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Introduction to Algebra
60 videos
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Lectures
01:32
Introduction to Algebra
Absolute Value - Example 1
In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.
Julie Silva
01:11
Introduction to Algebra
Absolute Value - Example 2
In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.
Julie Silva
00:59
Introduction to Algebra
Absolute Value - Example 3
In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.
Julie Silva
01:43
Introduction to Algebra
Absolute Value - Example 4
In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.
Julie Silva
04:56
Introduction to Algebra
Absolute Value - Overview
In mathematics, the absolute value or modulus |x| of a real number x is its numerical value without regard to its sign. The absolute value of a number may be thought of as its distance from zero along a number line; this interpretation is analogous to the distance function assigned to a real number in the real number system. For example, the absolute value of ?4 is 4, and the absolute value of 4 is 4, both without regard to sign.
Julie Silva
02:34
Introduction to Algebra
Adding and Subtracting Rational Numbers - Example 1
In mathematics, the term rational number refers to any number that can be expressed as the quotient or fraction of two integers, a numerator divided by a denominator. The set of all rational numbers is usually denoted by a boldface Q, and is thus the set of all fractions. Rational numbers include all integers, most fractions, and all other numbers that can be written as a/b, where a and b are integers and b is not zero. The numbers are formed by a sequence of numerals, where the denominator is either a single digit, or two or more digits.
Julie Silva
03:05
Introduction to Algebra
Adding and Subtracting Rational Numbers - Example 2
In mathematics, the term rational number refers to any number that can be expressed as the quotient or fraction of two integers, a numerator divided by a denominator. The set of all rational numbers is usually denoted by a boldface Q, and is thus the set of all fractions. Rational numbers include all integers, most fractions, and all other numbers that can be written as a/b, where a and b are integers and b is not zero. The numbers are formed by a sequence of numerals, where the denominator is either a single digit, or two or more digits.
Julie Silva
02:33
Introduction to Algebra
Adding and Subtracting Rational Numbers - Example 3
In mathematics, the term rational number refers to any number that can be expressed as the quotient or fraction of two integers, a numerator divided by a denominator. The set of all rational numbers is usually denoted by a boldface Q, and is thus the set of all fractions. Rational numbers include all integers, most fractions, and all other numbers that can be written as a/b, where a and b are integers and b is not zero. The numbers are formed by a sequence of numerals, where the denominator is either a single digit, or two or more digits.
Julie Silva
03:03
Introduction to Algebra
Adding and Subtracting Rational Numbers - Example 4
In mathematics, the term rational number refers to any number that can be expressed as the quotient or fraction of two integers, a numerator divided by a denominator. The set of all rational numbers is usually denoted by a boldface Q, and is thus the set of all fractions. Rational numbers include all integers, most fractions, and all other numbers that can be written as a/b, where a and b are integers and b is not zero. The numbers are formed by a sequence of numerals, where the denominator is either a single digit, or two or more digits.
Julie Silva
08:40
Introduction to Algebra
Adding and Subtracting Rational Numbers - Overview
In mathematics, the term rational number refers to any number that can be expressed as the quotient or fraction of two integers, a numerator divided by a denominator. The set of all rational numbers is usually denoted by a boldface Q, and is thus the set of all fractions. Rational numbers include all integers, most fractions, and all other numbers that can be written as a/b, where a and b are integers and b is not zero. The numbers are formed by a sequence of numerals, where the denominator is either a single digit, or two or more digits.
Julie Silva
01:51
Introduction to Algebra
Classifying Real Numbers - Example 1
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5, 4/3, or ?. The set of all real numbers includes the integers and rational numbers, such as the fraction 4/3, but excludes complex numbers. The real numbers include all the rational numbers, such as 4/3, and all the irrational numbers, such as the square root of 2. The real numbers can be constructed from the rational numbers by completion, using Cauchy sequences, Dedekind cuts, or infinite decimals, or by using power sets, cardinal numbers, or transfinite numbers. The term "real" in "real number" is used in contrast with "imaginary" numbers, for example in the phrase "real part of a complex number". A real number is called a "complemented number" if it is rational and greater than 0, or "a positive real number" if it is positive and less than 0.
