Questions and Answers
What is the result of a positive times a positive?
What is the result of a negative times a negative?
According to the order of operations (PEMDAS), which comes first?
How do you simplify 2x + 3x + 4?
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When adding fractions, you can add them directly without finding a common denominator.
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5 minus a negative number can be changed to ____.
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What do you need to do before dividing in an evaluation problem?
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Study Notes
Positives & Negatives - Multiplication & Division
- Mastery of positive and negative signs is crucial to avoid common mistakes.
- Multiplication rules:
- Positive × Positive = Positive
- Positive × Negative = Negative
- Negative × Positive = Negative
- Negative × Negative = Positive
- Division rules mirror multiplication rules:
- Positive ÷ Positive = Positive
- Positive ÷ Negative = Negative
- Negative ÷ Positive = Negative
- Negative ÷ Negative = Positive
- Perform multiple multiplications or divisions from left to right.
- Squaring a variable: x × x = x².
Fractions - Order of Operations
- Follow PEMDAS: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).
- Begin operations with division before multiplication if it appears first when reading left to right.
- Integers should be converted to fractions for calculations; for instance, 4 becomes 4/1.
Simplifying With Variables - Combining Like Terms
- Only combine like terms (terms with the same variable) during addition and subtraction.
- Example: 2x + 3x + 4 simplifies to 5x + 4 (cannot combine 4 with x terms).
- Coefficients precede variables; in 5x, the coefficient is 5.
- Absence of a visible coefficient indicates a coefficient of 1 (e.g., x is understood as 1x).
- Terms such as x and x² cannot be simplified together, as they are not like terms.
Absolute Value - Fractions
- This topic integrates various mathematical concepts: absolute value, order of operations, positive and negative number handling, and fraction manipulation.
Positives & Negatives - Addition & Subtraction
- Convert minus signs to plus a negative: e.g., 5 - 7 becomes 5 + (-7).
- Change minus a negative to plus a positive: e.g., 5 - (-7) becomes 5 + (+7).
- Visualize addition and subtraction using a number line: negative movements go left, positive movements go right (e.g., -3 + 6).
Order of Operations/Evaluation - Evaluation
- Understanding of positives and negatives and order of operations is essential for evaluation problems.
- Use parentheses while substituting to clarify operations.
- Replace parentheses with brackets when substituting to reduce confusion.
- Simplify both the numerator and denominator separately before conducting division operations.
Fractions - Addition & Subtraction
- Begin the addition or subtraction of fractions by determining the Least Common Denominator (LCD).
- For 1/4 + 2/3, the LCD is 12, requiring multiplication of the first fraction's numerator and denominator by 3, and the second by 4.
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Description
Test your understanding of the multiplication and division rules for positive and negative numbers in Algebra 1. This quiz will help reinforce the key concepts to avoid common mistakes involving signs. Mastering these rules is essential for success in algebra.
