Foundations for Algebra

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How Do You Evaluate an Algebraic Expression by Plugging In Values?

Sometimes you have an algebraic expression with variables, and you know the values of those variables exactly, and you just need to plug in those values and get the value of the expression. Well, if that's what you have to do, then you've come to the right place, because this tutorial will show you exactly how to do it!
How Do You Turn a Verbal Phrase into a Two-Step Algebraic Expression?

If you're turning a verbal phrase into math terms, start out by looking for key words that can help you start writing the mathematical expression. Follow along with this tutorial to see an example of writing a verbal phrase as math!
What are the Multiplication Properties of 0 and -1?

Understanding the multiplication properties of 0 and -1 are fundamental building blocks in learning all there is to know about the operation of multiplication. In this tutorial, you'll learn about these two important properties.
What are the Inverse Properties of Addition and Multiplication?

Inverse properties of addition and multiplication got you stumped? This tutorial should help! Check it out and learn these two important inverse properties.
How Do You Find the Absolute Value of Positive and Negative Numbers?

Finding the absolute value of a number is a breeze when you use a number line! Remember, absolute value is the distance from zero on the number line. This tutorial shows you how to use a number line to find absolute value.
What are Multiplicative Inverses?

Multiplicative inverses. That's a mouthful! Really, this term just refers to numbers that when multiplied together equal 1. These numbers are also called reciprocals of each other! Learn about multiplicative inverses by watching this tutorial.
How Do You Solve a Word Problem by Writing an Equation and Plugging in Values?

Setting up and solving an equation from a word problem can be tricky, but this tutorial can help. See all the steps, from defining variables to getting that final answer, and everything in between! With this tutorial, you'll learn what it takes to solve a word problem.
What are Exponents?

Did you know that another word for 'exponent' is 'power'? To learn the meaning of these words and to see some special cases involving exponents, check out this tutorial!
What are the Commutative Properties of Addition and Multiplication?

The commutative property is a fundamental building block of math, but it only works for addition and multiplication. This tutorial defines the commutative property and provides examples of how to use it.
What are the Identity Properties of Addition and Multiplication?

Let's identify an identity! Addition and subtraction have a different identity than multiplication and division. Learn about each of these identities with this tutorial!
How Do You Translate a Phrase with One Variable and Number Into a Mathematical Expression?

Need some practice translating phrases into mathematical expressions? Then this tutorial is for you! You'll get practice translating statements involving addition, subtraction, multiplication, or division into mathematical expressions.
What are Natural and Whole Numbers?

The natural numbers are also called the counting numbers. The whole numbers are almost exactly as the natural numbers the same except for one small difference! Watch this tutorial and learn the difference between natural and whole numbers.
How Do Different Categories of Numbers Compare To Each Other?

There are a bunch of different categories of numbers such as the rational numbers, the natural numbers, and the integers, just to name a few. See how they all relate to one another by watching this tutorial!
How Do You Write an Equation from a Word Problem?

Having difficulty turning a word problem into an algebra equation? Then this tutorial is for you! With this tutorial, you'll learn how to break down word problems and translate them into mathematical equations.
How Do You Simplify an Expression?

Simplifying an algebraic expression is a fundamental part of solving math problems. Get some practice putting an expression in simplest form by following along with this tutorial.
How Do You Use the Distributive Property to Simplify an Expression?

In this tutorial you'll see how to apply the distributive property. Remember that this is important when you are trying to simplify an expression and get rid of parentheses!
How Do You Use the Associative Property?

Learning the associative property of addition is one thing, but being able to use it can be a completely different challenge. In this tutorial, you'll see how to put this very useful property into action.
How Do You Evaluate an Algebraic Expression?

Plugging variables into an expression is essential for solving many algebra problems. See how to plug in variable values by watching this tutorial.
How Do You Use the Order of Operations?

If you're trying to simplify some math expressions, you have to do it in the right order. If you've ever wondered how to do that, check out this example tutorial where you'll see exactly what order you need to follow:)
What is a Variable?

You can't do algebra without working with variables, but variables can be confusing. If you've ever wondered what variables are, then this tutorial is for you!
What Are Some Words You Can Use To Write Word Problems?

Knowing the mathematical meaning of words allows you to decipher word problems and gives you the power to write your own word problems, too! Take a look at these words and learn their mathematical translations.
What are Like Terms?

Combining like terms together is a key part of simplifying mathematical expressions, so check out this tutorial to see how you can easily pick out like terms from an expression
What is Simplest Form?