Julie Silva
01:23
Introduction to Algebra
Classifying Real Numbers - Example 2
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5, 4/3, or ?. The set of all real numbers includes the integers and rational numbers, such as the fraction 4/3, but excludes complex numbers. The real numbers include all the rational numbers, such as 4/3, and all the irrational numbers, such as the square root of 2. The real numbers can be constructed from the rational numbers by completion, using Cauchy sequences, Dedekind cuts, or infinite decimals, or by using power sets, cardinal numbers, or transfinite numbers. The term "real" in "real number" is used in contrast with "imaginary" numbers, for example in the phrase "real part of a complex number". A real number is called a "complemented number" if it is rational and greater than 0, or "a positive real number" if it is positive and less than 0.
Julie Silva
01:43
Introduction to Algebra
Classifying Real Numbers - Example 3
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5, 4/3, or ?. The set of all real numbers includes the integers and rational numbers, such as the fraction 4/3, but excludes complex numbers. The real numbers include all the rational numbers, such as 4/3, and all the irrational numbers, such as the square root of 2. The real numbers can be constructed from the rational numbers by completion, using Cauchy sequences, Dedekind cuts, or infinite decimals, or by using power sets, cardinal numbers, or transfinite numbers. The term "real" in "real number" is used in contrast with "imaginary" numbers, for example in the phrase "real part of a complex number". A real number is called a "complemented number" if it is rational and greater than 0, or "a positive real number" if it is positive and less than 0.
Julie Silva
02:19
Introduction to Algebra
Classifying Real Numbers - Example 4
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5, 4/3, or ?. The set of all real numbers includes the integers and rational numbers, such as the fraction 4/3, but excludes complex numbers. The real numbers include all the rational numbers, such as 4/3, and all the irrational numbers, such as the square root of 2. The real numbers can be constructed from the rational numbers by completion, using Cauchy sequences, Dedekind cuts, or infinite decimals, or by using power sets, cardinal numbers, or transfinite numbers. The term "real" in "real number" is used in contrast with "imaginary" numbers, for example in the phrase "real part of a complex number". A real number is called a "complemented number" if it is rational and greater than 0, or "a positive real number" if it is positive and less than 0.
Julie Silva
04:42
Introduction to Algebra
Classifying Real Numbers - Overview
In mathematics, a real number is a value that represents a quantity along a continuum, such as -5, 4/3, or ?. The set of all real numbers includes the integers and rational numbers, such as the fraction 4/3, but excludes complex numbers. The real numbers include all the rational numbers, such as 4/3, and all the irrational numbers, such as the square root of 2. The real numbers can be constructed from the rational numbers by completion, using Cauchy sequences, Dedekind cuts, or infinite decimals, or by using power sets, cardinal numbers, or transfinite numbers. The term "real" in "real number" is used in contrast with "imaginary" numbers, for example in the phrase "real part of a complex number". A real number is called a "complemented number" if it is rational and greater than 0, or "a positive real number" if it is positive and less than 0.
Julie Silva
01:21
Introduction to Algebra
Divide Rational Numbers - Example 1
In mathematics, division is an arithmetic operation that is performed on two numbers, the dividend and the divisor, to produce a quotient and a remainder. For example, the division of 12 by 4 yields 3 with a remainder of 1.
Julie Silva
02:25
Introduction to Algebra
Divide Rational Numbers - Example 2
In mathematics, division is an arithmetic operation that is performed on two numbers, the dividend and the divisor, to produce a quotient and a remainder. For example, the division of 12 by 4 yields 3 with a remainder of 1.
