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Expression – Definition, Examples | EDU.COM

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Expression – Definition, Examples | EDU.COMEDU.COMResourcesBlogGuidePodcastPlanBackHomesvg]:size-3.5">Math Glossarysvg]:size-3.5">ExpressionmathExpression – Definition, ExamplesTable of ContentsDefinition of Mathematical Expressions

An expression in mathematics is a sentence that contains at least two numbers or variables and at least one mathematical operation (addition, subtraction, multiplication, or division). The basic structure follows the pattern: Number/variable, Math Operator, Number/variable. Examples of expressions include: 5+35 + 35+3, x−7x - 7x−7, and 4×y4 \times y4×y. It's important to note that expressions do not contain equality or inequality symbols. An expression is composed of several parts: constants (fixed numerical values), variables (symbols representing unknown values), terms (constants, variables, or constants multiplied by variables), and operators (mathematical symbols indicating operations).

There are different types of mathematical expressions. Numerical expressions consist solely of numbers and arithmetic operators without any variables or equality symbols (e.g., 65+9−465 + 9 - 465+9−4). Algebraic expressions include unknown variables along with numbers and arithmetic operators (e.g., 5z5z5z or 3x2+53x^2 + 53x2+5). Algebraic expressions are further classified based on the number of terms they contain: monomials have one term (4x4x4x), binomials have two unlike terms (2xy+x2xy + x2xy+x), trinomials have three unlike terms (3t2−4t+93t^2 - 4t + 93t2−4t+9), and polynomials have two or more terms, which includes binomials and trinomials.

Examples of Mathematical Expressions Example 1: Writing Word Phrases as Expressions Problem:

Write each word phrase as an expression:

The sum of 10 and 14 3 more than a number 7 Two times 11, increased by 1 19 less than the product of 15 and 4 The quotient of 33 and 3 Step-by-step solution:

First, identify the key mathematical terms in each phrase:

"Sum" indicates addition "More than" suggests addition "Times" and "increased by" indicate multiplication followed by addition "Less than" and "product" involve multiplication and subtraction "Quotient" refers to division

Next, translate each phrase into the corresponding mathematical operation:

The sum of 10 and 14: 10+1410 + 1410+14 3 more than a number 7: 7+37 + 37+3 Two times 11, increased by 1: 2×11+12 \times 11 + 12×11+1 19 less than the product of 15 and 4: 15×4−1915 \times 4 - 1915×4−19 The quotient of 33 and 3: 33÷333 \div 333÷3 Example 2: Word Problem with Expressions Problem:

A book has 250 pages. Ron has 62 pages left to read. Write an expression to find the number of pages he has read.

Step-by-step solution:

First, identify what we know:

Total number of pages in the book = 250 Pages Ron still needs to read = 62

Next, determine what we're looking for:

We want to know how many pages Ron has already read

Then, think about the relationship:

The pages Ron has read plus the pages left to read must equal the total pages So: Pages read + Pages left = Total pages Rearranging: Pages read = Total pages - Pages left

Finally, write the expression:

Pages Ron has read = 250−62250 - 62250−62 Example 3: Solving Complex Expressions Using PEDMAS Problem:

Evaluate the expression (15÷3×4−7)+(19−42)(15 \div 3 \times 4 - 7) + (19 - 4^2)(15÷3×4−7)+(19−42)

Step-by-step solution:

First, recall PEDMAS: Parentheses, Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)

Next, evaluate expressions inside the first parentheses (15÷3×4−7)(15 \div 3 \times 4 - 7)(15÷3×4−7):

Division first: 15÷3=515 \div 3 = 515÷3=5 Now we have: (5×4−7)(5 \times 4 - 7)(5×4−7) Multiplication: 5×4=205 \times 4 = 205×4=20 Subtraction: 20−7=1320 - 7 = 1320−7=13 First parentheses result: 131313

Then, evaluate expressions inside the second parentheses (19−42)(19 - 4^2)(19−42):

Exponent first: 42=164^2 = 1642=16 Subtraction: 19−16=319 - 16 = 319−16=3 Second parentheses result: 333

Finally, add the results from both parentheses:

13+3=1613 + 3 = 1613+3=16

Therefore, (15÷3×4−7)+(19−42)=16(15 \div 3 \times 4 - 7) + (19 - 4^2) = 16(15÷3×4−7)+(19−42)=16

Comments(8)PProgrammerLeoNovember 6, 2025I've used this expression definition with my students. It's clear and really helped them grasp the concept. Great resource!

AAnalystBobNovember 4, 2025This glossary def of 'expression' is great! I've used it to help my students grasp the concept. Clear examples make it super easy to understand.

NNatureLover92September 17, 2025I’ve used the clear definition and examples here to help my kids understand expressions better. The step-by-step problem-solving tips are a lifesaver for explaining tricky concepts!

MCMs. CarterSeptember 10, 2025I’ve been using this page to help my kids understand algebra better. The clear examples and step-by-step explanation of expressions really made it click for them. Great resource!

MCMs. CarterAugust 27, 2025This glossary page was super helpful! I used the clear examples to explain expressions to my 6th grader, and it really clicked for them. Love how it breaks down the difference between numerical and algebraic expressions!

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