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# Mathematical Expression

An algebraic expression is a mathematical phrase that can contain ordinary numbers, variables and operators. When we are working in algebra, we need to change words and phrases into some form of mathematical expression. When we hear "the subtraction of 35 from x" we know it refers to subtraction and we think x - 35.

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## What is a Mathematical Expression?

In mathematics, expression is a finite group of algebraic terms and mathematical symbols combined with no equal or in equality sign. In algebra and in other branches of mathematics, letters are used to represent numbers with unknown or unassigned values.

### Writing Mathematical Expressions

Writing expressions for single statements is as follows:

 Statement Mathematical Expressions 12 divided by a number m $\frac{12}{m}$ Product of 20 and a number x 20 * x A number x decreased by 28 x - 28 Difference of a number y and 23 y - 23

## Mathematical Expressions and Equations

An expression shows a mathematical relationship. To evaluate an expression, substitute values for the variables. The values changes if we substitute different numbers in for the variables. Whereas, an equation equates two expressions.  Equations, unlike expressions, can be solved.

### Solved Examples

Question 1: Find the value of f(0), f(1), f(2) for the expression f(x) = 10x - 12.
Solution:
Given f(x) = 10x - 12

f(0) = 10 * 0 - 12 = 0 - 12 = -12
f(1) = 10 * 1 - 12 = 10 - 12 = -2
f(2) = 10 * 2 - 12 = 20 - 12 = 8

Question 2: Solve for x, 10x - 12 = 25.
Solution:
Given 10x - 12 = 25
Isolate x by adding 12 to each side
10x - 12 + 12 = 25 + 12
10x = 37

Divide each side by 10
x = $\frac{37}{10}$ = 3.7

## Evaluating Mathematical Expressions

Given below are the steps to evaluate mathematical expressions:

Steps for Simplifying the Math Expressions :

Step 1: Group the terms containing the matching variable together in algebra expressions.

Step 2: Perform the operation in the parentheses for the variable and other.

Step 3: Rewrite the expressions and simplify the mathematical expressions.

Step 4: To check the equation, if there is able to simplify the expression, then repeat the step 1 to 4.

Basic Natural Law for Mathematical Expression:

In elementary algebra, we list the basic rules and properties of pre-algebra.

a + b = b + a

Commutative Property of Multiplication

a * b = b * a

(a + b) + c = a + (b + c)

Associative Property of Multiplication

(a * b) * c = a * (b * c)

Distributive Properties of Addition over Multiplication.

• a * (b + c) = a * b + a * c
• (a + b) * c = a * c + b * c

### Solved Example

Question: Solve 10x(2x + x2)
Solution:

Given 10x(2x + x2)

A(B + C) = AB + AC

Step 1: Determine what terms represent A, B and C in the given equation.

A represents 10x.

B represents 2x.

C represents x2

Step 2: Make the multiplication operation.

AB = 10x(2x) = 20x2

AC = 10x(x2) = 10x3

Step 3: Rewrite the problem.

10x(2x + x2) = 20x2 + 10x3

## Mathematical Expression Examples

Given below are some of the examples on mathematical expression.

### Solved Examples

Question 1: Find the value of y in 11y - 10 = 12 + 13y
Solution:
Given 11y - 10 = 12 + 13y

Combine the like terms
11y - 13y = 12 + 10
-3y = 22

Divide each side by -3
y = $\frac{-22}{3}$.

Question 2: Leesa's age is 5 year more than her sister. The sum of their ages is 45. Find the age of Lessa.
Solution:
Let the age of Lessa's sister = x years
Then, age of Lessa = x + 5 (Given)

Sum of their age = 45
Age of Leesa's sister + age of Leesa = 45
x + x + 5 = 45
2x + 5 = 45
2x = 45 - 5 = 40
x = $\frac{40}{2}$ = 20
Therefore, Leesa is of 20 + 5 = 25.

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