Sometimes what's simple for some is hard for others, and so simple seems like a pretty subjective word. But when it comes to algebra, the simplest form of an expressions is very well defined and is very specific- there's really nothing that subjective about it. So watch this tutorial and see exactly what simplest form means!
What is the Distributive Property?

The distributive property is a very deep math principle that helps make math work. It's the rule that lets you expand parentheses, and so it's really critical to understand if you want to get good at simplifying expressions. So check out the tutorial and let us know what you think!
What are the Associative Properties of Addition and Multiplication?

The associative property is one of those fundamental properties of math that make math work. You probably take this property for granted because it's so ingrained, but it's important to see how the guts of math work, so check out the tutorial and make sure you're solid on your fundamentals!
What's the Order of Operations?

Check out this tutorial where you'll see exactly what order you need to follow when you simplify expressions. You'll also see what happens when you don't follow these rules, and you'll find out why order of operations is so important!
What's a Coefficient?

There is a bunch of vocabulary that you just need to know when it comes to algebra, and coefficient is one of the key words that you have to feel 100% comfortable with. Check out the tutorial and let us know if you want to learn more about coefficients!
How Do You Find a Solution Set When You Have A Replacement Set?

Trying to figure out if the values in a replacement set are part of the solution set to an inequality? Learn how to find the answer to that question with this tutorial!
What's a Set?

This tutorial will help you understand what a set is, and the different kinds of sets that you may see when you're working on algebra problems :)
How Do You Do Long Division?

We know that calculators are everywhere, but that doesn't mean that long division isn't important! Sometimes you won't be allowed to use a calculator, and when those times occur, you'll be thankful that you watched this video!
What's a Dividend and What's a Divisor?

When you do division problems, you need to know the vocabulary that people use to describe what number is being divided, and what number is doing the dividing. This tutorial will help you keep that vocabulary straight!
How Do You Do Long Division with Decimals?

We know that calculators are everywhere, but that doesn't mean that long division isn't important! Sometimes you won't be allowed to use a calculator, and when those times occur, you'll be thankful that you watched this video!
How Do You Turn a Longer Verbal Phrase into an Algebraic Expression?

Looking for some practice translating words into a mathematical expression? Then take a look at this tutorial, and you'll learn how to break down those words and write the mathematical expression they describe!
How Do You Turn a Simple Equation into Words?

Get creative with math by turning a mathematical equation into a story. This tutorial shows you one example, but the possibilities are endless! Test your creativity by writing your own story to describe the given mathematical equation.
How Do You Turn a Simple Expression into Words?

Being able to translate words into a mathematical expression is an important skill, but being able to go the other way is just as crucial. This tutorial shows you how a mathematical expression can be turned into words.
How Do You Turn a More Complicated Equation into Words?

Let your creativity go wild by turning a mathematical equation into a story! Watch this tutorial to see one example, and then write your own story to describe the given equation. See how creative you can get with math!
How Do You Turn a More Complicated Expression into Words?

This tutorial shows you how a mathematical expression can be turned into words. The best part? You can be super creative with the statement you make up! Check out the example statement created in this tutorial, and then make up your own!
What's an Irrational Number?

Is an irrational number just a way to describe a number that's lost its mind? Not really. :) An irrational number is simply a number that cannot be written as a fraction. Check out the definition, learn an important property of these special numbers, and take a look at some examples of irrational numbers.
What's a Real Number?

Real numbers are numbers that can be found on the number line. This includes both the rational and irrational numbers. This tutorial explains real numbers and gives some great examples. Take a look!
How Do You Square a Number?

Want to square a number? Just take the number and multiply it by itself! If you square an integer, you get a perfect square! Check out squaring in this tutorial!
How Do You Find the Square Root of a Perfect Square?

Taking the square root of a perfect square always gives you an integer. This tutorial shows you how to take the square root of 36. When you finish watching this tutorial, try taking the square root of other perfect squares like 4, 9, 25, and 144.
How Do You Find the Square Root of a Fraction?

Trying to take the square root of a fraction? This tutorial shows you how to take the square root of a fraction involving perfect squares. Check it out!
How Do You Estimate the Square Root of a Non-Perfect Square?

Trying to take the square root of a number that is not a perfect square? Think you need a calculator? Think again! This tutorial will show you how to estimate the square root of a number that is not a perfect square without the use of a calculator!
How Do You Figure Out if a Square Root is Bigger than Another Number?

Comparing a square root to another number can be rough, unless you remember that squaring is opposite of taking the square root. Then things get much easier! See how it's done in this tutorial.
What Happens When You Square a Square Root?

