Questions and Answers
Simplify $-4(15)$
-60
Simplify $-5 - (-2)$
-3
Simplify $-6 - 2 + 5 - (-2)$
-1
Simplify $(-2)(-8)(-4)$
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Simplify $(-3)^2$
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What is $8^0$?
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Simplify $-90 / (-6)$
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Simplify $|12| - |-3|$
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Simplify $- \frac{10}{21} \left( - \frac{9}{25} \right)$
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Simplify $-\frac{3}{8} + \frac{5}{12}$
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Simplify $3 + 2(4 - 6 \div 2 \times 3)$
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Simplify $\frac{12}{35} \div \left( - \frac{8}{25} \right)$
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Find the length of the segment with endpoints -3 and 4.
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What is the coordinate of the segment's midpoint between -3 and 4?
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What conclusion can you draw about a nonzero real number if its absolute value is equal to its opposite?
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Study Notes
Simplifying Expressions
- Simplifying complex mathematical expressions involves following order of operations: parentheses, exponents, multiplication and division (left to right), addition and subtraction (left to right).
- Negative signs and absolute values play crucial roles in simplification.
Arithmetic Operations
- Multiplication of negative numbers results in a positive product.
- Division of two negative numbers yields a positive result.
- Summation should include careful consideration of negative signs, especially when combining integers and fractions.
Absolute Values
- The absolute value of a number is its distance from zero on the number line, always a non-negative number.
- Differences between absolute values can negate negative signs when computing.
Converting Units
- To convert miles to kilometers, multiply by 1.6 (1 mile = 1.6 km).
Evaluating Expressions
- Translating phrases into numerical expressions is essential for evaluation, such as finding the reciprocal or the opposite of a number.
- Use order of operations for expressions involving addition, subtraction, and multiplication of fractions.
Graphing Points on the Number Line
- Every point on a number line represents a unique value; placing points on the line helps visualize their relationships.
Segment Length and Midpoint
- Length of a segment can be calculated as the difference between its endpoints.
- Midpoint coordinates are found by averaging the x-coordinates of the endpoints.
Real Number Subsets
- Real numbers can be classified into subsets: natural numbers, whole numbers, integers, rational numbers, and irrational numbers.
- Understanding the positioning of numbers in these subsets is essential for proper classification.
Set Theory Operations
- Set operations, such as union (∪) and intersection (∩), involve combining or finding common elements from various sets.
- Venn diagrams are helpful tools to visualize relationships between sets and their elements.
Properties of Operations
- Commutative Property: Numbers can be added or multiplied in any order (e.g., a + b = b + a).
- Distributive Property: Multiplication distributes over addition (e.g., a(b + c) = ab + ac).
Absolute Value Conclusion
- A nonzero real number with an absolute value equal to its opposite indicates it must be zero, illustrating that absolute values only equal when both values are the same.
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Description
This quiz covers key concepts in simplifying mathematical expressions, including the order of operations, absolute values, and the effects of negative numbers. It also addresses unit conversions and evaluating expressions. Test your understanding of these fundamental math principles!
