Rational Numbers Summary
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Questions and Answers

What does the denominator of a fraction represent?

  • Multiplicative identity
  • Number of parts
  • Inverse operation
  • Size of the parts (correct)

    • What kind of numbers can be represented as the ratio of two integers?

  • Rational numbers (correct)
  • Whole numbers
  • Irrational numbers
  • Complex numbers

    • How can irrational numbers be distinguished from rational numbers?

  • By their decimal expansions (correct)
  • By being complex numbers
  • By their positive or negative values
  • By being whole numbers

    • How can someone add two fractions together?

    <p>Find a common denominator, then add the two numerators</p> Signup and view all the answers

    Which type of numbers include both the rational and irrational numbers?

    <p>Real numbers</p> Signup and view all the answers

    What is an additive inverse of a number?

    <p>A number that, when added to the original, gives zero</p> Signup and view all the answers

    Which operation undoes multiplication?

    <p>Division</p> Signup and view all the answers

    When comparing or ordering irrational numbers, what needs to be done to facilitate the process?

    <p>Approximate them as decimals</p> Signup and view all the answers

    What is the multiplicative inverse of a real number (except zero)?

    <p>Its reciprocal</p> Signup and view all the answers

    What branch of mathematics deals with basic operations like addition, subtraction, multiplication, and division?

    <p>Arithmetic</p> Signup and view all the answers

    What is a characteristic of rational numbers' decimal expansions?

    <p>They always terminate</p> Signup and view all the answers

    What happens to an exponent with a negative integer power?

    <p>Flip the entire exponent over the fraction line and change the power to positive</p> Signup and view all the answers

    What is the process by which an answer close to, but not exactly, the correct answer is found?

    <p>Estimation</p> Signup and view all the answers

    What is the result of multiplying a number by itself?

    <p>Perfect square</p> Signup and view all the answers

    What is the name of the number under the square root symbol?

    <p>Radicand</p> Signup and view all the answers

    How is a percent converted to a fraction?

    <p>$\frac{\text{percent}}{100}$</p> Signup and view all the answers

    What does 'percent' mean?

    <p>Per hundred</p> Signup and view all the answers

    What is the easiest, most efficient way to estimate numbers?

    <p>Estimating to the nearest multiple of ten</p> Signup and view all the answers

    What is the correct order for performing operations in an arithmetic expression?

    <p>Parentheses, Exponents, Multiplication, Division, Addition, Subtraction</p> Signup and view all the answers

    When adding or subtracting fractions, what should be done first?

    <p>Find the least common denominator (LCD) of the fractions</p> Signup and view all the answers

    When multiplying integers with the same sign, the result is:

    <p>Positive</p> Signup and view all the answers

    What is the result of dividing any integer by zero?

    <p>Undefined</p> Signup and view all the answers

    Which of the following is NOT a property of arithmetic operations?

    <p>Distributive Property</p> Signup and view all the answers

    What does the numerator of a fraction represent?

    <p>The number of parts being considered</p> Signup and view all the answers

    What is exponential notation used for?

    <p>To represent repeated multiplication of a base number</p> Signup and view all the answers

    When comparing numbers in scientific notation, what is the first step?

    <p>Compare the exponents of 10</p> Signup and view all the answers

    What is the relationship between square roots and exponents?

    <p>They follow the same rules for multiplication and division</p> Signup and view all the answers

    When front-end rounding whole numbers, what should be done if the digit to the right of the place value being rounded is 5 or more?

    <p>Round up and change all other digits to zero</p> Signup and view all the answers

    What is the purpose of front-end estimation?

    <p>To approximate a calculation by rounding numbers first</p> Signup and view all the answers

    When solving one- or two-step decimal problems, what should be the first step?

    <p>Look for any addition or subtraction involving the variable</p> Signup and view all the answers

    What does the phrase '45 percent of 80' translate to?

    <p>45 * 80/100</p> Signup and view all the answers

    If a phrase uses the word 'out of' between two numbers, what operation does it represent?

    <p>Division</p> Signup and view all the answers

    What is the first step in solving problems involving percentages?

    <p>Identify what is being asked in the problem</p> Signup and view all the answers

    What does a percent represent?

    <p>A portion of a whole, written as a number with a percent sign</p> Signup and view all the answers

    What is a ratio?

    <p>A pair of numbers that describe a mathematical relationship between a portion of a whole and the whole itself</p> Signup and view all the answers

    What does the numerator in a ratio represent?

    <p>The portion of the whole</p> Signup and view all the answers

    What is the process to find a percentage of a number?

    <p>Divide the percentage by 100, then multiply the result by the number</p> Signup and view all the answers

    When working with percentages greater than 100, how is the process different from percentages less than 100?

    <p>The process is the same, but the result is greater than the original number</p> Signup and view all the answers

    What does the phrase 'per hundred' mean?

    <p>Out of 100</p> Signup and view all the answers

    When finding a percentage of a number, if the percentage is greater than 100, how many times the original number is the result?

    <p>Greater than the original number</p> Signup and view all the answers

    What type of numbers make up the set of real numbers when combined with irrational numbers?

    <p>Rational numbers</p> Signup and view all the answers

    When comparing or ordering irrational numbers, what should be converted to facilitate the process?