Remember that addition and subtraction are opposite operations and multiplication and division are opposite operations? Turns out, squaring and taking the square root are opposite operations too! See why in this tutorial!
How Do You Subtract Fractions with Different Denominators?

Subtracting fractions with unlike denominators doesn't have to be a nightmare. Just find a common denominator and everything calms down! See how to keep your fraction subtraction calm with this tutorial.
How Do You Subtract Fractions with the Same Denominator?

Subtracting fractions with like denominators? Just subtract the numerators and put the result over the common denominator! To see this process in action, check out this tutorial!
What's an Inequality?

Inequalities come up all the time when you're working algebra problems. In this tutorial you'll learn what an inequality is, and you'll see all the common inequality symbols that you're likely to see :)
How Do You Multiply and Divide Numbers with Different Signs?

A positive times a positive is a positive. A negative times a negative is a positive. What about a negative times a positive? This tutorial gives you the answer by showing you how multiply (and divide!) with mixed signs.
How Do You Find a Common Denominator and a Least Common Denominator?

This tutorial gives you some practice finding a common denominator and the least common denominator of three fractions. There's only one least common denominator, but there are many common denominators. This tutorial gives you one. Can you find another?
How Do You Multiply Fractions?

Working with fractions can be intimidating, but if you arm yourself with the right tools, you'll find that working with fractions is no harder than working with basic numbers. In this tutorial you'll see the process for multiplying 3 very simple fractions. Enjoy!
How Do You Add Fractions with Different Denominators?

Trying to add fractions with unlike denominators? You're going to need a common denominator first! Follow along with this tutorial and see what you need to do to add these fractions together.
How Do You Add a Negative Number to a Positive Number?

How do you combine a positive and a negative number? This tutorial shows you how. You even get to see it explained with a number line!
How Do You Figure Out Which of Two Fractions is Bigger?

Comparing fractions with unlike denominators? Don't want to find a common denominator? You don't have to if you take the cross product! Learn how to do this and make the comparison in this tutorial.
How Do You Multiply a Whole Number by a Fraction?

Multiplying a whole number and a fraction can be confusing, but this tutorial helps to sort things out. Check it out!
How Do You Multiply A Whole Number By A Fraction?

Multiplying a whole number and a fraction can be confusing, but this tutorial helps to sort things out. Check it out!
What Does Absolute Value Mean?

In this tutorial you'll see how you can think of absolute value in a very intuitive way. Let us know if you have any questions about it!
How Do You Figure Out the Sign of a Product or Quotient?

Multiplying and dividing numbers takes a good amount of thinking, and it's easy to make a mistake. But you can make sure that you're on the right track if you check whether the answer should be positive or negative. In this tutorial you'll see exactly how to tell if your answer will be positive or negative, even if you don't know the exact value of the answer. That way you'll always be able to check your answers!
What's a Prime Number?

Prime numbers aren't too hard to define, but they still puzzle professional mathematicians. Believe it or not, all over the word computers are chugging away, trying to find the next biggest prime! Bigger and bigger prime numbers help keep your credit card info safe through really cool encryption techniques. So prime numbers really matter every day, and you can learn how they are defined in this tutorial.
How Do You Add Fractions with the Same Denominator?

While adding fractions can be hard, adding fractions with the same denominator is just as easy as adding numbers. That's why when you add fractions you first get all of them to have the same denominator, and then add them up. In this tutorial you get to see just how easy it is to add up fractions once they have the same denominator!
How Do You Subtract a Positive Number from a Negative Number?

Subtracting a positive from a negative? Just remember: subtracting a positive is the same as adding a negative. See how it works in this tutorial!
How Do You Subtract a Negative Number from a Positive Number?

Subtracting a negative from a positive? Just remember: subtracting a negative is the same as adding a positive. See how it works in this tutorial!
What's a Venn Diagram, and How Do You Find the Intersection and Union of a Set?

Venn Diagrams are really great tools for visualizing sets, especially when it comes to how sets intersect and come together. Check out this tutorial and see what we mean!
How Do You Name a Set That's Graphed on a Number Line?

If you have ever stared at a number line with dots on it and wondered 'How could I summarize these dots?', then this is the tutorial for you!
How Do You Graph a Set on a Number Line?

Number lines are great ways to represent a group of numbers, and in this tutorial you'll see how to graph a group of numbers on a number line
How Do You Graph an Inequality or an Infinite Set on a Number Line?

Number lines are really useful in visualizing an inequality or a set. In this tutorial, you'll see how to graph both. Take a look!
How Do You Write an Inequality from a Number Line Graph?

