Last updated on July 6th, 2025
In mathematics, there are four basic arithmetic operations such as addition, subtraction, multiplication, and division. The process of finding the result when numbers are multiplied. To calculate the total cost, area, and scaling values, we use multiplication. In this article, we will learn about the product in math.
In mathematics, the product is the result of multiplying two or more numbers together. The numbers being multiplied are called factors, and the operation used is multiplication (×).
Products are used in real-life situations like calculating area, total cost, or scaling up quantities. Multiplication follows properties such as commutative, associative, and distributive, which make it the fundamental operation in arithmetic and algebra.
Multiplication involves different parts and each has a unique function. Let us discuss the parts in detail.
The result of multiplying a number by any whole number is the multiple.
For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on.
The multiplier is the number that tells how many times the multiplicand is being multiplied.
For example, in the equation 5 × 3 = 15, 3 is the multiplier.
The number that is multiplied is the multiplicand.
For example, in 5 × 3 = 15, 5 is the multiplicand because it is the number being multiplied by 3.
We learned the parts of multiplication. So, now let us learn what is the product of a fraction and the product of a decimal:
A fraction is a type of number; it is written in the form pq. The product of a fraction is the result of multiplying two or more fractions. To multiply fractions, follow these steps:
Step 1: Multiply the Numerators:
The numerators are the part of fractions; it is written above the fraction bar. To multiply a fraction, we first multiply the numerators.
For example,
When 23 × 45, we first multiply the numerators,
Here, the numerators are 2 and 4,
The product of the numerators is 2 × 4 = 8
Step 2: Multiply the Denominators:
Next, we have to multiply the bottom numbers (denominators) of the given fractions.
In 23 × 45, the denominators are 3 and 5
The product of the denominators is 3 × 5 = 15
Step 3: The Result:
After multiplying, we will get the result:
815
Step 4: Simplify if needed:
We then simplify the fraction. If the denominator and numerator share a common factor, simplify the fraction.
The product of the decimals is the result of multiplying two or more decimals. To multiply decimals, we first multiply the numbers and add, then place the decimal points. Follow these steps to multiply decimals:
Step 1: Ignore the Decimals and Multiply the Whole Number
For multiplying two decimal numbers, we should focus on multiplying the numbers, ignoring the decimal points. The numbers should be considered as natural numbers, for example, 2.5 × 1.2 = 25 × 12 = 300
Step 2: Count the Total Decimal Places:
After calculating the product of the numbers, we have to count the decimal places in both numbers. Here, the decimal points are:
2.5 has one decimal place
1.2 has one decimal place
Total decimal places = 2
Step 3: Place the Decimal in the Product:
After counting the decimal points, we place the decimal in the product so that it has the same number of decimal places as of the multipliers starting from right.
Here,
The total number of decimal places is 2, adding the decimal points to the 300. So the final product is 3.00
In mathematics, there are four properties that are applicable to mathematical operations. All these properties are applicable to the product; let's learn them in detail.
Commutative Property:
In this property, the order of the numbers does not matter. The product remains the same no matter what the order of multiplier and multiplicand is. The property in an equation is represented as: a × b = b × a.
Associative Property:
If three or more numbers are multiplied together, the product remains the same even if the order of those numbers changes. The property in an equation is represented as: (a × b) x c = (b × c) x a = (a × c) x b.
Multiplicative Identity Property:
According to this property, the product of multiplying any number by 1 results in the number itself. The property in an equation is represented as: (a × 1) = a
Distributive Property:
The sum of any two numbers when multiplied by a third number can be expressed as the sum of each one of the addends multiplied by the third number.
The property is represented as: a × (b + c) = (a ×b) + (a × c)
When multiplying numbers, students tend to make mistakes and they even repeat the same errors. Let us see some common mistakes and how to avoid them, in product in math:
The product in math is used in various fields. Let us explore how the product in math is used in different areas:
What is the product of 8 and 6?
48
8×6=48
Multiplication means repeated addition. 8 × 6 is the same as adding 8 six times (8 + 8 + 8 + 8 + 8 + 8 = 48).
What is the product of 15 and 0?
0
15×0=0
Any number multiplied by 0 is always 0.
Find the product of (-7) x 4
-28
(−5) × (−9) = 45
Two negative numbers multiplied together results in a positive number.
What is the product of ⅔ x ⅘?
8/15
2/3 × 4/5 = 2 * 4 / 3 * 5 = 815
Multiply the numerators and multiply the denominators.
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.