Diamond Problem Calculator (2024)

What is a diamond problem? Diamond math problems

Despite what you might think, the diamond problem doesn't have a lot in common with gemstones💎 or diamond rings💍 — though we can teach you how to calculate a diamond's weight. It is more closely related to what is often called a diamond in math ♦️ or cards🃏 - the rhombus, a quadrilateral shape. The diamond problem is a type of exercise that happens in a diamond shape 💠 - which we can also represent as a cross with 4 sections.

There are three main types of diamond problems, and the diamond problem calculator can deal with all of them. If you're wondering how to do diamond problems in each of these cases, scroll down to the next sections.

How to do diamond problems? Case 1: Given two factors

This is the easiest case: you have two numbers, A and B, and you need to find the sum and product of them. For example, let's say that we want to solve the diamond problem for factors $13$13 and $4$4:

You might meet this type of a diamond math problem in the first lesson about the diamonds - when your teacher first introduces the concept.

Case 2: Given one factor, and the product or sum

$$\text{factor}\ A + \text{factor}\ B = \text{sum}$$factorA+factorB=sum

And

$$\text{factor}\ B = \text{sum} - \text{factor}\ A$$factorB=sum−factorA

So:

$$\text{factor}\ B = 11-6 = 5$$factorB=11−6=5

With both factors in hand, simply multiply them to get the last number: product $= 5 \times 6 = 30$=5×6=30.

b) If you know one factor and the product, divide the product by the factor to find the second product:

$$\text{factor}\ A \times \text{factor}\ B = \text{product}$$factorA×factorB=product

And:

$$\frac{\text{factor}\ B}{ \text{product}} = \text{factor}\ A$$productfactorB​=factorA

So:

$$\text{factor}\ B = \frac{63}{9} = 7$$factorB=963​=7

Then calculate the sum, use the following expression: sum $= \text{factor}\ A + \text{factor}\ B = 9 + 7 = 16$=factorA+factorB=9+7=16.

Remember, you can always quickly solve these diamonds or verify your answers with our diamond problem calculator.

Case 3: Given product and sum, while searching for factors

$$x^2+7x+12$$x2+7x+12

We would like to factor this equation, meaning that we'd like to present it in a form:

$$(x+...)(x+...)$$(x+...)(x+...)

How to find these numbers - the roots of the quadratic equation? You know that their product must be equal to $12$12, and that their sum is equal to $7$7. And that's exactly what you're trying to find out in the diamond problem! 🙂 You can rewrite this question in the form of a diamond:

$$\quad\quad\begin{split}12&=1\times12\\12&=2\times6\\12&=3\times4\end{split}$$121212​=1×12=2×6=3×4​

Don't forget the negative numbers:

$$\quad\quad\begin{split}12&=-1\times-12\\12&=-2\times-6\\12&=-3\times-4\end{split}$$121212​=−1×−12=−2×−6=−3×−4​

$$\quad\quad\begin{split}&\color{red}{1+12=13}\\&\color{red}{2+6=8}\\&\color{green}{3+4=7}\\\end{split}$$​1+12=132+6=83+4=7​

And here it is! We can stop here, as we've found the two numbers which meet the condition 🎉

Sometimes it's very easy to guess the solution, as there are not many options. We're sure that you'll solve this a diamond problem in no time!

If not, enter the numbers into our diamond problem solver. That wasn't so difficult, was it? 🤦

How to use diamond problem calculator

FAQ

What are the other numbers in the diamond if the left and right are -4 and 8?

The top number is -32, and the bottom is 4. To find the top, we multiply the side numbers. We add them together to find the bottom.

What is the diamond problem used for in mathematics?

We use the diamond problem in addition, subtraction, multiplication, and division in maths. It is used to calculate integers, decimals, and fractions and for factoring trinomials.

How do I solve the diamond for fractions?

How do I find the right and left numbers in the diamond?