Elementary Algebra Test Review Modules 1-3

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.