Find the Product: Step-by-Step Examples for Whole Numbers, Fractions, and Decimals
"Find the product" just means "multiply." This guide walks through worked examples with whole numbers, fractions, decimals, and word problems so you can answer any "find the product" question on the spot.
"Find the product" is just another way of saying "multiply." The product is the answer you get when you multiply two or more numbers together. Whatever the numbers look like (whole numbers, fractions, decimals, or mixed numbers), the instruction never changes:
product = factor × factor.
Every "find the product" problem works the same way. The only thing that changes is what kind of numbers you are multiplying. Here is how to handle each type.
Whole numbers multiply in any order
Multiply the numbers together. Order does not matter, so you can start with whichever pair is easiest.
When there are more than two numbers, multiply any two first, then multiply that result by the next. The final answer is the same no matter which pair you start with.
Fractions multiply straight across
Multiply the top numbers (numerators) and the bottom numbers (denominators) separately, then simplify at the end.
If one of the numbers is a whole number, put it over one first.
Multiplying fractions does not need a common denominator. That step is only for adding and subtracting. If you need one, our LCD calculator handles it.
Decimals: multiply, then place the point
Multiply the numbers as if the decimal points were not there. Then count the total decimal places in the two original numbers and move the decimal point that many places to the left in your answer.
Mixed numbers: convert first
Convert each mixed number to an improper fraction, then multiply straight across. Do not multiply the whole parts and fraction parts separately, because that does not give the right answer.
Word problems hide the word "product"
"Find the product" often hides inside everyday phrasing. Any question involving "each," "per," "rate," "area," or "total quantity of groups" is a product question. These all mean the same thing as multiply.
Three mistakes that cost points
Adding instead of multiplying. Product means multiply and sum means add. If you see "product" and write a plus sign, the answer will be wrong.
Misplacing the decimal. Count the decimal places in both factors before placing the point, or the answer lands an order of magnitude off.
Finding a common denominator for fraction multiplication. You never need one to multiply fractions. That step only applies to addition and subtraction.
Products of vectors and matrices
"Find the product" starts appearing with vectors and matrices in later algebra, and the definition extends. The dot product of two vectors is a single number, and the determinant of a matrix is built from products of entries. The underlying idea, multiply then combine, does not change.
Use our dot product calculator for vectors or the determinant calculator for matrices when the numbers get ugly.
The fastest way to spot a "find the product" question is the keyword itself, plus "each," "per," "rate," or "area." See them, and you multiply. For a deeper look at what "product" means across math, read what does product mean in math.
Common questions
It means multiply the numbers together. The product is the result of multiplication, the same way the sum is the result of addition. So "find the product of two numbers" is asking for product = factor × factor.
No. Multiply the numerators together and the denominators together, then simplify. Common denominators are only needed for adding and subtracting fractions, not for multiplying them.
Multiply the numbers as if there were no decimal points. Then count the total number of decimal places across both factors and place that many decimal places in the answer, counting from the right.
It is always zero. Multiplying any number by zero gives zero, no matter how large the other factor is.
Yes. Multiplication is commutative, so the order of the factors does not change the product. You can also regroup three or more factors in any way and get the same answer.
