Math Problem Statement

Which number could replace the question mark in this pattern?

Solution

To determine the missing number in the given pattern, let's analyze the relationships between the numbers in each diagram.

Observations:

Each diagram has four numbers arranged as follows:

  • Top number, bottom number, left number, and right number.

We need to identify the rule connecting these numbers.

Analyzing the First Diagram:

For the first diagram:

  • Top number = 2
  • Bottom number = 6
  • Left number = 8
  • Right number = 4

Notice the pattern: Top number×Bottom number=Left number+Right number.\text{Top number} \times \text{Bottom number} = \text{Left number} + \text{Right number}.

  • 2×6=8+42 \times 6 = 8 + 4
  • 12=1212 = 12

Analyzing the Second Diagram:

For the second diagram:

  • Top number = 3
  • Bottom number = 5
  • Left number = 7
  • Right number = 8

Verify the same rule: Top number×Bottom number=Left number+Right number.\text{Top number} \times \text{Bottom number} = \text{Left number} + \text{Right number}.

  • 3×5=7+83 \times 5 = 7 + 8
  • 15=1515 = 15

Analyzing the Third Diagram:

For the third diagram:

  • Top number = 9
  • Bottom number = 2
  • Left number = 6
  • Right number = 12

Verify the same rule: Top number×Bottom number=Left number+Right number.\text{Top number} \times \text{Bottom number} = \text{Left number} + \text{Right number}.

  • 9×2=6+129 \times 2 = 6 + 12
  • 18=1818 = 18

Solving for the Fourth Diagram:

For the fourth diagram:

  • Top number = 4
  • Bottom number = 3
  • Left number = 2
  • Right number = ?

We need to find the missing number ?? such that: Top number×Bottom number=Left number+Right number.\text{Top number} \times \text{Bottom number} = \text{Left number} + \text{Right number}. Substitute known values: 4×3=2+?.4 \times 3 = 2 + ?. Simplify: 12=2+?.12 = 2 + ?. Solve for ??: ?=122=10.? = 12 - 2 = 10.

Final Answer:

The missing number is 10.

Answer: a) 10


Would you like me to explain this in more detail or go over additional examples?

Related Questions:

  1. What is another mathematical approach to verify this pattern?
  2. Can the same rule apply with subtraction or division?
  3. How do you determine patterns when the rule is not obvious?
  4. How can this method be used for more complex number puzzles?
  5. Are there other patterns where multiplication equals a sum?

Tip:

When solving number puzzles, test multiple arithmetic operations (addition, subtraction, multiplication, and division) to uncover hidden patterns quickly.

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Math Problem Analysis

Mathematical Concepts

Basic Arithmetic
Patterns and Relationships

Formulas

Top Number × Bottom Number = Left Number + Right Number

Theorems

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Suitable Grade Level

Grades 5-7