Combining Like Terms Flashcards

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Questions and Answers

What is the simplified form of the expression 5x + 7 + 9x?

14x + 7

What is the simplified form of the expression 2x + 9 + 8 + 3x?

5x + 17

What is the simplified form of the expression 9 - 6 + 7x - 2x + 3?

5x + 6

What is the simplified form of the expression 3x - 7 + 9x?

12x - 7 Signup and view all the answers

What is the simplified form of the expression 4x - 8 + 10 - x?

3x + 2 Signup and view all the answers

What is the simplified form of the expression x + 5 + x - 2?

2x + 3 Signup and view all the answers

What is a numerical expression?

Contains only numbers and operations and does not have an equal sign Signup and view all the answers

What is an algebraic expression?

Contains variables, operations and numbers and does not have an equal sign Signup and view all the answers

What is a variable?

A letter or symbol that stands for an unknown number Signup and view all the answers

What are terms in an algebraic expression?

Part(s) of an algebraic expression or equation that are separated by operations Signup and view all the answers

What are like terms?

The terms that have the same variables Signup and view all the answers

What does combining like terms mean?

In order to simplify an expression, you must combine the like terms. Signup and view all the answers

What does it mean to simplify an expression?

To put an expression in its simplest form by combining like terms. Signup and view all the answers

What is the commutative property?

The property that says that two or more numbers can be added or multiplied in any order without changing the result. Signup and view all the answers

What is the associative property?

Changing the grouping of numbers will NOT change the value. Signup and view all the answers

What is '5 more than a number' expressed algebraically?

x + 5 Signup and view all the answers

What is 'the difference of a number and 5' expressed algebraically?

x - 5 Signup and view all the answers

What does '5 divided by a number' look like algebraically?

5 ÷ x Signup and view all the answers

How is '5 minus a number' expressed algebraically?

5 - x Signup and view all the answers

How is 'the sum of 5 and a number' represented?

5 + x Signup and view all the answers

What is 'the product of 5 and a number' expressed like?

5x Signup and view all the answers

What is 0.22 expressed as a fraction?

Signup and view all the answers

What is 10% expressed as a decimal?

0.1 Signup and view all the answers

What is 98.2% expressed as a decimal?

0.982 Signup and view all the answers

What is 69/100 as a percentage?

69% Signup and view all the answers

Study Notes

Combining Like Terms Concepts

Combining Like Terms: Process of simplifying expressions by adding or subtracting terms that have the same variables.
Like Terms: Terms that contain the same variables raised to the same power, and constants are also categorized as like terms.

Algebraic Expressions

Algebraic Expression: Comprises variables, numbers, and operations without an equal sign; often requires simplification.
Numerical Expression: Only consists of numbers and operations without variables or an equal sign.

Key Terms in Algebra

Variable: A symbol (commonly a letter) representing an unknown number.
Terms: Components of an expression separated by operations; include the sign preceding each term.

Simplification Techniques

Simplify: To express an algebraic expression in the simplest form by combining like terms.
Example Expressions:
- 5x + 7 + 9x simplifies to 14x + 7.
- 2x + 9 + 8 + 3x simplifies to 5x + 17.
- 9 - 6 + 7x - 2x + 3 simplifies to 5x + 6.

Mathematical Properties

Commutative Property: Addition or multiplication can be performed in any order without changing the result.
Associative Property: Changing the grouping of numbers during addition or multiplication does not alter the total.

Expressions with Numbers

5 more than a number: Expressed as x + 5.
The difference of a number and 5: Written as x - 5.
5 divided by a number: Represented as 5 ÷ x.
5 minus a number: Denoted as 5 - x.

Converting Numbers

Converting to Percent: For example, 10% is expressed as 0.10.
Decimal to Percent Conversion: 98.2 corresponds to 982%.
Fraction Representation: 69% can be written as 69/100.

General Notes

Understanding these concepts is essential for solving algebraic equations and simplifying expressions effectively.
Practice combining like terms and using properties of operations to enhance problem-solving skills in algebra.

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Description

Test your understanding of combining like terms with these flashcards. Each card presents an expression and its simplified form, helping you sharpen your algebra skills. Ideal for students learning basic algebra concepts.