Rational Numbers Summary

What does the denominator of a fraction represent?

Size of the parts

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

Rational numbers

How can irrational numbers be distinguished from rational numbers?

By their decimal expansions

How can someone add two fractions together?

Find a common denominator, then add the two numerators Signup and view all the answers

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

Real numbers Signup and view all the answers

What is an additive inverse of a number?

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

Which operation undoes multiplication?

Division Signup and view all the answers

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

Approximate them as decimals Signup and view all the answers

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

Its reciprocal Signup and view all the answers

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

Arithmetic Signup and view all the answers

What is a characteristic of rational numbers' decimal expansions?

They always terminate Signup and view all the answers

What happens to an exponent with a negative integer power?

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

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

Estimation Signup and view all the answers

What is the result of multiplying a number by itself?

Perfect square Signup and view all the answers

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

Radicand Signup and view all the answers

How is a percent converted to a fraction?

$\frac{\text{percent}}{100}$ Signup and view all the answers

What does 'percent' mean?

Per hundred Signup and view all the answers

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

Estimating to the nearest multiple of ten Signup and view all the answers

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

Parentheses, Exponents, Multiplication, Division, Addition, Subtraction Signup and view all the answers

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

Find the least common denominator (LCD) of the fractions Signup and view all the answers

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

Positive Signup and view all the answers

What is the result of dividing any integer by zero?

Undefined Signup and view all the answers

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

Distributive Property Signup and view all the answers

What does the numerator of a fraction represent?

The number of parts being considered Signup and view all the answers

What is exponential notation used for?

To represent repeated multiplication of a base number Signup and view all the answers

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

Compare the exponents of 10 Signup and view all the answers

What is the relationship between square roots and exponents?

They follow the same rules for multiplication and division 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?

Round up and change all other digits to zero Signup and view all the answers

What is the purpose of front-end estimation?

To approximate a calculation by rounding numbers first Signup and view all the answers

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

Look for any addition or subtraction involving the variable Signup and view all the answers

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

45 * 80/100 Signup and view all the answers

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

Division Signup and view all the answers

What is the first step in solving problems involving percentages?

Identify what is being asked in the problem Signup and view all the answers

What does a percent represent?

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

What is a ratio?

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

What does the numerator in a ratio represent?

The portion of the whole Signup and view all the answers

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

Divide the percentage by 100, then multiply the result by the number Signup and view all the answers

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

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

What does the phrase 'per hundred' mean?

Out of 100 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?

Greater than the original number Signup and view all the answers

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

Rational numbers Signup and view all the answers

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

Decimal Signup and view all the answers

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

Irrational numbers Signup and view all the answers

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

Arithmetic Signup and view all the answers

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

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

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

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

What is the additive inverse of a positive number?

It becomes negative Signup and view all the answers

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

Multiply numerators and denominators separately Signup and view all the answers

What is the multiplicative inverse of -3?

-1/3 Signup and view all the answers

What operation is the inverse of division?

Multiplication Signup and view all the answers

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

One Signup and view all the answers

What is the purpose of using exponents in mathematics?

To simplify repeated multiplication Signup and view all the answers

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

Parentheses, Exponents, Addition, Multiplication, Division Signup and view all the answers

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

The result is undefined Signup and view all the answers

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

Commutative Property 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?

Find the Least Common Denominator (LCD) 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?

PEMDAS Signup and view all the answers

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

Add and use the sign of the larger number Signup and view all the answers

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

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

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

Per one hundred Signup and view all the answers

How is a percent converted to a decimal?

Drop the sign and move the decimal two places to the left 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?

Round up by 1 Signup and view all the answers

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

Radicand Signup and view all the answers

What does it mean to find a perfect square?

Multiplying any number by itself Signup and view all the answers

What does the denominator of an exponential fraction represent?

The index of the root enclosing the exponential Signup and view all the answers

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

Compare the powers first, then the coefficients if the powers are equal Signup and view all the answers

What is the relationship between square roots and exponents?

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

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

To create a clear understanding of division involving square roots 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?

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

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

Identify any addition or subtraction operations involving the variable Signup and view all the answers

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

It means to divide the first number by the second number Signup and view all the answers

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

Determine what is being asked Signup and view all the answers

What is a ratio in mathematical terms?

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

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

Divide n by 100 Signup and view all the answers

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

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

What does a percentage represent mathematically?

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

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

1 divided by 100 Signup and view all the answers

"45 percent of 80" translates into:

$45 \times 80$ Signup and view all the answers

"124 out of 516" translates into:

$124 \div 516$ Signup and view all the answers

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

$\frac{124}{516}$ Signup and view all the answers

Rational Numbers Summary

Questions and Answers

What does the denominator of a fraction represent?

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

How can irrational numbers be distinguished from rational numbers?

How can someone add two fractions together?

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

What is an additive inverse of a number?

Which operation undoes multiplication?

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

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

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

What is a characteristic of rational numbers' decimal expansions?

What happens to an exponent with a negative integer power?

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

What is the result of multiplying a number by itself?

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

How is a percent converted to a fraction?

What does 'percent' mean?

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

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

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

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

What is the result of dividing any integer by zero?

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

What does the numerator of a fraction represent?

What is exponential notation used for?

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

What is the relationship between square roots and exponents?

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?

What is the purpose of front-end estimation?

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

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

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

What is the first step in solving problems involving percentages?

What does a percent represent?

What is a ratio?

What does the numerator in a ratio represent?

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

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

What does the phrase 'per hundred' mean?

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

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

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

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

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

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

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

What is the additive inverse of a positive number?

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

What is the multiplicative inverse of -3?

What operation is the inverse of division?

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

What is the purpose of using exponents in mathematics?

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

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

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

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

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

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

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

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

How is a percent converted to a decimal?

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

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

What does it mean to find a perfect square?

What does the denominator of an exponential fraction represent?

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

What is the relationship between square roots and exponents?

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

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?

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

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

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

What is a ratio in mathematical terms?

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

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

What does a percentage represent mathematically?

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

"45 percent of 80" translates into: