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Pattern-Based Arithmetic Quiz: Solve 9 + 5 = ??? with Hidden Math Rule
Mathematics
Grade 6 of Primary School
Question Content
Solve the pattern-based math quiz: 2 + 3 = 10; 8 + 4 = 96; 7 + 2 = 63; 6 + 5 = 66; 9 + 5 = ???
Correct Answer
126
Detailed Solution Steps
1
Step 1: Identify the hidden pattern in the given equations. Observe that for each equation a + b = c, the formula is c = (a + b) × a.
2
Step 2: Verify the pattern with the given examples: (2+3)×2=5×2=10; (8+4)×8=12×8=96; (7+2)×7=9×7=63; (6+5)×6=11×6=66. All match the provided results.
3
Step 3: Apply the pattern to the unknown equation 9 + 5. Calculate (9 + 5) × 9 = 14 × 9 = 126.
Knowledge Points Involved
1
Pattern Recognition in Arithmetic
This refers to identifying consistent mathematical rules or formulas that govern a set of seemingly non-standard arithmetic equations. It requires analyzing given examples to find a repeatable logic, which is often used to test critical thinking and inductive reasoning skills in elementary math.
2
Order of Operations (PEMDAS/BODMAS)
This rule dictates the sequence of calculations: Parentheses/Brackets first, then Exponents/Orders, followed by Multiplication and Division, and finally Addition and Subtraction. In this problem, we first calculate the sum inside the parentheses, then perform the multiplication, which follows the order of operations.
3
Inductive Reasoning
Inductive reasoning involves deriving a general rule from specific examples. Here, we use the four given equations to induce the universal formula for all the equations in the quiz, then apply that rule to solve the unknown problem.
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