Rational Numbers Summary

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

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 (B)</p> Signup and view all the answers

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

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

Which operation undoes multiplication?

<p>Division (B)</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 (C)</p> Signup and view all the answers

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

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

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

<p>Arithmetic (B)</p> Signup and view all the answers

What is a characteristic of rational numbers' decimal expansions?

<p>They always terminate (D)</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 (A)</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 (D)</p> Signup and view all the answers

What is the result of multiplying a number by itself?

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

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

<p>Radicand (B)</p> Signup and view all the answers

How is a percent converted to a fraction?

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

What does 'percent' mean?

<p>Per hundred (D)</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 (C)</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 (A)</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 (D)</p> Signup and view all the answers

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

<p>Positive (B)</p> Signup and view all the answers

What is the result of dividing any integer by zero?

<p>Undefined (D)</p> Signup and view all the answers

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

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

What does the numerator of a fraction represent?

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

What is exponential notation used for?

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

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

<p>Compare the exponents of 10 (C)</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 (B)</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 (D)</p> Signup and view all the answers

What is the purpose of front-end estimation?

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

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

<p>45 * 80/100 (D)</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 (D)</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 (D)</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 (D)</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 (A)</p> Signup and view all the answers

What does the numerator in a ratio represent?

<p>The portion of the whole (A)</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 (A)</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 (D)</p> Signup and view all the answers

What does the phrase 'per hundred' mean?

<p>Out of 100 (D)</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 (B)</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 (B)</p> Signup and view all the answers

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

<p>Decimal (B)</p> Signup and view all the answers

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

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

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

<p>Arithmetic (A)</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. (B)</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. (D)</p> Signup and view all the answers

What is the additive inverse of a positive number?

<p>It becomes negative (C)</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 (B)</p> Signup and view all the answers

What is the multiplicative inverse of -3?

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

What operation is the inverse of division?

<p>Multiplication (A)</p> Signup and view all the answers

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

<p>One (A)</p> Signup and view all the answers

What is the purpose of using exponents in mathematics?

<p>To simplify repeated multiplication (D)</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 (C)</p> Signup and view all the answers

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

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

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

<p>Commutative Property (C)</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) (D)</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 (D)</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 (C)</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 (B)</p> Signup and view all the answers

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

<p>Per one hundred (B)</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 (C)</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 (C)</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 (A)</p> Signup and view all the answers

What does it mean to find a perfect square?

<p>Multiplying any number by itself (C)</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 (D)</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 (B)</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 (A)</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 (B)</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 (A)</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 (C)</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 (D)</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 (D)</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 (D)</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 (B)</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 (D)</p> Signup and view all the answers

What does a percentage represent mathematically?

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

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

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

"45 percent of 80" translates into:

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

"124 out of 516" translates into:

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

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

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

Flashcards are hidden until you start studying

More Like This

Use Quizgecko on...
Browser
Open
Browser
Browser