Elementary Algebra Test Review Modules 1-3

Questions and Answers

Simplify this problem completely: -18 + 24

Simplify this problem completely: -25 - 15

-40

Simplify this problem completely: 18 - 24 + ( -8 ) - 12

-26

Simplify this problem completely: 4 / 5 - 2 / 3

2/15 Signup and view all the answers

Simplify this problem completely: 4 / 5 divided by 2 / 3

1 & 1/5 or 6/5 Signup and view all the answers

Find the absolute value of this problem: - |12 - 18|

-6 Signup and view all the answers

Find the absolute value of this problem: -3 - |-4|

-7 Signup and view all the answers

Find the absolute value of this problem: |-7| - |-20|

-13 Signup and view all the answers

Evaluate this problem: -5 - 3(-2)

1 Signup and view all the answers

Evaluate this problem: 12(0) - 17(2) + (-6)

-40 Signup and view all the answers

Simplify this: -7 squared

49 Signup and view all the answers

Simplify this: (-3) cubed

-27 Signup and view all the answers

Simplify this: (-20 + 16) squared

16 Signup and view all the answers

Determine the property of this problem: 26 + (14 + 19) = (26 + 14) + 19

Associative Property of Addition Signup and view all the answers

Determine the property of this problem: 3/4 + (-3/4) = 0

Additive Inverse Property Signup and view all the answers

Determine the property of this problem: 9 * 1/9 = 1

Inverse Property of Multiplication Signup and view all the answers

Determine the property of this problem: -2(3X - 4) = -6X + 8

Distributive Property Signup and view all the answers

Simplify this problem using PEMDAS: 28 - [4 - (7 - 9)] - 12 divided by (-3)

26 Signup and view all the answers

Simplify this problem by using PEMDAS: 75 divided by 3 * 2 divided by 10 squared divided by 4

2 Signup and view all the answers

Simplify this problem by using PEMDAS: -28(-3/7)

12 Signup and view all the answers

Simplify this problem using Distributive Property: 3(X - 9)

3X - 27 Signup and view all the answers

Simplify this problem using Distributive Property: -4(A + B)

-4A - 4B Signup and view all the answers

Simplify this problem using Distributive Property: 10(M + K) - 2M

8M + 10K Signup and view all the answers

Simplify this problem using Distributive Property: 5X - 3(2Y + 4X) - 7Y

-7X - 13Y Signup and view all the answers

Study Notes

Basic Arithmetic Operations

Simplification of -18 + 24 results in 6.
Simplification of -25 - 15 yields -40.
Simplifying 18 - 24 + (-8) - 12 gives -26.

Fractions and Division

The operation 4/5 - 2/3 simplifies to 2/15.
4/5 divided by 2/3 can be expressed as 1 & 1/5 or 6/5.

Absolute Value

The absolute value of -|12 - 18| is -6.
Calculation of -3 - |-4| results in -7.
The absolute difference |-7| - |-20| leads to -13.

Evaluations

Evaluating -5 - 3(-2) results in 1.
The expression 12(0) - 17(2) + (-6) equals -40.

Powers and Exponents

Squaring -7 gives 49.
Cubing -3 results in -27.
The expression (-20 + 16) squared equals 16.

Algebraic Properties

Associative Property of Addition is demonstrated by 26 + (14 + 19) = (26 + 14) + 19.
The Additive Inverse Property is shown with 3/4 + (-3/4) = 0.
The Inverse Property of Multiplication is represented by 9 × 1/9 = 1.
The Distributive Property is represented by -2(3X - 4) = -6X + 8.

Application of PEMDAS

Using PEMDAS, the expression 28 - [4 - (7 - 9)] - 12 ÷ (-3) simplifies to 26.
The calculation of 75 ÷ 3 × 2 ÷ 10² ÷ 4 results in 2.
The expression -28(-3/7) simplifies to 12.

Distributive Property Applications

Simplifying 3(X - 9) gives 3X - 27.
The expression -4(A + B) simplifies to -4A - 4B.
The operation 10(M + K) - 2M simplifies to 8M + 10K.
Simplifying 5X - 3(2Y + 4X) - 7Y results in -7X - 13Y.

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Prepare for your Math 098 test with these flashcards focusing on simplification problems. Each card presents a mathematical expression to simplify, helping reinforce your understanding of key concepts from Modules 1 to 3. Get ready to ace your exam with this quick review!