Writing inequalities from a graph on a number line isn't so bad if you know what to do. Watch this tutorial to learn how!
How Do You Solve a Word Problem By Writing an Inequality?

Got an inequality in a word problem? This tutorial will show you how to define variables, translate a word problem into an inequality, and understand what it all means!
What's a Rational Number?

There are lots of different kind of numbers that you should know about, and that includes rational numbers. Check out the tutorial!
What's an Integer?

There are lots of different kinds of numbers that you'll come across in algebra, and a lot of these kinds of numbers are related to each other. Before you learn how they are related, you've got to learn about them separately, and in this tutorial you'll how to define integers :)
What's the Reciprocal Rule of Division?

When you divide fractions, the trick is to rewrite division as a multiplication. But the truth is that you can always rewrite division as a multiplication, and in this tutorial you'll see the rule that makes that possible!
What's a Reciprocal?

Reciprocals are important when it comes to dividing fractions, finding perpendicular lines, dealing with inverse proportions, and so much more! In this tutorial you can review the basics about reciprocals.
How Do You Find a Union and Intersection from a Venn Diagram?

Venn Diagrams are a convenient way to figure out the union and intersection of sets. Use this tutorial to get some practice with union, intersection, and Venn Diagrams.
How Do You Add and Subtract a Bunch of Numbers with Different Signs?

Some problems require adding and subtracting a combination of positive and negative numbers. Watch this tutorial and learn how to keep everything organized so you can find the answer!
How Do You Rewrite Subtraction as Addition?

Subtracting a positive is the same thing as adding a negative. Subtracting a negative is the same as adding a positive. Get a closer look with this tutorial!
How Do You Add Two Negative Numbers?

Adding two negative numbers together? Just add the absolute value of each number together, put a negative sign in front, and you have your answer! See how it's done in this tutorial.
How Do You Solve a Word Problem Where You Multiply and Subtract Whole Numbers and Fractions?

Word problems are a great way to see math in the real world. In this tutorial, you'll see how to translate a word problem to a mathematical equation. Then, see how to use the order of operations to get the answer!
How Do You Subtract a Whole Number from a Fraction?

Subtracting a whole number from a fraction can be tricky. Luckily, watching this tutorial can make this subtraction no big deal!
How Do You Subtract Decimals?

Doing math with paper and pencil can come in real handy, so make sure you're comfortable subtracting decimals by hand. After all, you don't want the calculator to be a crutch!
How Do You Add Decimals?

Doing math with paper and pencil can come in real handy, so make sure you're comfortable adding decimals by hand. After all, you don't want the calculator to be a crutch!
How Do You Multiply Decimals?

Doing math with paper and pencil can come in real handy, so make sure you're comfortable multiplying decimals by hand. After all, you don't want the calculator to be a crutch!
What are Trailing Zeros?

Ever wondered about the zeros that come at the end of a decimal number? What are those things anyway? Do they actually matter in terms of the value of the number? Watch the tutorial and see for yourself :)
How Do You Graph the Intersection of Two Inequalities?

Number lines help make graphing the intersection of two inequalities a breeze! This tutorial shows you how to graph two inequalities on the same number line and then find the intersection. Take a look!
How Do You Graph the Union of Two Inequalities?

Number lines help make graphing the union of two inequalities a breeze! This tutorial shows you how to graph two inequalities on the same number line and then find the union. Check it out!
How Do You Distribute With Whole Numbers and Fractions?

This tutorial shows you how to distribute a whole number into the sum of fractions. It's an important skill to have when you're solving equations, and you never know when it can come up. Be sure to check out this tutorial!
What are Consecutive Numbers?

Consecutive numbers are numbers in counting order. They tend to come up in words problems. Take a look at this tutorial to learn all about consecutive numbers!
How Do You Add Fractions with Variables?

Want to add fractions with the same variables but with unlike denominators? You'll need to find a common denominator! Don't worry. This tutorial will show you how!
How Do You Subtract Fractions with Variables?

Want to subtract fractions with the same variables but with unlike denominators? You'll need to find a common denominator! Don't worry. This tutorial will show you how!
How Do You Write Inequalities in Set Builder Notation?

Need some extra practice converting solution phrases into set builder notation? This tutorial was made for you! Follow along as this tutorial shows you how to dissect each phrase and turn it into a solution in set builder notation.
What Are Some Words We Use When We Have Inequalities?

Knowing the definition for a compound inequality is one thing, but being able to identify one in a word problem or phrase can be an entirely different challenge. Arm yourself by learning some of the common phrases used to describe a compound inequality and an absolute value inequality.
What is a Constant?

