REVIEW:
Complex Fractions

Ratios


Ratios are amazing and used a lot in engineering, especially conversions. They are basically fractions, but they are a little different, because they describe a relationship between the numerator (top ) and the denominator (bottom ) such as π /180

Ratio -A story

Let's say you are woodworking with a partner. You are from the U.S and he European. Thus you both have two different measuring sticks;Your's is in feet. His is in meters. You will both need to know how to convert between the two measurements. How is this done?

The Solution

Step 1. Realize that you will have to convert feet to yards and then yards to meters. Sounds hard but it's very simple. There are 3feet in 1yard and 1 yard in 0.9144meters

Step 2: Make a fraction(ratio) with those numbers

When making the fraction put what you want to get rid of in the bottom

EXAMPLE:

3yard/1foot

The foot is in the bottom so we can cancel out the ft units

Solving the Problem

36ft * 3yard/1foot    = 108yards

108yards* 0.9144meters/1yard = 118.10988yards

Apply ratios to Trigonometry?

Mathematics and the trig functions such as sin( ) and cos() take in an angle that is in radians not degrees, but with a simple conversions you can still use degrees.

CONVERT to degrees to Radians:

36° * πradians/180° = 0.62831853071radians

The degrees cancel out and we are left with only radian units


What is a proportion?

it is two ratios equal to each other such as 1 tent / 5people = x tent / 20people You want to solve for x or in other words how many tents would you need for 20 people. Simple as that.

How to solve

Imagine you are camping. You realize you need 1 tent for every 5 people (1/5 ). Your last trip you had exactly five people so you only needed 1 tent. However, on your next trip you will have 20 people ( x / 5 )!

You cross multiply then solve for x.

Write them as fractions

1/5 = x / 20

Cross Multiply

1* 20 = 20

5*x = 5x

5x = 20

Isolate x

divide 5 by x and divide 20 by 5

x = 4. We need 4 tents

Tent Original

Tents Needed

x

Person Original

Persons Coming


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