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Questions and Answers
Questions and Answers
What is the result of simplifying 6(-5)?
What is the result of simplifying 6(-5)?
-30
What is the sum of -54 and 18?
What is the sum of -54 and 18?
-36
What is the multiplicative inverse of 1/2?
What is the multiplicative inverse of 1/2?
2
What is the result of 15 - (-11)?
What is the result of 15 - (-11)?
What is A squared when A is -3?
What is A squared when A is -3?
What do you get when you simplify (-5) + (-4) + (7)?
What do you get when you simplify (-5) + (-4) + (7)?
What is the simplified form of 6r · s · 4rt?
What is the simplified form of 6r · s · 4rt?
What is the coefficient when simplifying (-2/3 x)(3y)(-2x)?
What is the coefficient when simplifying (-2/3 x)(3y)(-2x)?
How many terms are present in the expression x^2 - 10xy + 3y + y^2 - 1?
How many terms are present in the expression x^2 - 10xy + 3y + y^2 - 1?
What is the result of simplifying -|-5 + 2|?
What is the result of simplifying -|-5 + 2|?
What does 6 - (-2) - 3(-5) simplify to?
What does 6 - (-2) - 3(-5) simplify to?
Integers are _____ irrational numbers.
Integers are _____ irrational numbers.
Select all of the following expressions that are equivalent to 0.25.
Select all of the following expressions that are equivalent to 0.25.
What is the correct order of the following numbers: (1/2) to the 2nd power, 2/3, 0.45?
What is the correct order of the following numbers: (1/2) to the 2nd power, 2/3, 0.45?
What is the simplified form of 5m - 13n - n + 4m?
What is the simplified form of 5m - 13n - n + 4m?
What is the value of 21 - 18 ÷ 3 · 2?
What is the value of 21 - 18 ÷ 3 · 2?
What is the result of simplifying 9 - {x - (7 + x)}?
What is the result of simplifying 9 - {x - (7 + x)}?
Evaluate x^2/y + x^2/z when x = 10, y = -5, and z = -2.
Evaluate x^2/y + x^2/z when x = 10, y = -5, and z = -2.
What is the value of 7 + (-3x^2) when x = 0?
What is the value of 7 + (-3x^2) when x = 0?
What is the result of evaluating 5x^3 + 2 when x = -1?
What is the result of evaluating 5x^3 + 2 when x = -1?
What do you get when you simplify 7(x + 3)?
What do you get when you simplify 7(x + 3)?
10q - 20 is equivalent to _____.
10q - 20 is equivalent to _____.
What is the expression for 'the difference between five times a number and twice that number'?
What is the expression for 'the difference between five times a number and twice that number'?
What is the result of simplifying 6x + 6 + 5x - 8?
What is the result of simplifying 6x + 6 + 5x - 8?
What do you get when you simplify 3(x - 4) + 8(x + 2)?
What do you get when you simplify 3(x - 4) + 8(x + 2)?
Questions and Answers
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Study Notes
Study Notes
Basic Operations and Simplifications
- Simplifying expressions often involves combining like terms, e.g., 6(-5) simplifies to -30.
- Adding negative numbers requires careful arithmetic, e.g., -54 + 18 results in -36.
- The multiplicative inverse of a fraction like 1/2 is found by flipping it, giving a result of 2.
Evaluating Expressions
- Performing operations with both addition and subtraction can change results significantly, e.g., 15 - (-11) equals 26.
- The value of a variable raised to a power can be evaluated, as A^2 for A = -3 is 9.
- When simplifying sums of negative and positive values, such as (-5) + (-4) + (7), the result is -2.
Variable Operations
- In algebraic expressions, factorization helps simplify products, e.g., 6r · s · 4rt simplifies to 24r²st.
- When multiplying variables, like (-2/3 x)(3y)(-2x), the coefficient can be extracted, giving a result of 4.
Identifying Terms
- Counting terms in polynomial expressions is straightforward, e.g., the expression x² - 10xy + 3y + y² - 1 contains 5 terms.
Absolute Values and Negatives
- Absolute values influence simplification; for instance, -|-5 + 2| simplifies to -3.
- Evaluating mixed arithmetic expressions can vary widely, demonstrated by 6 - (-2) - 3(-5) simplifying to 23.
Integer Properties
- Integers are classified as never irrational numbers, showcasing their clear numerical nature.
Equivalency and Comparison
- Recognizing equivalent expressions is crucial; e.g., 0.25 can be represented as (0.5)², |-3 + 2.75|, or -(-0.25).
- When ordering fractions and decimals, (1/2)², 0.45, and 2/3 can be sequenced from smallest to largest.
Expression Simplification Techniques
- Collecting like terms and simplifying linear expressions is key; simplifying 5m - 13n - n + 4m results in 9m - 14n.
- The order of operations in arithmetic affects the evaluation; for 21 - 18 ÷ 3 · 2, the result is 9.
Advanced Evaluations
- Substitution into expressions reveals values, e.g., x²/y + x²/z with x = 10, y = -5, and z = -2 evaluates to -70.
- Plugging in values for x allows for straightforward evaluations, e.g., 7 + (-3x²) when x = 0 results in 7.
Additional Operation Handling
- Polynomial forms can be transformed: simplifying 7(x + 3) gives 7x + 21, illustrating distribution.
- Identifying equivalent expressions aids in simplifying, for instance, 10q - 20 can be factored as 10(q - 2).
Expression Construction
- Formulating expressions based on descriptions helps in problem-solving, e.g., "the difference between five times a number and twice that number" translates to 5N - 2N.
Final Simplifications
- Addition and subtraction within expressions such as 6x + 6 + 5x - 8 can be simplified to 11x - 2.
- Expression distribution is emphasized with 3(x - 4) + 8(x + 2) simplifying to 11x + 4.
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