Constants are parts of algebraic expressions that don't change. Check out this tutorial to see exactly what a constant looks like and why it doesn't change.
What's Another Definition for an Integer?

Integers are everywhere in math, so it's important to know what an integer is. This tutorial explains this special type of number so that you can identify one when you see it! Sometimes, a number is an integer even though it doesn't look like one. Watch this tutorial to see how to identify those too!
What's a Term?

Polynomials are those expressions that have variables raised to all sorts of powers and multiplied by all types of numbers. When you work with polynomials you need to know a bit of vocabulary, and one of the words you need to feel comfortable with is 'term'. So check out this tutorial, where you'll learn exactly what a 'term' in a polynomial is all about.
What's Another Definition for Prime and Composite Numbers?

If the only factors a number are 1 and itself, then that number is prime. A number that is not prime is called composite. Learn about prime and composite numbers by watching this tutorial!
What's a Perfect Square?

Anytime you square an integer, the result is a perfect square! The numbers 4, 9, 16, and 25 are just a few perfect squares, but there are infinitely more! Check out this tutorial, and then see if you can find some more perfect squares!
What are Equivalent Expressions?

If two things are equivalent, they are the same. Equivalent expressions are expressions that are the same, even though they may look a little different. If you plug in the same variable value into equivalent expressions, they will each give you the same value when you simplify. Learn more about equivalent expression by watching this tutorial!
Why Can't You Divide By 0?

Why can't you divide by 0? This may be one of the most asked math questions. Get this question answered once and for all by watching this tutorial!
What Does Absolute Value Mean In the Real World?

You may know how to calculate the absolute value of a number, but what are you really finding? This tutorial uses a real world example to help you gain a better understanding of absolute value.
What Are Numerical and Algebraic Expressions?

An expression is just a mathematical phrase. In this tutorial, you'll learn about two popular types of expressions: numerical and algebraic expressions. A numerical expression contains numbers and operations. An algebraic expression is almost exactly the same except it also contains variables. Check out this tutorial to learn about these two popular kinds of expressions!
What is the Substitution Property of Equality?

If you ever plug a value in for a variable into an expression or equation, you're using the Substitution Property of Equality. This property allows you to substitute quantities for each other into an expression as long as those quantities are equal. Watch this tutorial to learn about this useful property!
What are the Rules for Using Absolute Values to Add Integers?

When you're combining numbers, there are some helpful rules to make that process a little easier. This tutorial shows you the rules for using absolute values to combine integers with the same sign or with opposite signs. Take a look!
What is the Opposite, or Additive Inverse, of a Number?

Have you ever combined two numbers together and found their sum to be zero? When that happens, those numbers are called additive inverses of each other! In this tutorial, you'll learn the definition for additive inverse and see examples of how to find the additive inverse of a given value.
How Do You Add Variables that Are the Same?

Variables are a big part of algebra, so it's good to be comfortable working with them! In this tutorial, you'll see how to combine variables that are alike.
How Do You Add Like Terms?

If you work with variables, you need to know how to add like variables together. This tutorial shows you exactly that! Follow along and see how to add like terms together.
How Do You Subtract Like Terms?

Subtracting like terms is a lot like subtracting numbers! This tutorial shows you how to perform subtractions with like terms.
How Do You Determine if a Value is a Solution to an Inequality?

If you're not sure if a value is a solution to an inequality, you an always plug it in and see. This tutorial shows you how to determine if a value is a solution to an inequality.
How Do You Evaluate an Expression with Exponents?

Need to plug in a variable value into an expression? Great! Does the expression have an exponent in it? Even better! Follow along with this tutorial as you see how to simplify an expression for a given variable value.
How Do You Evaluate an Exponent?

Exponents just indicate repeated multiplication. Watch this tutorial to see how you can evaluate an exponent by first writing it in expanded form. Take a look!
How Do You Divide a Decimal by a Decimal?

Dividing decimals? Then this tutorial is a must see! Follow along and learn how you can divide decimals by rewriting the problem as a fraction and then using long division to solve. Check it out!
How Do You Divide Fractions?

Dividing fractions? Change that division to a multiplication by multiplying the dividend by the reciprocal of the divisor. Learn all about it by watching this tutorial!
How Do You Put Real Numbers in Order?

Ordering numbers from least to greatest? Are the numbers in different forms? To make comparing easier, convert all the numbers to decimals. Then, plot those decimals on a number line and compare them! This tutorial shows you how!