Number Sense - Expression
- What is an Expression?
- Some Examples of Mathematical Expressions
- Parts of an Expression
- Translating Situations to Expressions
- Types of Algebraic Expressions
- How Is an Expression Different from an Equation?
- How to Simplify Expressions?
- Solved Examples
- Practice problems
- Frequently Asked Questions
What is an Expression?
An expression is a math statement with at least two numbers or variables and a minimum of one mathematical operation. Addition `(+)`, subtraction `(-)`, multiplication `(×)`, and division `(÷)` are some mathematical operations that can be used in an expression.
Some Examples of Mathematical Expressions
Expression | Description |
`8a+19` | Operation: `+` Variable: `a` Numbers: `8, 19` |
`11x^2+10x+100` | Operation: `+` Variable: `x` Numbers: `11, 10, 100` |
`8y ÷ 19` | Operation: `÷` Variable: `y` Numbers: `8, 19` |
`6 × 2` | Operation: `×` Variables: None Numbers: `6, 2` |
Given below are some statements which are not expressions:
- `40`
- `a`
- `5.002`
Parts of an Expression
The following are the parts of an expression:
- Constant: In an expression, a value that never changes is called a constant.
For example: `1, 65.1, 100`
- Variables: A variable is a value in an expression that does not have a fixed value.
For example: `x, y, p`
- Terms: Terms can be anything be it a constant, a variable, a product of constant(s) and variable(s), or a product of variables. Terms are separated by mathematical operations in an expression.
For example: In `3x+9y, 3x` and `9y` are the terms of the expression.
- Operators: There are various math operations like `+, -, ÷, x,` etc. that can be used used in an expression.
Translating Situations to Expressions
There are many situations we come across daily. Let us look at one of them and how we can translate the situation into a math expression.
Ronald has a son who is `x` years old and Ronald is twice as old as his son.
This means Ronald is `2x` years old.
Next, Ronald asks to calculate the sum of his and his son’s age which would be equal to `2x + x` years.
Types of Algebraic Expressions
Some algebraic expressions have a single term. Some have two, three or more terms. Based on the number of terms in an algebraic expression, they are classified as follows:
- Monomial Expressions contain only one term. For example: `3x`
- Binomial Expressions contain two terms. For example: `4y + 9`
- Trinomial Expressions contain three terms. For example: `51x + 11y + 10`
- Polynomial Expressions contain two or more terms. For example: `9x + 6y + 8z + 1`
How Is an Expression Different from an Equation?
Expression | Equation |
Expressions are statements in which variables, numbers and operators are only on one side. | Equations are statements that have equals to sign. The variables, numbers and operators are there on both sides of the equals to sign. |
Result of solving an expression gives us a numerical value. | When solving an equation a value is obtained to verify both sides of an equation. |
Example: `4x - 9` | Example: `6x + 2 = 26` |
How to Simplify Expressions?
Expressions are simplified using PEMDAS. PEMDAS indicates the order in which the operations must be performed to simplify an expression. In this approach, Parentheses come first, next is Exponents, followed by Multiplication and Division, and finally Addition and Subtraction. Multiplication and division have the same priority and are preferably performed from left to right. Similarly, addition and subtraction have the same priority. Priority tells us which operation to perform first.
Example:
\((16 \div 4 + 8 + 6) \times 3^2\)
\((4 + 8 + 6) \times 3^2\)
\((12 + 6) \times 3^2\)
\((18) \times 3^2\)
\(18 \times 9\)
\(162\)
Solved Examples
Example `1`: Write the terms in the expression: `5x + 90yz + 9m + 11`
Solution: The terms of the expression are `5x, 90yz, 9m,` and `11`.
Example `2`: Harry has `56` apples in a basket, he has already eaten `21` apples. Write an expression to find the number of apples left in the basket.
Solution: `56 - 21`
Example `3`: Write an expression for this statement: ‘`4 times 5` is decreased by `6`’
Solution: `4 \times 5 - 6`
Practice Problems
Q`1`. Sally earns `$7.50` per hour for a job. Write an expression to show how much she earns in `36` hours.
- \(7.50 \times 36\)
- \(36 \div 7.50\)
- \(7.50 + 36\)
- \(36 - 7.50\)
Answer: a
Q`2`. Translate the following statement into an expression: “Six added to twice of `30` ”
- \(2 + 30 \times 6\)
- \(6 \times 2 + 30\)
- \(2 + 30 \times 6\)
- \(6 + 2 \times 30\)
Answer: d
Q`3`. What is the name given to an expression that has only two terms?
- Monomial
- Binomial
- Trinomial
- Polynomial
Answer: b
Frequently Asked Questions
Q`1`: What is an expression in math?
Answer: In mathematics, an expression is a combination of numbers, variables, and operations (such as addition, subtraction, multiplication, and division) that represents a mathematical phrase or statement. Expressions do not have an equal sign and can be simplified or evaluated.
Q`2`: What are the types of expressions?
Answer: There are various types of expressions in mathematics, including:
- Numeric Expression: Consists of numbers and operations (e.g., \(3 + 5\)).
- Algebraic Expression: Involves variables, numbers, and operations, representing algebraic relationships (e.g., \(3a - 2b\)).
- Arithmetic Expression: Involves basic arithmetic operations like addition, subtraction, multiplication, and division (e.g., \(2 \times (4 + 7)\)).
Q`3`: Can we solve a math expression?
Answer: No, we can't solve a math expression because it doesn't have an 'equal to' sign, but we can simplify it.
Q`4`: What is the difference between an arithmetic expression and an algebraic expression?
Answer: The key difference lies in the inclusion of variables.
Arithmetic Expression: Involves basic arithmetic operations with numbers but does not include variables (e.g., \(3 + 2 \times 7\)).
Algebraic Expression: Contains variables, numbers, and operations, allowing for the representation of relationships and patterns in algebra (e.g., \(2x - 5\)).