Applying Algebraic Properties of Equality – Practice Problems

Having fun while studying, practice your skills by solving these exercises!

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Do you need help? Watch the Video Lesson for this Practice Problem.

After this lesson, you will be able to rewrite and modify equations by applying the different properties of equality.

The lesson begins by teaching you how to write an equation representing a real-life problem and to apply the addition property of equality to rewrite it. It leads you to learn how to combine like terms on the same side of the equation and isolate the variable used in the equation by applying the subtraction property of equality. It concludes with determining the solution of the equation by applying the other properties of equality such as the associative properties of multiplication and addition and the commutative property of addition.

Learn about rewriting an equation using the different properties of equality by helping the flobbit Wilbo compute for the length of time that he shall spend on napping so he could complete all his tasks for the day!

This video introduces new concepts, notation, and vocabulary such as the Addition Property (adding equal quantities to both sides of the equation will retain the equality of the two sides); Subtraction Property (subtracting equal quantities from both sides of the equation will retain the equality of the two sides); Associative Property of Multiplication (given a multiplication operation involving more than two factors, the order in which factors are grouped will not affect the product); Associative Property of Addition (given an addition problem involving more than two addends, the order in which addends are grouped will not affect the sum; and Commutative Property of Addition (the order of the addends in an addition problem will not affect the sum).

Before watching this video, you should already be familiar with variables, like terms, equations, and writing an equation to represent a word problem.

After watching this video, you will be prepared to learn how to solve more word problems involving equations such as distance, age, and unknown angle word problems algebraically.

Common Core Standard(s) in focus: 7.EE.B.3 and 7.EE.B.4
A video intended for math students in the 7th grade
Recommended for students who are 12-13 years old

Go to Video Lesson
Exercises in this Practice Problem
Explain the addition and subtraction properties of equality.
Match the properties of equalities with their corresponding general equations.
Determine which statements are true about properties of equalities.
Label each calculation with the property of equality being used.
Identify which expressions equal the given values.
Decide which property of equality is being used in each step of the calculation.