Julie Silva
02:30
Introduction to Algebra
Divide Rational Numbers - Example 3
In mathematics, division is an arithmetic operation that is performed on two numbers, the dividend and the divisor, to produce a quotient and a remainder. For example, the division of 12 by 4 yields 3 with a remainder of 1.
Julie Silva
02:54
Introduction to Algebra
Divide Rational Numbers - Example 4
In mathematics, division is an arithmetic operation that is performed on two numbers, the dividend and the divisor, to produce a quotient and a remainder. For example, the division of 12 by 4 yields 3 with a remainder of 1.
Julie Silva
03:06
Introduction to Algebra
Divide Rational Numbers - Overview
In mathematics, division is an arithmetic operation that is performed on two numbers, the dividend and the divisor, to produce a quotient and a remainder. For example, the division of 12 by 4 yields 3 with a remainder of 1.
Julie Silva
01:59
Introduction to Algebra
Equations and Inequalities - Example 1
In mathematics, an equation is a statement that two mathematical expressions have the same value. Solving the equation consists of determining what that value is. An equation is an algebraic equation if it is written in the form of two expressions, one on the left side of the equals sign and the other on the right side, with the two sides being connected by an equals sign. The two expressions may contain different variables, allowing for the possibility of more than one solution. An example of an algebraic equation is "x" + "y" = 3, which states that the sum of "x" and "y" is equal to 3. An equation is a functional equation if it is an equation involving two or more unknown functions. An example of a functional equation is "F"("x") = "x" + "y", which states that the function "F"("x") is equal to "x" + "y".
Julie Silva
01:40
Introduction to Algebra
Equations and Inequalities - Example 2
In mathematics, an equation is a statement that two mathematical expressions have the same value. Solving the equation consists of determining what that value is. An equation is an algebraic equation if it is written in the form of two expressions, one on the left side of the equals sign and the other on the right side, with the two sides being connected by an equals sign. The two expressions may contain different variables, allowing for the possibility of more than one solution. An example of an algebraic equation is "x" + "y" = 3, which states that the sum of "x" and "y" is equal to 3. An equation is a functional equation if it is an equation involving two or more unknown functions. An example of a functional equation is "F"("x") = "x" + "y", which states that the function "F"("x") is equal to "x" + "y".
Julie Silva
02:34
Introduction to Algebra
Equations and Inequalities - Example 3
In mathematics, an equation is a statement that two mathematical expressions have the same value. Solving the equation consists of determining what that value is. An equation is an algebraic equation if it is written in the form of two expressions, one on the left side of the equals sign and the other on the right side, with the two sides being connected by an equals sign. The two expressions may contain different variables, allowing for the possibility of more than one solution. An example of an algebraic equation is "x" + "y" = 3, which states that the sum of "x" and "y" is equal to 3. An equation is a functional equation if it is an equation involving two or more unknown functions. An example of a functional equation is "F"("x") = "x" + "y", which states that the function "F"("x") is equal to "x" + "y".
Julie Silva
02:42
Introduction to Algebra
Equations and Inequalities - Example 4
In mathematics, an equation is a statement that two mathematical expressions have the same value. Solving the equation consists of determining what that value is. An equation is an algebraic equation if it is written in the form of two expressions, one on the left side of the equals sign and the other on the right side, with the two sides being connected by an equals sign. The two expressions may contain different variables, allowing for the possibility of more than one solution. An example of an algebraic equation is "x" + "y" = 3, which states that the sum of "x" and "y" is equal to 3. An equation is a functional equation if it is an equation involving two or more unknown functions. An example of a functional equation is "F"("x") = "x" + "y", which states that the function "F"("x") is equal to "x" + "y".
