“Queen of Science” status belongs to mathematics. It deals with numbers, shapes, and letters. Everywhere we go, every day, and practically always, we apply mathematical concepts.
In this post, we’ll talk about “what is an expression in math?” and the many types of expressions. For a better understanding, we will also learn the differences between an expression and an equation and the many types of expressions with examples.
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What is an expression in Math?
An expression in math refers to a sentence that has a minimum of two numbers or variables and at least one mathematical operation.
Let’s learn to write expressions. A number is 7 more than half of another number, and that other number is called x. In a mathematical expression, this sentence is represented as x/2 + 7. Difficult puzzles can be solved using mathematical expressions.
Let’s break down each element of an expression in detail.
A mathematical operation, such as subtraction, addition, multiplication, or division, is used to combine words into an expression. In a mathematical expression, the following terms are included:
- A constant: A fixed numerical value.
- A variable: A symbol without a fixed value.
- A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.
- A coefficient is a number that is multiplied by a variable in an expression.
Types of Expressions in Math
The three main categories of mathematical expressions are as follows. They can be categorized as algebraic expressions, fractional expressions, or arithmetic/numerical expressions depending on the terms they include. Let’s examine each of them in further detail using the information in the table below:
| Types of Mathematical Expressions | Definition of Expression | List of Mathematical Expressions | ||||
|---|---|---|---|---|---|---|
| Numerical Expression | Includes only numbers and mathematical operators | 90-13+1 | ||||
| Fractional Expression | Includes fractional numbers and mathematical operators | 16/7 - 5/6 | ||||
| Algebraic Expression | Includes numbers, variables, and mathematical operators | x+5y |
Now, algebraic expressions are further divided into monomials, binomials, trinomials, etc. They are also known as polynomials. Let’s examine the different categories of algebraic expressions in the following table:
|
Category |
Definition of Expression |
Examples |
|
Monomial |
An expression with a single term made up of exponential integers that are not negative. |
3x2 |
|
Binomial |
An expression created by adding or subtracting two monomials. |
3x2+2xy |
|
Trinomial |
An expression created by adding or subtracting three monomials. |
3x2+2xy+5yz |
|
Polynomial |
An expression created by one or more monomials. |
3x2+2xy+5yz+y+1 |
Expression vs Equation: Key differences
Expressions and equations are 2 separate concepts in math. Let’s begin to grasp how they differ from one another. A number, a variable, or a mixture of numbers and variables related by addition, subtraction, multiplication, and division are all examples of expressions.
However, an equation is the relationship of equality between two expressions. For a better understanding, have a look at the table below:
| Expression | Equation | |||||
|---|---|---|---|---|---|---|
| Expressions have only one-sided. | Equations have two-sided (left and right side) | |||||
| Expressions can be simplified to provide a number as the result. | Equations can be solved to check for equality or to find out the missing values. | |||||
| An expression is a group of terms with operators between them. | An equation is the combination of two expressions joined by the symbol "equal to" (=). | |||||
| Example: 2x-3 | Example: 2x-3=20 |
Read more >> What Is A Composite Number? Definitions & Examples
Math Expression Simplification
An answer can be created by simplifying expressions.
For instance, 2+3-1 can be reduced to 4 as an expression.
Both algebraic and arithmetic expressions can be simplified in two distinct ways. To simplify them, we apply the BODMAS rule (PEMDAS rule). Similar words can be added or deleted from algebraic formulas to simplify them. When a variable is raised to the same power, terms are said to be like. Therefore, by combining the coefficients of two or more similar terms, we can simply add or remove them.
For instance, the equation 6x+3x gives 9x, but 2ab-3b includes two dissimilar terms that cannot be added.
We use the PEMDAS rule for dealing with expressions that contain numerous words and operators (BODMAS rule).
Let’s simplify 16 – 6 + 4 × 3 as an example. Since there are no brackets or exponents, in this case, we shall first determine that 4 × 3 = 12. The formula is now 16-6+12.
The two operators available right now are addition and subtraction. We shall subtract 6 from 12 (= 6), as they are both operations of the same level, and subtraction is performed first from the left side. Now, our equation is 16+6, which equals 22, and 22 is the value of the shortened value of the expression 16 – 6 + 4 × 3.
When do kids learn about equations and expressions?
When students start learning about algebra in Year 4 (Key Stage 2) of primary school, they often come across expressions and equations for the first time. Even though before entering fourth grade, students will have probably studied mathematical expressions and equations, they will have probably only ever heard of them as “math problems.”
Students will continue to investigate the language of algebra as a way of resolving a range of issues as they go into Years 5 and 6. These issues include estimating the area or perimeter of forms or resolving equations with missing values.
By the end of Key Stage 2, students should have learned how to:
- apply basic formulas.
- create, define, and explain linear number sequences.
- algebraically express missing number issues.
- find the pairs of integers that the two unknowns in an equation equal.
- list all possible two-variable combinations.
FAQs
How can you tell whether two mathematical expressions have similar terms?
In an expression, like terms have the same variables increased to the same power. Examples of similar terms are 2x, -x, and 4x.
How can you write a math expression?
The addition, subtraction, multiplication, and division mathematical operations are used to create mathematical expressions. For instance, the phrase for “4 added to 2” in mathematics is 2+4.
What is a numerical expression?
The elements of a numerical expression are numbers and operators. The term “number expressions” also applies to numerical expressions. Number expressions include 9 – 7, 2 + 6 x 4 – 3, among others.
What number of terms are in an expression?
An expression may have any number of terms. A mathematical expression is a group of terms with operators separating them. Therefore, we can have an expression with a single term, two words, three terms, or n terms.
What distinguishes algebraic expression from mathematical expression?
Algebraic expressions often contain both numbers and variables, separated by operators, whereas mathematical or numerical expressions typically just contain numbers and operators.
Can you solve a mathematical expression?
We cannot solve expressions because they lack the “equal to” symbol (=). Using the provided mathematical operators, we could only simplify expressions and determine their reduced form.
Summary
Your children will have a basic understanding of “what is an expression in math” and be able to classify and deal with many kinds of algebraic expressions after they can recognize a coefficient, variable, algebraic operation, and constant.
From there, algebraic expressions are used by your children at various math levels. If you are planning to teach your kids about this essential topic, you can make your own collections of Expression worksheets using our worksheet maker tool.
