Algebra 1 Chapter 2: Signed Numbers, Absolute Value, Word Problems, and Charts (Video Study Notes)

Vocabulary-style flashcards covering the key concepts from Signed Numbers, Absolute Value, Word Problems, and Chart strategies.

Signed Numbers

Numbers that have a sign (positive or negative) used in arithmetic.

Addition with Same Signs

If two numbers share the same sign, add their absolute values and keep that sign.

Addition with Different Signs

If signs differ, subtract the smaller absolute value from the larger and keep the sign of the larger absolute value.

Subtraction Rule

Subtract by adding the opposite: a – b becomes a + (−b).

Multiplication/Division Sign Rule

Product or quotient is positive when the signs are the same, and negative when they differ.

Absolute Value

The distance of a number from zero on the number line; always nonnegative.

Simplify inside absolute value

First simplify the expression inside the bars, then apply the absolute value.

Key words for translating word problems

Sum = add, Difference = subtract, Product = multiply, Quotient = divide.

Translation example

Seven more than twice a number translates to 2x + 7; example equation: 2x + 7 = 15.

Chart problem solving

Use a chart/table to organize information before writing equations.

Value Problem (coin example)

A dime and a quarter together total $0.35; use x dimes and (5 − x) quarters with equation 0.10x + 0.25(5 − x) = 0.35.

Distance Problem formula

Distance = Rate × Time.

Evaluating Expressions

Substitute given values into expressions, then simplify.

Common Errors to Avoid

Forgetting absolute value signs, misreading phrases (e.g., 'less than'), not organizing charts, and dropping negative signs.