Expressions in Math

A mathematical expression is a statement that contains at least two numbers, variables, or both, connected by an arithmetic operation. Two commonly used types of expressions are numerical and algebraic. 
For example, if a number is 6 more than twice another number, we write it as 2x + 6. The expressions in math are often applied to solve puzzles and find unknown numbers.
 

Expressions and equations are two interrelated mathematical concepts that are often confused by students. Understanding their key differences will help you identify them easily. Let’s look at a few major differences between them.

An expression consists of different components. It is important to understand the basic terms of expression. Let’s look at a few of them:

Variable

A variable in a mathematical expression can have any value. For example 4x+6y=z, here x, y, z are the variables.

Constant

A constant is a fixed value in an expression. It can be any numerical value. For example: 5, -3, 0, 2/7

Coefficient

The number in an equation that multiplies a variable is called a coefficient. It could be whole, fractional, positive, negative, or even irrational.
For example: 5 in 5x, and -3 in -3y^2.
 

There are different types of expressions in mathematics. Let’s learn about each type with examples:

Numerical Expression

A numerical expression is a mathematical statement made up of only numerical values connected by arithmetic operations. We can obtain its value by simplifying the expression. 
For example: 

• 12 ÷ 3 + 5 simplifies to 9

•  8 + 4 –3 simplifies to 9

Algebraic Expression

An algebraic expression includes variables and numbers combined using arithmetic operations.
For example: 

• 3abc (monomial)

• 5x + 3 (binomial)

• 6x2 –3y + 9 (polynomial)

Fractional Expression

An expression is considered fractional if it contains only fractional terms.

For example: 

• 2/x + 8/15

• 2a²/(b – 4)

Radical Expression

A radical expression includes roots of different degrees, such as square roots, cube roots, or higher-order roots.
For example: 

• 2√(5) – 6

• √(3y²) + ⅔
   

To write expressions in math, we need to understand the steps given below:

Step 1: Understand the given sentence and look for keywords associated with arithmetic operations.

Step 2: Substitute the identified keywords with the correct mathematical symbols (e.g., +, –, ×, ÷). 
Replace:

• “and” with “+”
• “from” with “–”
• “of” with “×”
• “By” with “÷”

Step 3: We need to apply the order of operations when the expression includes more than one operation. 

Step 4: To get the final result, simplify the obtained answer.
For example: Write an expression for: The sum of 10 and the product of -3 and y:
 → 10 + (−3 × y) 
 Simplified: 10 − 3y.
 

Understanding expressions in math not only helps students solve math problems but also equips them to deal with various real-life situations. Let’s look at how they can be applied in real life.

• Expressions in math can be applied to find the final price of a product after a discount. For example, the final price of an item with an original price of x dollars after applying a 10% discount is given by: Final price = x - 0.1x = 0.9x.

• We also use the expressions to solve for the distance covered by a vehicle. The distance covered by a car moving at 60 km/h for t hours can be expressed as Distance = Speed × Time = 60 × t.

• Similarly, we can determine the area of a rectangular room using expressions.  For example, the area of a room with length l and width w can be expressed as: A = l × w.