Julie Silva
06:44
Introduction to Algebra
Equations and Inequalities - Overview
In mathematics, an equation is a statement that two mathematical expressions have the same value. Solving the equation consists of determining what that value is. An equation is an algebraic equation if it is written in the form of two expressions, one on the left side of the equals sign and the other on the right side, with the two sides being connected by an equals sign. The two expressions may contain different variables, allowing for the possibility of more than one solution. An example of an algebraic equation is "x" + "y" = 3, which states that the sum of "x" and "y" is equal to 3. An equation is a functional equation if it is an equation involving two or more unknown functions. An example of a functional equation is "F"("x") = "x" + "y", which states that the function "F"("x") is equal to "x" + "y".
Julie Silva
01:08
Introduction to Algebra
Evaluate Algebraic Expressions - Example 1
In mathematics, evaluation is a term for the process of finding a numerical value of a mathematical expression. The term is commonly used in computer programming, where it is an essential part of the interpretation of expressions. In most programming languages, expressions are not evaluated until they are needed, i.e., until they are used in a larger expression or in a statement.
Julie Silva
02:15
Introduction to Algebra
Evaluate Algebraic Expressions - Example 2
In mathematics, evaluation is a term for the process of finding a numerical value of a mathematical expression. The term is commonly used in computer programming, where it is an essential part of the interpretation of expressions. In most programming languages, expressions are not evaluated until they are needed, i.e., until they are used in a larger expression or in a statement.
Julie Silva
02:56
Introduction to Algebra
Evaluate Algebraic Expressions - Example 3
In mathematics, evaluation is a term for the process of finding a numerical value of a mathematical expression. The term is commonly used in computer programming, where it is an essential part of the interpretation of expressions. In most programming languages, expressions are not evaluated until they are needed, i.e., until they are used in a larger expression or in a statement.
Julie Silva
03:24
Introduction to Algebra
Evaluate Algebraic Expressions - Example 4
In mathematics, evaluation is a term for the process of finding a numerical value of a mathematical expression. The term is commonly used in computer programming, where it is an essential part of the interpretation of expressions. In most programming languages, expressions are not evaluated until they are needed, i.e., until they are used in a larger expression or in a statement.
Julie Silva
02:43
Introduction to Algebra
Evaluate Algebraic Expressions - Overview
In mathematics, evaluation is a term for the process of finding a numerical value of a mathematical expression. The term is commonly used in computer programming, where it is an essential part of the interpretation of expressions. In most programming languages, expressions are not evaluated until they are needed, i.e., until they are used in a larger expression or in a statement.
Julie Silva
01:46
Introduction to Algebra
Exponents and Powers - Example 1
In mathematics, exponentiation is a mathematical operation, written as a^n, whose value is the product of the values a for n number of times, where "n" is an integer.
Julie Silva
01:55
Introduction to Algebra
Exponents and Powers - Example 2
In mathematics, exponentiation is a mathematical operation, written as a^n, whose value is the product of the values a for n number of times, where "n" is an integer.
Julie Silva
02:48
Introduction to Algebra
Exponents and Powers - Example 3
In mathematics, exponentiation is a mathematical operation, written as a^n, whose value is the product of the values a for n number of times, where "n" is an integer.
Julie Silva
01:58
Introduction to Algebra
Exponents and Powers - Example 4
In mathematics, exponentiation is a mathematical operation, written as a^n, whose value is the product of the values a for n number of times, where "n" is an integer.
Julie Silva
04:46
Introduction to Algebra
Exponents and Powers - Overview
In mathematics, exponentiation is a mathematical operation, written as a^n, whose value is the product of the values a for n number of times, where "n" is an integer.
Julie Silva
01:12
Introduction to Algebra
Multiply Rational Numbers - Example 1
Multiplication of rational numbers is an extension of the multiplication of integers. It is the multiplication of two fractions with the same denominator. The product of two rational numbers is a rational number.
Julie Silva
02:33
Introduction to Algebra
Multiply Rational Numbers - Example 2
Multiplication of rational numbers is an extension of the multiplication of integers. It is the multiplication of two fractions with the same denominator. The product of two rational numbers is a rational number.
