Product In Math — Definition & How To Find

Product Math Definition

The product in math is the answer to a multiplication problem. The result of multiplying two numbers together is the product.

Parts Of A Multiplication Problem

When you multiply, every part of the problem has a name. In a multiplication sentence, you have the multiplicand, the multiplier, and the product.

Here is a sample multiplication sentence:

$11 \times 9 = 99$

You can read this sentence as the multiplicand times the multiplier equals the product.

The multiplicand is the first number, the $\times$ or $*$ means $times$, the multiplier is the second number, the $=$ sign means $equals$ and the answer is the product.

Find the product in these multiplication sentences to be sure you have the idea:

1. $12 \times 12 = 144$
2. $2x * 9 = 18x$
3. $2\left(10 + 5\right) = 30$
4. $17 = 2 * 8.5$

The products in those multiplication sentences were $144$, $18x$, $30$, and $17$.

Notice in the last sentence that the product preceded the multiplicand and multiplier. That's perfectly fine to do. Notice also in $2(10 + 5)$, we dropped the $\times$ or $*$ altogether, implying multiplication by the parentheses.

How To Find The Product

To find the product, you must solve the multiplication problem. You can solve multiplication problems through repeated or fast addition.

Perhaps a high school student has a part-time job placing Gala apples in cardboard trays to fill fruit boxes. The trays have four rows of six depressions to hold the apples.

How many apples go on a tray?

You could add, $6 + 6 + 6 + 6$, and get a sum of $24$ Gala apples. A sum is the answer to an addition problem.

But with multiplication, you can say we have $6$ Gala apples in one row, and we take the one row four times:

• $6 times 4 equals 24$
• $6 \times 4 = 24$
• $6 * 4 = 24$

The product of $6$ apples times $4$ rows is $24$ Gala apples.

You can use a calculator or a times table to multiply large numbers or numbers you can't quickly do in your head.

This works the same way for negative numbers. Suppose you are clearing the try and what to know how many apples you removed from the four rows.

That would mean $4$ rows times $-6$, because you see each row had six indentions for apples to sit in. The negative sign means you subtracted six ($-6$) from each row.

$4 \times \left(-6\right) = -24$

Your answer is $-24$. You removed $24$ apples from the tray.

When you multiply a negative number times a positive number, you will always write your product as a negative number.

Properties Of Multiplication

Multiplication has four properties, presented here in alphabetical order because none outranks another:

1. Associative Property
2. Commutative Property
3. Distributive Property
4. Identity Property of Multiplication

Learn more about the basic properties of multiplication.

Special Cases Of Products In Math

Two special products appear when working with multiplication. One has been identified for you already, the identity property of multiplication – any number times $1$ gives back the original number.

The other special case is the multiplication property of $0$. Any number times $0$ gives a product in math of $0$.