# Equation Manipulation

Manipulating the equation by rearranging and making it easier to solve for the unknown. If you know how to do this then you can solve many problems.

We will make it real simple so that it is easy to understand. Remember, what ever you do on one side of the equation do the same on the other side

##### Example 1

12 = a + 4 solving foraby getting a by itself on one side of the equation to solve for a you will have to cancel the + 4. you do that by subtracting 4 from a + 4 What ever you do on one side of the equation do the same on the other side and you end up with 12 - 4 = a + 4 - 4 -- the plus 4 and minus 4 cancel each other out and you end up with 12 - 4 = a

##### Example 2

12 = a - 4 here to isolateayou have to add a 4 to both sides 12 + 4 = a - 4 + 4 which becomes 12 + 4 = a

##### Example 3

12 = a * 4 here to isolate theadivide both sides of the equation by 4 12 / 4 = a * 4 / 4 --- the multiply by 4 and divide by 4 cancels each other and it becomes 12 / 4 = a

##### Example 4

12 = a / 4 here to isolate theamultiply both sides of the equation by 4 12 * 4 = a / 4 * 4 --- the divide by 4 and then multiply by 4 cancels each other and it becomes 12 * 4 = a

##### Example 5

12 = a + b here to isolateayou have subtract b from both sides 12 - b = a + b - b --- the plus and minus b cancel each other and the equation looks like this 12 - b = a

##### Example 6

12 = a * b this time we isolate thebto do that divide both sides by a 12 / a = a * b / a ---multiplying a * b and then dividing it by a cancels each other and you are left with 12 / a = b

If you understand all this then you should have little problem with solving sides and angles.

##### Example 7

Using the tangent function solving for an unknown side or angle in a triangletan A = opposite / adjacent

to solve something like this you need to know 2 of the values

If you know the angle and one side you can use the tangent function

A = 25°

b the adjacent side = 12 the equation would look like this

tan 25° = opposite / 12

You can get the value for tan 25° by looking it up in a natural tangent's chart or use a calculator set to degrees, punch in 25 and hit the tan button = 0.4663 rounded to 4 digits.

The equation then looks like this:

0.4663 = opposite / 12

To make it easier to solve rearrange the equation

0.4663 = opposite / 12 --- isolate opposite by multiplying both sides by 12 0.4663 * 12 = opposite / 12 * 12 --- dividing and multiplying by 12 cancels each other and you end up with 0.4663 * 12 = opposite --- 0.4663 * 12 = 5.5956

##### Example 8

Same problem as before but this time you know the 2 sides and need to solve the angle.You can't use the tangent function. The tangent function takes an angle measurement as input and returns a ratio as the result. Arc tan takes a ratio as an input and returns an angle measurement as the result.

arctan A = opposite / adjacent

opposite = 6

adjacent = 12

arctan A = 6/12

arctan A = 0.5 on your calculator punch in the shift key, the up arrow, and 0.5 tan -1 and the result should look like 26.5651°

##### Construction Math Calculators

#### Area Calculation

#### Arithmetic

#### Estimating / Multiplier

#### Fractions and Decimals

#### How to do things

- Convert Feet in Decimal Format to Foot, Inch and Fraction
- Calculate the Square Footage of a Rectangle Shaped Area
- Equation Manipulation
- Calculating with Percentages

#### Solving a Duel Pitch

- What can you do with the roof pitch?
- Solving for length's aa and ab
- Calculating the Height
- Solving the Angles