Julie Silva
03:01
Introduction to Algebra
Multiply Rational Numbers - Example 3
Multiplication of rational numbers is an extension of the multiplication of integers. It is the multiplication of two fractions with the same denominator. The product of two rational numbers is a rational number.
Julie Silva
03:02
Introduction to Algebra
Multiply Rational Numbers - Example 4
Multiplication of rational numbers is an extension of the multiplication of integers. It is the multiplication of two fractions with the same denominator. The product of two rational numbers is a rational number.
Julie Silva
02:55
Introduction to Algebra
Multiply Rational Numbers - Overview
Multiplication of rational numbers is an extension of the multiplication of integers. It is the multiplication of two fractions with the same denominator. The product of two rational numbers is a rational number.
Julie Silva
01:28
Introduction to Algebra
Order of Operations - Example 1
In mathematics, the order of operations is the sequential order in which mathematical operations are performed. The order of operations is not universal, and may vary from country to country, or even within a country. The order of operations is not a single, uniform rule, but rather a set of rules, which have exceptions. The phrase was coined by the French mathematician AndrĂ©-Marie AmpĂ¨re (1775â€“1836).
Julie Silva
01:45
Introduction to Algebra
Order of Operations - Example 2
In mathematics, the order of operations is the sequential order in which mathematical operations are performed. The order of operations is not universal, and may vary from country to country, or even within a country. The order of operations is not a single, uniform rule, but rather a set of rules, which have exceptions. The phrase was coined by the French mathematician AndrĂ©-Marie AmpĂ¨re (1775â€“1836).
Julie Silva
02:14
Introduction to Algebra
Order of Operations - Example 3
In mathematics, the order of operations is the sequential order in which mathematical operations are performed. The order of operations is not universal, and may vary from country to country, or even within a country. The order of operations is not a single, uniform rule, but rather a set of rules, which have exceptions. The phrase was coined by the French mathematician AndrĂ©-Marie AmpĂ¨re (1775â€“1836).
Julie Silva
02:55
Introduction to Algebra
Order of Operations - Example 4
In mathematics, the order of operations is the sequential order in which mathematical operations are performed. The order of operations is not universal, and may vary from country to country, or even within a country. The order of operations is not a single, uniform rule, but rather a set of rules, which have exceptions. The phrase was coined by the French mathematician AndrĂ©-Marie AmpĂ¨re (1775â€“1836).
Julie Silva
03:42
Introduction to Algebra
Order of Operations - Overview
In mathematics, the order of operations is the sequential order in which mathematical operations are performed. The order of operations is not universal, and may vary from country to country, or even within a country. The order of operations is not a single, uniform rule, but rather a set of rules, which have exceptions. The phrase was coined by the French mathematician AndrĂ©-Marie AmpĂ¨re (1775â€“1836).
Julie Silva
03:10
Introduction to Algebra
Simplify Expressions and the Distributive Property - Example 1
In mathematics, the distributive property is a property of some binary operations. It regulates the process of multiplying a number or variable with the expression inside the bracket.
Julie Silva
02:26
Introduction to Algebra
Simplify Expressions and the Distributive Property - Example 2
In mathematics, the distributive property is a property of some binary operations. It regulates the process of multiplying a number or variable with the expression inside the bracket.
Julie Silva
02:02
Introduction to Algebra
Simplify Expressions and the Distributive Property - Example 3
In mathematics, the distributive property is a property of some binary operations. It regulates the process of multiplying a number or variable with the expression inside the bracket.
Julie Silva
02:32
Introduction to Algebra
Simplify Expressions and the Distributive Property - Example 4
In mathematics, the distributive property is a property of some binary operations. It regulates the process of multiplying a number or variable with the expression inside the bracket.
Julie Silva
05:31
Introduction to Algebra
Simplify Expressions and the Distributive Property - Overview
In mathematics, the distributive property is a property of some binary operations. It regulates the process of multiplying a number or variable with the expression inside the bracket.
