# Expression – Definition with Examples

» Expression – Definition with Examples

## What is an Expression?

An expression is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is:

Expression is (Number/Variable, Math Operator, Number/Variable)

Examples of Expressions:

Non Examples of Expressions:

Example 1:         $\text{a}$

Example 2:          $4$

Example 3:          $7.89$

In all the given expressions, a math operator is used between the two numbers.

## Parts of an Expression

Constant is a fixed numerical value.

Example: $7$, $45$, $4^{\frac{1}{3}}$, $−18$, $\sqrt{5}$, $7 + \sqrt{11}$

Variables do not take fixed values. Values are assigned according to the requirement.

Example: a, p, z

Terms can be constants, variables, or constants multiplied by variable/(s). Each term in an expression is separated by ‘+’ sign or ‘−’ sign

Example: In 5a + 2b – 7, the terms are: 5a, 2b, and 7.

Operators are addition (+), subtraction (−), multiplication (×), and division (÷) used to combine the terms of expression.

## Types of Expression

Numerical Expression

The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols.

Example:

$65 + 9 – 4$

$\frac{25}{4}+\frac{36}{5}$

$42 \div 7 \times 4 – 9 + 7$

$14.5 + 9$

Algebraic Expression

The expression consists of unknown variables, numbers, and arithmetic operators.

$5\text{z}$

$3x^2 + 5$

$\frac{2}{5}\text{a} – \frac{7}{11}\text{b}+4.5\text{c}$

$0.2 \text{p}^3\text{q}^2 + \frac{2}{5}\text{p}^2\text{q}$

## Expression vs Equation

A math expression is different from a math equation. An equation will always use an equal (=) operator between two math expressions.

For example,

Where are expressions used?

Expressions help us solve a problem. Math expressions are formed using the words of a problem.

Let’s consider the following problem as an example:

Let’s consider a word problem.

1. Tom has to fill a box with oranges and apples. The number of apples should be 5 more than oranges. Tom picks 3 oranges each time and repeats it 5 times. Count the total number of oranges and apples.

To solve this, formulate the math expressions as follows:

Number of oranges = $3\times 5$

Number of oranges = $15$

Number of apples = $\text{Number of oranges} + 5$

Number of apples = $15 + 5$

Number of apples = $20$

Total number of fruits = Number of oranges + Number of apples

Third math expression will be:

Total number of fruits = $15 + 20$  (Substituting the value of number of oranges and apples) $= 35$

2. A class of students are going on a trip. Each student has to pay an individual fee of \$8 and a group fee of \$30. Write an algebraic expression for the total cost of the trip. Find the total cost of the trip if there are 56 students going on the trip.

Let n represent the number of students.

Algebraic expression will be:

\$8n + \$30

To find the total cost of the trip, when n = 56.

\$8n + \$30

\$8(56) + \$30         (Substituting n with 56)

\$448 + \$30

\$478 ## PEDMAS PEDMAS is an acronym where P stands for parenthesis, E for exponents, D for division, M for multiplication, A for addition, and S for subtraction. The order of the letters indicate the order in which the operation must be performed. The operations of multiplication and division have the same level of priority. Always perform the operation that appears first from left to right. Similarly, addition and subtraction have the same level of priority. Here too, perform the one that appears first from left to right. Example:$(15\div 3\times 4 − 7) + (19 − 4^2)= (5\times 4 − 7) + (19 − 16)= (20 − 7) + 3= 13 + 3= 16$Application: The knowledge of applying math operations on numbers is the first step towards building basic arithmetic reasoning and logic in children. The formulation of math expressions using the respective skill lays a strong foundation to learn algebra and translate real-life problems in suitable mathematical models. ## Solved Examples on Expression: Example 1: Write whether each is an expression or an equation. Solution: Example 2: Write each word phrase as an expression. 1. The sum of 10 and 14 2. 3 more than a number 7 3. Two times 11, increased by 1 4. 19 less than the product of 15 and 4 5. The quotient of 33 and 3 Solution: 1.$10 + 14$2.$7 + 3$3.$2\times 11 + 1$4.$15\times 4 – 19$5.$33\div 3$Example 3: Classify the following expression as arithmetic or algebraic. 1.$4\text{a} – 7\text{b}$2.$23 + 42 – 6$3.$\frac{7}{15}-\frac{9}{11}$4.$2 – \frac{5\text{x}}{9\text{y}}$5.$22 – 5 + 8$6.$7\text{y} + 19\text{x} – 4\text{z}$Solution: Example 4: A book has 250 pages. Ron has 62 pages left to read. Write an expression to find the number of pages he has read. Solution:$250 – 62$## Practice Problem ### 1Which of these is an expression?$6 + 8 = 140 – 16 = –16\frac{4}{7}+ \frac{4}{7}-\frac{1}{7}5\text{x}-7\text{y}=15$CorrectIncorrect Correct answer is:$\frac{4}{7}+ \frac{4}{7}-\frac{1}{7}$As it has numbers (fraction) and mathematical operators, other options are equations as it has equal (=) operator between two math expressions ### 2Which of these is algebraic expressions?$3\text{a}+7\text{b}-6\text{c}=5\text{x}9-5\text{w}\frac{1}{2}+\frac{3}{4}44 + 55$CorrectIncorrect Correct answer is:$9-5\text{w}$It contains variables, numbers, and mathematical operator.Option (a) is an equation, option (c) and option (d) are arithmetic expressions not algebraic as no variables are involved. ### 3Thomas earns \$$9.75 an hour as a librarian. Which of these expressions shows how much he earns in 40 hours? \$$(9.75 + 40)$
\$$(40 – 9.75) \$$(9.75\times 40)$\$$(9.75 – 40) CorrectIncorrect Correct answer is: \$$(9.75\times 40)$
Amount earned in an hour = \$$9.75 Amount earned in 40 hours = \$$(9.75\times 40)\$

An expression is a set of numbers or variables combined using the operations +,  –, × or ÷.

Arithmetic expression that contains only numbers and mathematical operators and algebraic expression that contains variables, numbers and mathematical operators.

No, we cannot solve a math expression as it does not have an ‘equal to’ sign ( = ) but we can simplify expressions.

Mathematical expressions have only numbers and operators, while algebraic expressions have both numbers and variables in terms, separated by operators in between.

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