Properties of Equality

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Questions and Answers

What is the Addition Property of Equality?

If you add the same number to each side of an equation, the two sides remain equal.

What is the Subtraction Property of Equality?

If you subtract the same number from each side of an equation, the two sides remain equal.

What is the Multiplication Property of Equality?

If you multiply each side of an equation by the same nonzero number, the two sides remain equal.

What is the Division Property of Equality?

If you divide each side of an equation by the same nonzero number, the two sides remain equal. Signup and view all the answers

What are inverse operations?

Operations (+, -, ×, ÷) that 'undo' each other. Signup and view all the answers

What property is being used in the equation X - 7 = 34?

Addition Property of Equality Signup and view all the answers

What property is being used in the equation Y + 24 = 63?

Subtraction Property of Equality Signup and view all the answers

What property is being used in the equation L × 8 = 104?

Division Property of Equality Signup and view all the answers

What property is being used in the equation W ÷ 4 = 13?

Multiplication Property of Equality Signup and view all the answers

What is a variable?

A symbol used to represent a quantity. Signup and view all the answers

What are algebraic expressions?

An expression that contains at least one variable. Signup and view all the answers

What are word phrases for addition?

plus, increased by, and, combined. Signup and view all the answers

What are word phrases for subtraction?

Difference of, minus, subtracting, negative, reduced by. Signup and view all the answers

What are word phrases for multiplication?

Product of, multiplied by, times. Signup and view all the answers

What are word phrases for division?

quotient, divided by. Signup and view all the answers

What is an equation?

A mathematical sentence that contains an equals sign. Signup and view all the answers

What is an open sentence?

An equation with one or more variables. Signup and view all the answers

What is a solution in the context of equations?

A value for a variable that makes an equation true. Signup and view all the answers

What property is being used in the equation x/2 - 5 = 25?

Addition Property of Equality Signup and view all the answers

What type of property of equality is Subtraction?

Subtraction. Signup and view all the answers

Study Notes

Addition Property of Equality: Adding the same number to both sides of an equation keeps the equation balanced.
Subtraction Property of Equality: Subtracting the same number from both sides of an equation maintains equality.
Multiplication Property of Equality: Multiplying both sides of an equation by the same nonzero number keeps them equal.
Division Property of Equality: Dividing both sides of an equation by the same nonzero number maintains their equality.

Inverse Operations

Inverse operations include addition, subtraction, multiplication, and division, and they "undo" each other effectively.

Key Questions when Solving Equations

Determine if the expression is an equation.
Identify if there is a variable present.
Assess if the variable is isolated or alone.

Examples of Properties in Use

X - 7 = 34: Utilizes the Addition Property of Equality; solution gives X = 41.
Y + 24 = 63: Applies the Subtraction Property of Equality; results in Y = 39.
L x 8 = 104: Demonstrates the Division Property of Equality; solution is L = 13.
W ÷ 4 = 13: Uses the Multiplication Property of Equality; solution yields W = 52.
X/2 - 5 = 25: Involves both the Multiplication and Addition Properties of Equality; gives X = 60.

Definitions in Algebra

Variable: A symbol that represents an unknown quantity.
Algebraic Expressions: Expressions that include at least one variable.

Word Phrases for Mathematical Operations

Addition: plus, increased by, and, combined.
Subtraction: difference of, minus, subtracting, negative, reduced by.
Division: quotient, divided by.
Multiplication: product of, multiplied by, times.

Mathematical Symbols

Addition Symbol: +
Subtraction Symbol: -
Multiplication Symbols: x, *, ab, (c)
Division Symbols: ÷, a/b

Types of Mathematical Sentences

Equation: A mathematical statement containing an equals sign.
Open Sentence: An equation that has one or more variables.
Solution: A value that, when substituted for a variable, makes the equation true.

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Description

Explore the fundamental properties of equality in mathematics, including Addition, Subtraction, and Multiplication. This quiz provides definitions and examples to help reinforce your understanding of these essential concepts in algebra. Test your knowledge and improve your skills!