Algebra Camp

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Introduction to Algebra

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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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".

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".

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".

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".

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".

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 André-Marie Ampère (1775–1836).

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 André-Marie Ampère (1775–1836).

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 André-Marie Ampère (1775–1836).

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 André-Marie Ampère (1775–1836).

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 André-Marie Ampère (1775–1836).

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.