Product | ||
---|---|---|

A | B | |

Sum |

Directions: Enter values in any two fields, see the answer below.

Product | ||
---|---|---|

A | B | |

Sum |

Directions: Enter values in any two fields, see the answer below.

**What is the diamond math problem?**

The diamond math problem, sometimes called the “diamond puzzle,” is a visual representation of a factoring exercise. The problem is represented by a diamond – or a large cross shaped like the letter “X” – with four slots for numbers. The left and right slots represent factors A and B, respectively. The number at the top of the diamond is the product of A and B, while the number at the bottom is their sum. The problem may be presented with any two values missing. Solving for the missing values is the task of the diamond problem.

**How to solve the diamond math problem**

There are four cases of the diamond problem you may encounter. Each can be solved using the formulas for products and sums. Recall that the product of A and B is defined as Product = A * B, and the sum is defined as Sum = A + B. The four possible cases are outlined below.

**Case 1: Given two factors A and B**

This is the most straightforward case of the diamond problem and likely the first you will encounter. Given factors A and B, plug the values into the product and sum formulas given above.

**Case 2: Given one factor and the sum**

Though slightly more complicated, this case can also be solved using the abovementioned formulas. First, you must reorganize the sum formula to solve for the second factor. For example, if you are given factor A, you can reorganize the formula as follows: B = Sum – A From there, plug in your known values and solve for factor B.

**Case 3: Given one factor and the product**

As mentioned above, we can reorganize the product formula to solve for the missing factor. Given factor A and the product, we rearrange the formula as follows:

B = Product divided by A

**Case 4: Given product and sum**

This is the most common case of the diamond problem and is helpful in learning about factoring quadratic equations. There are several ways to solve this case, but the simplest is as follows: 1. Consider all possible factors for the top number – the product. Which integers can be multiplied together to produce that value? Don’t forget the negatives! 2. Check the sum of each pair of factors. When you’ve found a pair of factors that add up to the bottom value – the sum – you’ve solved for factors A and B.

**How to use the Diamond Math Problem Calculator at Calculator Town**

Using the Diamond Math Problem Calculator at Calculator Town is simple. This tool can save you time and help you check your work on diamond problems. The calculator has input fields for four values: factor A, factor B, the product, and the sum. Input the known values from your diamond problem, leaving the unknown fields blank. The solved diamond problem will automatically appear at the bottom of the screen. To solve another problem, click “Reset” and enter your new values.

**See Also**

Diamond Problem Worksheet Creator This web page can create a worksheet of Diamond Math Problems for you.

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