Julie Silva
01:58
Introduction to Algebra
Translate Words into Algebraic Expressions - Example 1
In mathematics, a polynomial is a degree of a polynomial is the largest exponent of the variable in the polynomial. For example, the polynomial x^0 has a degree of 0, the polynomial x+10 has a degree of 1, and the polynomial x^2+x+8 has a degree of 2. The term "polynomial" is also used for a polynomial expression, in which case "degree" means the highest power of the variable that occurs in the expression.
Julie Silva
02:07
Introduction to Algebra
Translate Words into Algebraic Expressions - Example 2
In mathematics, a polynomial is a degree of a polynomial is the largest exponent of the variable in the polynomial. For example, the polynomial x^0 has a degree of 0, the polynomial x+10 has a degree of 1, and the polynomial x^2+x+8 has a degree of 2. The term "polynomial" is also used for a polynomial expression, in which case "degree" means the highest power of the variable that occurs in the expression.
Julie Silva
01:38
Introduction to Algebra
Translate Words into Algebraic Expressions - Example 3
In mathematics, a polynomial is a degree of a polynomial is the largest exponent of the variable in the polynomial. For example, the polynomial x^0 has a degree of 0, the polynomial x+10 has a degree of 1, and the polynomial x^2+x+8 has a degree of 2. The term "polynomial" is also used for a polynomial expression, in which case "degree" means the highest power of the variable that occurs in the expression.
Julie Silva
01:54
Introduction to Algebra
Translate Words into Algebraic Expressions - Example 4
In mathematics, a polynomial is a degree of a polynomial is the largest exponent of the variable in the polynomial. For example, the polynomial x^0 has a degree of 0, the polynomial x+10 has a degree of 1, and the polynomial x^2+x+8 has a degree of 2. The term "polynomial" is also used for a polynomial expression, in which case "degree" means the highest power of the variable that occurs in the expression.
Julie Silva
04:21
Introduction to Algebra
Translate Words into Algebraic Expressions - Overview
In mathematics, a polynomial is a degree of a polynomial is the largest exponent of the variable in the polynomial. For example, the polynomial x^0 has a degree of 0, the polynomial x+10 has a degree of 1, and the polynomial x^2+x+8 has a degree of 2. The term "polynomial" is also used for a polynomial expression, in which case "degree" means the highest power of the variable that occurs in the expression.
Julie Silva
01:15
Introduction to Algebra
Variables and Expressions - Example 1
In mathematics, a variable is a value that may change. The term is used in many different senses, which can lead to confusion. A variable can be a real number, a complex number, a function, a set, an expression, a quantity, etc. The value of a variable is not fixed and may change as the program executes.
Julie Silva
01:11
Introduction to Algebra
Variables and Expressions - Example 2
In mathematics, a variable is a value that may change. The term is used in many different senses, which can lead to confusion. A variable can be a real number, a complex number, a function, a set, an expression, a quantity, etc. The value of a variable is not fixed and may change as the program executes.
Julie Silva
01:05
Introduction to Algebra
Variables and Expressions - Example 3
In mathematics, a variable is a value that may change. The term is used in many different senses, which can lead to confusion. A variable can be a real number, a complex number, a function, a set, an expression, a quantity, etc. The value of a variable is not fixed and may change as the program executes.
Julie Silva
00:50
Introduction to Algebra
Variables and Expressions - Example 4
In mathematics, a variable is a value that may change. The term is used in many different senses, which can lead to confusion. A variable can be a real number, a complex number, a function, a set, an expression, a quantity, etc. The value of a variable is not fixed and may change as the program executes.
Julie Silva
08:58
Introduction to Algebra
Variables and Expressions - Overview
In mathematics, a variable is a value that may change. The term is used in many different senses, which can lead to confusion. A variable can be a real number, a complex number, a function, a set, an expression, a quantity, etc. The value of a variable is not fixed and may change as the program executes.
Julie Silva