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Quizzes > High School Quizzes > Mathematics

Properties of Equality Practice Quiz

Sharpen Your Skills with Engaging Exercises

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Colorful paper art promoting Equality Rules Quiz for high school algebra review and exam prep.

Which property of equality states that a number is equal to itself?
Symmetric Property
Transitive Property
Addition Property
Reflexive Property
The reflexive property of equality tells us that any quantity is equal to itself, which is a fundamental concept in algebra. This property is foundational in understanding and establishing equations.
What does the Addition Property of Equality state?
The sum of both sides of an equation is always zero.
Adding different numbers to each side maintains the equality.
You can only add positive numbers to both sides of an equation.
Adding the same number to both sides of an equation does not affect the equality.
The Addition Property of Equality asserts that when the same number is added to both sides of an equation, the equality is maintained. This rule is essential when solving algebraic equations.
If a = b, which property allows you to state that b = a?
Reflexive Property
Symmetric Property
Transitive Property
Substitution Property
The symmetric property of equality states that if one quantity equals another, then the reverse is also true. This showcases the inherent balance in any equation.
Which property justifies subtracting the same number from both sides of an equation?
Distributive Property
Subtraction Property of Equality
Commutative Property
Multiplicative Property of Equality
The Subtraction Property of Equality allows you to subtract the same amount from both sides of an equation without disturbing the balance. This property is vital in the process of isolating variables.
In the equation 3 + x = 7, which operation should be performed to solve for x?
Divide both sides by x
Subtract 3 from both sides
Multiply both sides by 3
Add 3 to both sides
Subtracting 3 from both sides of the equation isolates the variable x, yielding x = 4. This operation demonstrates the proper use of the Subtraction Property of Equality.
Solve for x using the Addition Property of Equality: x - 5 = 10.
x = 15
x = -5
x = 10
x = 5
By adding 5 to both sides of the equation, the variable x is isolated, resulting in x = 15. This follows directly from the Addition Property of Equality.
Which property of equality allows you to infer that if a = b and b = c, then a = c?
Symmetric Property
Reflexive Property
Addition Property
Transitive Property
The Transitive Property of Equality states that if one value equals a second value and that second value equals a third, then the first value equals the third. This property is essential in linking equations together.
Solve for y using the Subtraction Property of Equality: y + 8 = 12.
y = 4
y = 12
y = -4
y = 8
Subtracting 8 from both sides of the equation isolates y, resulting in y = 4. This process is a direct application of the Subtraction Property of Equality.
Which property allows you to multiply both sides of an equation by the same nonzero number without affecting the equality?
Multiplicative Property of Equality
Division Property of Equality
Subtraction Property of Equality
Addition Property of Equality
The Multiplicative Property of Equality ensures that multiplying both sides of an equation by the same nonzero number does not affect the equality. This property is frequently used to eliminate fractions.
Solve for x in the equation: 2x = 16.
x = 8
x = 2
x = 16
x = 32
Dividing both sides of the equation by 2 isolates x, which gives x = 8. This uses the Division Property of Equality to maintain balance in the equation.
In the equation 3x + 5 = 20, which step correctly uses the properties of equality to isolate the variable?
Divide both sides by 3
Multiply both sides by 5
Subtract 5 from both sides
Add 5 to both sides
Subtracting 5 from both sides is the correct method to start isolating x. This approach directly applies the Addition/Subtraction Property of Equality.
Solve for z in the equation: z/2 = 9.
z = 4.5
z = 9
z = 18
z = 2
Multiplying both sides by 2, the reciprocal of 1/2, isolates z and gives z = 18. This demonstrates the Multiplicative Property of Equality in action.
Why is it valid to perform the same operation on both sides of an equation?
It simplifies only the left side of the equation.
It rearranges the numbers but alters the value.
It preserves the balance and maintains the equality.
It only changes one side of the equation.
Performing the same operation on both sides of an equation ensures that the equality remains balanced. This principle is the basis for many steps in solving equations.
Determine the correct method to solve 5 + x = 12.
Divide both sides by 5 to find x = 2.4.
Subtract x from both sides to find x = 7.
Subtract 5 from both sides to find x = 7.
Add 5 to both sides to find x = 17.
Subtracting 5 from both sides isolates the variable x, resulting in x = 7. This is a simple application of the Subtraction Property of Equality.
Solve for a in the equation: 4a - 7 = 9.
a = 4
a = -4
a = 16
a = 2
Adding 7 to both sides gives 4a = 16, and dividing both sides by 4 yields a = 4. This step-by-step process follows the properties of equality perfectly.
Solve for x: 3(x - 2) = 2(x + 4).
x = 8
x = 14
x = 10
x = 12
Expanding both sides gives 3x - 6 = 2x + 8. Subtracting 2x from both sides results in x - 6 = 8, and adding 6 to both sides yields x = 14. This exercise combines distribution with the properties of equality.
Solve for y: 2(3y - 4) = 4(y + 1).
y = 2
y = 4
y = 6
y = 8
After expanding, the equation becomes 6y - 8 = 4y + 4. Subtracting 4y and then adding 8 to both sides leads to 2y = 12, so y = 6. This problem tests moderate algebraic manipulation.
Solve for x in the equation: 4(x/2 - 3) + 5 = x.
x = 3
x = 5
x = 7
x = 10
First, distribute the 4 to obtain 2x - 12, then add 5 to get 2x - 7 = x. Subtracting x from both sides results in x - 7 = 0, so x = 7. This problem requires careful application of both distribution and the properties of equality.
Solve for x: 5(x - 2) + 2 = 3(x + 4) - 1.
x = 5
x = 19/2
x = 7
x = 10
Begin by expanding both sides: 5x - 10 + 2 becomes 5x - 8, and 3x + 12 - 1 becomes 3x + 11. Setting these equal gives 5x - 8 = 3x + 11; subtracting 3x from both sides leads to 2x = 19, so x = 19/2. This problem integrates distribution with fundamental equality properties.
Which of the following best explains the error if, when solving 2x + 4 = 10, one divides only the term 2x by 2 instead of every term?
It violates the Division Property of Equality, which requires dividing every term equally.
It is acceptable as long as the constant is eventually subtracted.
It uses the Distributive Property incorrectly, which has no effect on solving the equation.
It correctly applies the Division Property since only the variable term is divided.
Dividing only a part of an equation disrupts its balance, violating the Division Property of Equality. Every term must be divided by the same nonzero number to maintain the equation's integrity.
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Study Outcomes

