Isolate Variable

Isolate a variable by:
1) Changing all "-" signs to "+ the opposite"
2) Use the distributive property
3) Identify like terms
4) Combine like terms
5)Add the opposite
6)Divide since division is the opposite of multiply

Showing a triangle is a right triangle by using algebra.

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Volume in cubic miles

We must think of the irregularly shaped object as a collection of known geometric shapes. Remember the formulas for are of a rectangle and a semicircle. We need to recall that the formula for Volume is area of base multiplied by height.

Isolate variable with mixed numbers

Container word problem

Here we recall "times" means multiply and we let a variable represent the unknown quantity.

Finding a point with certian constraints.

Simplifying an expression invoving exponents.

Irregularly shaped object volume

Consecutive Integers

Translating words to mathematical symbols is the key here.

Inverse Function

In this example you must exchange the place of the x and y variable and then isolate the y.

PERCENTAGE

In this example there are alternative methods utilized. Here we must focus on the English language. What is described by the word "is"? What is described by the word "of"? What is associated with the word "percentage"? The answers to these questions are what guide us in the solution.

ratios

A ratio can be a  gnarly thing. In particular this ratio is not very nice.

pythagorean triplets

multiples are very important here.

Simplifying a Rational Expression

We honor mathematical properties here.

Consecutive Even Integers

Calculating the Volume of a Pyramid

The formula is 1/3 of the area of the base of the pyramid multiplied by the height or the pyramid.

Graphing an exponential equation with out a graphing calculator

Here I demonstrate how our grandparents did it.

Calculating Volume involving liters and centimeters.

A rectangular solid with a base measuring 96 square cm has 1.2 liters of liquid in it. What is the height of the liquid.

We must remember that 1 cubic centimeter is equal to 1 millimeter. 1000 cubic centimeters equals 1 liter.

Motion problem with equal Distance

Substitution and observing the distance between the school and the house is the same regardless of whether you are going to or coming from school is the key in this example.

Volume Displacement

Here we think of the irregularly shaped rock with volume 300 cubic centimeters as a rectangular solid with the same volume.

Evaluate Variable Expression

Care must be taken when substituting your values for your variables.

Isolate Variable Example

I refrain from explaining in great detail given my prior post.

Polynomial Division

It is critically important when dividing polynomials to honor the euclidean algorithm. You can't think in terms of "how many times does the divisor go into the dividend?" You must instead repeatedly ask the question "what do I multiply the first term in my divisor by to get the first term in my dividend?" Once this question is answered you MUST honor the distributive property and handle your subtraction with care.

Finding the X and Y intercepts of a Linear Equation

This concepts becomes clear when we realize what is happening to our coordinates when we are on the respective axis. Substitution yields the solution.

Isolate a variable

"Isolating a variable" is the way to describe the process we do when finding the value for a variable in an equation. All operations in mathematics can be paired with their inverse operation. When thinking of the solution to x+2=5 most student's brain is saying "what number do I add to 2 to get a 5?" This is all fine and dandy until you get to a more complicated problem. That is why certain language of the discipline must be introduced. Words and phrases such as: inverse operation, multiplication property of equality, addition property of equality, and combining like terms. With this language in place we can now think of x+2=5 as actually saying "what number do i get when I subtract 2 from 5?"

Classifying Triangles

Here I identify the various words for classifying a triangle. Every triangle can have two words associated with it. One word describes some information about the triangle's side lengths (scalene, equilateral, or isosceles) the other word describes some information about the triangle's angle measures (acute, right, or obtuse).

Simplifying Rational Expressions

In this post I sum two rational expressions. I use the Least Common Multiple. Although there are Polynomials for denominators I treat them as if they were numbers. Polynomials behave like numbers.

Uniform Motion

Here we investigate the classic train station type problem. 

 

Dividing fractions

Here is an example involving division of two mixed numbers. We first change the mixed numbers to improper fraction then we honor the definition of division.