"A fraction represents a part of a whole or, more generally, any number of equal parts."
The process of finding the sum or difference of two or more fractions.
Fractions: This covers the basics of fractions, including definitions of numerator and denominator, equivalent fractions, and simplifying fractions.
Like and unlike fractions: It covers how to compare fractions with the same denominator and fractions with different denominators.
Common Denominator: This topic involves finding the common denominator of two or more fractions with different denominators, and rewriting them in a way that has the same denominator.
Fraction addition: This topic deals with the addition of fractions with the same denominator and those with different denominators.
Fraction subtraction: This topic explains how to subtract fractions with the same denominator and those with different denominators.
Mixed numbers: It covers conversion of mixed numbers to improper fractions, and vice versa.
Simplification of fractions: It covers reducing fractions to their simplest form by dividing both numerator and the denominator.
Fraction word problems: This topic involves using fraction arithmetic to solve word problems such as how much pizza left, and fractions of money.
Addition and subtraction error checks: It covers how to check the correctness of fractions addition and subtraction.
Changing fractions to decimals: It teaches you how to convert fractions to decimals for easier computation.
Fractional order of operations: It covers the correct order to follow when carrying out addition and subtraction of fractions in complex expressions.
Like fractions: Fractions with the same denominator are called like fractions. To add or subtract like fractions, simply add or subtract the numerators and retain the denominator.
Unlike fractions: Fractions with different denominators are called unlike fractions. To add or subtract unlike fractions, they must be converted into like fractions first. This can be done by finding the least common multiple (LCM) of the denominators and then expressing each fraction in terms of that LCM.
Mixed numbers: A mixed number is a whole number combined with a fraction. To add or subtract mixed numbers, they must first be converted to improper fractions.
Improper fractions: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To add or subtract improper fractions, the same steps used for adding or subtracting like fractions are followed.
Adding and subtracting fractions with different signs: When adding or subtracting fractions with different signs (positive and negative), the process is similar to adding or subtracting integers. The numerator of the fraction with the larger absolute value is subtracted from the numerator of the fraction with the smaller absolute value. The sign of the result is the same as the sign of the fraction with the larger absolute value, and the denominator remains the same.
Adding and subtracting mixed numbers with different signs: When adding or subtracting mixed numbers with different signs, the fractional parts are first added or subtracted according to the rules for adding or subtracting fractions, and then the integers are added or subtracted according to the rules for adding or subtracting integers.
Adding and subtracting fractions with variables: When adding or subtracting fractions with variables, the fractions are first simplified by finding a common denominator if necessary, and then the numerators are added or subtracted. The result is then simplified if possible.
"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. Examples are: 1/2 and 17/3."
"The numerator represents a number of equal parts."
"The denominator indicates how many of those parts make up a unit or a whole."
"Yes, the fraction 3/4 can also be used to represent the ratio 3:4 (the ratio of the part to the whole)."
"Yes, the fraction 3/4 can also represent the division 3 ÷ 4 (three divided by four)."
"Yes, we can also write negative fractions, which represent the opposite of a positive fraction."
"Because of the rules of division of signed numbers, negative fractions and their positive counterparts represent the same fraction."
"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."
"Rational numbers are represented by the symbol Q or ℚ, which stands for quotient."
"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."
"An example of an algebraic fraction is a quotient of algebraic expressions."
"Yes, expressions that contain irrational numbers, such as √2/2 (see square root of 2) and π/4 (see proof that π is irrational), can also be referred to as fractions."
"The word 'fraction' comes from Latin: fractus, meaning 'broken'."
"A fraction describes how many parts of a certain size there are."
"A vulgar or simple fraction consists of an integer numerator displayed above a line or before a slash, and a non-zero integer denominator displayed below or after that line."
"In the fraction 3/4, the numerator 3 indicates that the fraction represents 3 equal parts, and the denominator 4 indicates that 4 parts make up a whole."
"The set of rational numbers represents all numbers that can be expressed in the form a/b, where a and b are integers and b is not zero."