  1. Analyze reflexive, symmetric, and transitive properties in algebraic equations.
  2. Apply equality rules to manipulate and solve algebraic equations.
  3. Evaluate the validity of algebraic transformations using equality principles.
  4. Interpret and explain the rationale behind each step in solving equations.
  5. Synthesize multiple equality rules to verify the consistency of solutions.

Properties of Equality Cheat Sheet

  1. Addition Property of Equality - When you add the same number to both sides of an equation, it stays perfectly balanced - just like two sides of a scale! This trick is super handy for moving terms around and isolating that sneaky variable. Give it a try next time you need to simplify an equation. Splash Learn
  2. Subtraction Property of Equality - Subtracting an identical value from both sides keeps the equation fair and square, so nothing tips over. It's a powerful move for clearing out extra terms and zeroing in on your variable. Watch how rapidly you can peel away layers of an equation! Splash Learn
  3. Multiplication Property of Equality - Multiply both sides by the same non-zero number, and the equality holds true - like doubling two clones in perfect sync! This is especially useful when you're tackling fractions or scaling up expressions. Harness this property to simplify messy denominators in a flash. Splash Learn
  4. Division Property of Equality - When you divide both sides by the same non-zero number, the balance stays intact - think of slicing a cake equally for friends. This move is essential for breaking down coefficients and slimming down equations. Next time you see a big coefficient, divide and conquer! Splash Learn
  5. Reflexive Property of Equality - Every number is equal to itself - no surprises there! It's the foundation of all equations, reminding us that a = a is always true. Keep this in mind as the ultimate self-check in your algebra toolkit. Splash Learn
  6. Symmetric Property of Equality - If one quantity equals another, you can flip them like a pancake: a = b means b = a. This flexibility lets you reorder equations for easier solving and clearer insights. Embrace the switcheroo to keep your math smooth. Splash Learn
  7. Transitive Property of Equality - Chain equalities together: if a = b and b = c, then a = c. It's like linking puzzle pieces - once they connect, the picture is clear. Use this to bridge gaps between multiple equations and discover hidden relationships. Splash Learn
  8. Substitution Property of Equality - Swap equal values into any expression: if a = b, you can replace a with b anywhere. This is your best friend when simplifying complex formulas or solving systems of equations. Get ready to substitute for success! Splash Learn
  9. Square Root Property of Equality - When two numbers are equal, their positive square roots match too: if a = b, then √a = √b. This comes in clutch for solving quadratics and checking answers. Treat it as your shortcut to unlocking squared mysteries. Splash Learn
  10. Distributive Property of Equality - Distribute a factor across a sum: a(b + c) = ab + ac, spreading the factor evenly like butter on toast. This property makes expanding and simplifying expressions a breeze. Master this move to crush algebraic expansions! Story of Mathematics
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