"A fraction represents a part of a whole or, more generally, any number of equal parts."
Numbers that combine whole numbers and fractions, and fractions that have a numerator greater than or equal to the denominator.
What are Mixed Numbers?: Mixed numbers are a combination of a whole number and a fraction. They can be converted to improper fractions or vice versa.
What are Improper Fractions?: Improper fractions have a numerator that is greater than or equal to the denominator. They can be converted to mixed numbers or simplified.
Converting Mixed Numbers to Improper Fractions: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. The result is the new numerator, and the denominator remains the same.
Converting Improper Fractions to Mixed Numbers: To convert an improper fraction to a mixed number, divide the numerator by the denominator, the quotient is the whole number, and the remainder becomes the numerator of the fraction part.
Adding and Subtracting Mixed Numbers: To add or subtract mixed numbers, convert them to improper fractions, find a common denominator, perform the operation, and simplify the result.
Adding and Subtracting Improper Fractions: To add or subtract improper fractions, find a common denominator, perform the operation, and simplify the result.
Multiplying Mixed Numbers: To multiply mixed numbers, convert them to improper fractions, multiply the numerators and denominators, and simplify the result.
Multiplying Improper Fractions: To multiply improper fractions, multiply the numerators and denominators, and simplify the result.
Dividing Mixed Numbers: To divide mixed numbers, convert them to improper fractions, invert the second fraction, multiply the numerators and denominators, and simplify the result.
Dividing Improper Fractions: To divide improper fractions, invert the second fraction, multiply the numerators and denominators, and simplify the result.
Comparing and Ordering Mixed Numbers and Improper Fractions: To compare or order mixed numbers or improper fractions, convert them to improper fractions, find a common denominator, and compare the numerators.
Simplifying Mixed Numbers and Improper Fractions: To simplify a mixed number or an improper fraction, divide the numerator and denominator by their greatest common factor.
Proper mixed number: A mixed number where the fraction part is less than one whole, such as 3 1/2.
Whole number: A mixed number where the fraction part is zero, such as 6 0/2, which is equivalent to 6.
Improper mixed number: A mixed number where the fraction part is greater than or equal to one whole, such as 4 3/2.
Proper fraction: A fraction where the numerator is less than the denominator, such as 2/3.
Whole fraction: A fraction where the numerator is equal to the denominator, such as 5/5, which is equivalent to 1 whole.
Improper fraction: A fraction where the numerator is greater than the denominator, such as 7/4.
"When spoken in everyday English, a fraction describes how many parts of a certain size there are."
"A common, vulgar, or simple fraction consists of an integer numerator, displayed above a line (or before a slash like 1⁄2), and a non-zero integer denominator, displayed below (or after) that line."
"If these integers are positive, then the numerator represents a number of equal parts."
"The denominator indicates how many of those parts make up a unit or a whole."
"Yes, fractions can be used to represent ratios and division."
"The fraction 3/4 can also be used to represent the ratio 3:4 (the ratio of the part to the whole), and the division 3 ÷ 4 (three divided by four)."
"We can also write negative fractions, which represent the opposite of a positive fraction."
"If 1/2 represents a half-dollar profit, then −1/2 represents a half-dollar loss."
"−1/2 represents the same fraction – negative one-half."
"The set of all numbers that can be expressed in the form a/b, where a and b are integers and b is not zero, is called the set of rational numbers."
"Q or ℚ stands for quotient, representing the set of rational numbers."
"A number is a rational number precisely when it can be written in the form a/b (i.e., as a common fraction)."
"Yes, the word fraction can also be used to describe mathematical expressions that are not rational numbers."
"Examples of these usages include algebraic fractions (quotients of algebraic expressions)."
"Expressions that contain irrational numbers, such as 2/2 (see square root of 2) and π/4 (see proof that π is irrational)."
"A fraction (from Latin: fractus, 'broken')..."
"When spoken in everyday English, a fraction describes how many parts of a certain size there are..."
"A common, vulgar, or simple fraction consists of an integer numerator, displayed above a line (or before a slash like 1⁄2), and a non-zero integer denominator..."
"We can also write negative fractions, which represent the opposite of a positive fraction..."