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, such as calculating area, total cost, or scaling 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. 

 

Multiple: 

The result of multiplying a number by a whole number is called a multiple. 

For example, the multiples of 3 are 3, 6, 9, 12, 15, and so on. 
 

Multiplier: 

The multiplier is the number that tells how many times the multiplicand is being multiplied.

For example, in the equation 5 × 3 = 15, 5 is the multiplicand, and 3 is the multiplier.

Multiplicand:

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:
 

Product of a Fraction:

A fraction is written in the form p/q, where p is the numerator and q is the denominator. 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, 2/3 × 4/5:
Multiply the numerators: 2 × 4 = 8. 
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:
8/15
 

Step 4: Simplify if needed:
We then simplify the fraction. If the denominator and numerator share a common factor, simplify the fraction. 

 

Product of Decimals:

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 → ignore decimals → 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.
 300 → place decimal → 3.00
So the final product is 3.00

In mathematics, four key properties apply to multiplication. 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) × c = a × (b × c)

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)

The product in math is used in various fields. Let's explore some examples: 
 

• Shopping and Budgeting: 
  
  When we buy multiple products or items, to calculate the total cost, we multiply the cost per item by the number of items. This helps us in budgeting and helps to maintain the limit.

• Construction and Architecture: 
  
  For calculating the materials needed for construction, builders use basic multiplication. For example, if a floor has 10 rows of tiles and each row has 15 tiles, the total number of tiles required is 10 × 15 = 150. It helps to calculate the cost and avoid the wastage of materials. 
   
• Cooking and Recipe Adjustment:
  
  When cooking, to adjust the ingredients based on the number of servings, we use multiplication. For example, if a recipe requires 2 cups of flour for 1 cake, and they want to make 3 cakes, they multiply 2 × 3 = 6 cups. This helps them get the correct proportion of ingredients.