty