Diamond Problem Calculator
Solve diamond problems by finding missing factors, products, or sums
Diamond Problem Solver
Getting Started
Enter any two values (factors, product, or sum) and the calculator will find the missing values automatically.
Example Problems
Example 1: Both factors given
Given: Factor A = 3, Factor B = 4
Solution:
• Product = 3 × 4 = 12
• Sum = 3 + 4 = 7
Diamond: Top = 12, Left = 3, Right = 4, Bottom = 7
Example 2: One factor and sum given
Given: Factor A = 6, Sum = 11
Solution:
• Factor B = Sum - Factor A = 11 - 6 = 5
• Product = 6 × 5 = 30
Diamond: Top = 30, Left = 6, Right = 5, Bottom = 11
Example 3: Product and sum given
Given: Product = 12, Sum = 7
Solution:
• Find factors of 12: (1,12), (2,6), (3,4), (-1,-12), (-2,-6), (-3,-4)
• Check which pair sums to 7: 3 + 4 = 7 ✓
• Therefore: Factor A = 3, Factor B = 4
Diamond: Top = 12, Left = 3, Right = 4, Bottom = 7
Diamond Problem Types
Case 1: Both Factors
Calculate product and sum from two given factors
Case 2: One Factor + Sum/Product
Find missing factor using basic arithmetic
Case 3: Product + Sum
Factor the product to find pairs that sum correctly
Diamond Structure
Quick Tips
Enter any two values to solve the diamond
Works with positive, negative, and decimal numbers
Useful for factoring quadratic expressions
Check your work by verifying all relationships
Some problems may have multiple solutions
Understanding Diamond Problems
What is a Diamond Problem?
A diamond problem is a visual method for finding relationships between four numbers: two factors and their product and sum. The diamond shape helps organize these relationships in an intuitive way.
Diamond Layout
- •Top: Product of the two factors
- •Left & Right: The two factors
- •Bottom: Sum of the two factors
Applications
Factoring Quadratics:
x² + 7x + 12 = (x + ?)(x + ?)
Find numbers that multiply to 12 and add to 7
Problem-Solving Strategy
- •List factor pairs of the product
- •Test which pair gives the correct sum
- •Consider both positive and negative factors
- •Verify your solution in the diamond
Connection to Quadratic Factoring
Standard Form
ax² + bx + c
Find factors of c that sum to b
Factored Form
(x + m)(x + n)
Where m × n = c and m + n = b