    <p>Decimal</p> Signup and view all the answers

    What type of numbers are decimals that do not terminate or repeat?

    <p>Irrational numbers</p> Signup and view all the answers

    Which branch of mathematics deals with basic operations like addition, subtraction, multiplication, and division?

    <p>Arithmetic</p> Signup and view all the answers

    What is the primary difference between rational and irrational numbers when represented as decimals?

    <p>Rational numbers are terminating decimals, while irrational numbers are non-terminating.</p> Signup and view all the answers

    What is the defining characteristic of irrational numbers when comparing them to rational numbers?

    <p>Irrational numbers have non-repeating, non-terminating decimal expansions.</p> Signup and view all the answers

    What is the additive inverse of a positive number?

    <p>It becomes negative</p> Signup and view all the answers

    When multiplying two fractions, what should be done with the numerators and denominators?

    <p>Multiply numerators and denominators separately</p> Signup and view all the answers

    What is the multiplicative inverse of -3?

    <p>-1/3</p> Signup and view all the answers

    What operation is the inverse of division?

    <p>Multiplication</p> Signup and view all the answers

    What does raising a number to the power zero result in?

    <p>One</p> Signup and view all the answers

    What is the purpose of using exponents in mathematics?

    <p>To simplify repeated multiplication</p> Signup and view all the answers

    What is the correct sequence of functions in the Order of Operations when solving a math problem?

    <p>Parentheses, Exponents, Addition, Multiplication, Division</p> Signup and view all the answers

    When dividing by zero, what is the result according to the text?

    <p>The result is undefined</p> Signup and view all the answers

    What property does not hold true for subtraction or division in arithmetic operations?

    <p>Commutative Property</p> Signup and view all the answers

    In adding or subtracting fractions with different denominators, what should be done to find a common denominator according to the text?

    <p>Find the Least Common Denominator (LCD)</p> Signup and view all the answers

    What is the acronym used to remember the Order of Operations that defines the proper sequence of mathematical functions?

    <p>PEMDAS</p> Signup and view all the answers

    When multiplying integers with opposite signs according to the text, what operation should be applied?

    <p>Add and use the sign of the larger number</p> Signup and view all the answers

    What is the process to approximate the square root of an imperfect square number without using a calculator?

    <p>Finding the perfect squares above and below the radicand and dividing by one of the nearby perfect squares</p> Signup and view all the answers

    What is the meaning of 'per hundred' when referring to percentages?

    <p>Per one hundred</p> Signup and view all the answers

    How is a percent converted to a decimal?

    <p>Drop the sign and move the decimal two places to the left</p> Signup and view all the answers

    When rounding decimal numbers, what should be done if the digit to the right of the place value is 5 or greater?

    <p>Round up by 1</p> Signup and view all the answers

    What is the name of the number under the square root symbol in a radical expression?

    <p>Radicand</p> Signup and view all the answers

    What does it mean to find a perfect square?

    <p>Multiplying any number by itself</p> Signup and view all the answers

    What does the denominator of an exponential fraction represent?

    <p>The index of the root enclosing the exponential</p> Signup and view all the answers

    What is the process of comparing numbers written in scientific notation?

    <p>Compare the powers first, then the coefficients if the powers are equal</p> Signup and view all the answers

    What is the relationship between square roots and exponents?

    <p>Square roots and exponents follow the same properties for multiplication and division, but not addition or subtraction</p> Signup and view all the answers

    What is the purpose of rationalizing the denominator in expressions involving square roots?

    <p>To create a clear understanding of division involving square roots</p> Signup and view all the answers

    When front-end rounding whole numbers, what should be done if the digit to the right of the place value being rounded is less than 5?

    <p>Round down by keeping the place value being rounded as the same digit, and change all other digits to zero</p> Signup and view all the answers

    What is the first step when solving one- or two-step decimal problems?

    <p>Identify any addition or subtraction operations involving the variable</p> Signup and view all the answers

    What does it mean when a phrase states 'a number out of another number'?

    <p>It means to divide the first number by the second number</p> Signup and view all the answers

    When solving problems involving percentages, what is the first step according to the lesson summary?

    <p>Determine what is being asked</p> Signup and view all the answers

    What is a ratio in mathematical terms?

    <p>A pair of numbers describing a relationship between a portion and the whole</p> Signup and view all the answers

    When finding n% of a number x, what should you do first as per the lesson summary?

    <p>Divide n by 100</p> Signup and view all the answers

    How is a percentage greater than 100 handled in calculations according to the text?

    <p>It is treated as if it were less than 100</p> Signup and view all the answers

    What does a percentage represent mathematically?

    <p>A portion of a whole expressed as parts per hundred</p> Signup and view all the answers

    What is a percent in relation to 'per hundred'?

    <p><strong>1</strong> divided by 100</p> Signup and view all the answers

    "45 percent of 80" translates into:

    <p>$45 \times 80$</p> Signup and view all the answers

    "124 out of 516" translates into:

    <p>$124 \div 516$</p> Signup and view all the answers

    "124 out of 516" can also be interpreted as:

    <p>$\frac{124}{516}$</p> Signup and view all the answers

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