125 Math Tutorials

These Math tutorials are written by experienced educators, all of whom also offer private tutoring lessons. Get the Math help you need, whether through these tutorials or through private tutoring lessons.

Probability of Drawing a Full House

We are going to randomly select 5 cards from a standard deck of 52 playing cards. We will find the probability of drawing a full house. First let us define a full house. A full house is a combination of a three of a kind and a pair. Ex: Three aces with two kings A…

One-Step Equation

Solving a One-Step equation is to find the solution for an unknown.

Differential Equations

Handling of Materials Suppose that we have a tank containing water. Suppose also that we have 2 pumps — one pump can drain the tank in 6 hours, and the other can drain the tank in 5 hours. How long will it take to drain the tank with both pumps running? Since one pump can…

Evaluate variable expressions involving integers

Starting with the basics is variables (symbols for an unknown number, usually a letter like x or y) involving integers (an integer is a whole number, not a fraction). “Evaluate variable expressions involving integers” is the same as saying “solve for x using whole numbers”. With this, we need to know the following: 1) We…

Evaluate variable expressions involving rational numbers

Variable expressions involving rational numbers are one of the first lessons in Algebra 2. A rational number is basically a fraction or a decimal, but it can’t repeat forever (infinity). Technically, it’s “any number that can be expressed as the quotient or fraction p/q of two integers.”-mathforum.org. For example, .8, which can be expressed as…

Defining Units

Labor Imagine doing some labor. All things being equal, you would expect to do twice as much work in 2 hours as you would in only 1 hour. Using much the same reasoning, you would also expect, if you had another person helping you, to perform twice as much labor in a given 1 hour…

The Birthday Problem

The subject does say statistics, I couldn’t find probability so I found the closest relative. This infamous problem confuses the heck out of most people when first come across. The question at hand is: suppose you are at a birthday party and you make a bet with a friend. You say you can find at…

Introduction to the Substitution Method for Linear Equations

The substitution method is one algebraic way to find the point where two lines intersect, or in other words, solve the system of equations. The first step to this is to solve for one of the variables, in this case we’ll call it “y” in one of the two equations. Next, you would SUBSTITUTE the…

Derivatives and Integrals

Fine a derivative and an integral that are the same.

Dividing Fractions quicker when denominators are equal

I have to divide a fraction by a fraction. Normally, I need to ‘flip’ the divisor and then multiply. Is there a quicker or easier way to do it?

^