Ratio and Proportion

A ratio is the relationship between two numbers. A ratio can be written using a colon such as:

1:2, 5:9, 20:60 or as a fraction 1/2, 5/9 or 20/60

A proportion exists when the relationship between one ratio is the same as the relationship between the second ratio. To determine if the ratio is proportional or not – they are cross multiplied and if the answer is equal they are proportional.

Examples: –

1. Determine if 3/9 is proportional to 6/18.

Again – cross multiply = 3 X 18 = 54 and 9 X 6 = 54 = Proportional

2. Is 5:9 and 6:20 proportional?

Still cross multiply = 5 X 20 = 100 and 9 X 6 = 54 = Not Proportional

To use this process, we need to discuss one more major step and then provide some basic rules. The first step is what to do when one part of the ratio is unknown:

2/15 and ?/50

Again cross multiply = 2 X 50 = 15 X ?

Remember how we moved the numbers to other sides of the = to solve for the (?) by dividing both sides by 15

X = (2 X 50) / (15)

(100) / (15) = 6.67

Example:

If it takes 5 pounds of calcium hypochlorite to give the correct dosage in a 35 gallon tank, then how many pounds will it take to make 12 gallons?

Step 1 – Set up the proportion with the same types of units on one side of the colon.

Pounds : Gallons

Step 2 – The numerators must contain the same size of units (either larger or small units), and the denominator must contain the same size units (either larger or smaller) or: (Smaller Value)/(Larger Value):(Smaller Value) / (Larger Value) or:

(Larger Value) / (Smaller Value):(Larger Value) / (Smaller Value)

Step 3 – Solve for the mixing number

Step 4 – Set up this problem:

(5 lbs)/(?) : (35 gal)/(12 gal)

Cross multiply – (5 lbs X 12 gal) = (? X 35 gal), get ? by itself by dividing both sides by 35 lbs

(?) = (5 lbs X 12 lbs) / (35 gal) = 1.7 lbs

Example:

If one chlorine cylinder is used in 20 days, how many will be used in 100 days?

Step 1 – Set up proportion – 1 cylinder is to 20 days as X cylinders is to 100 days

(1 cylinder / ?):(20 days / 100 days)

Step 2 – Cross multiply – (? cylinders X 20 days) = (1 cylinder X 100 days)

Step 3 – Rearrange to get the ? on the left by itself by dividing both sides by 20 days

? cylinders = (1 cylinder X 100 days) / (20 days) = 5 cylinders

Practice Problems:

1. It takes 6 gallons of chlorine solution to get a proper residual when the flow is 45,000 gpd. How many gallons will it take when the flow is 62,000 gpd?

2. A motor is rated at 41 amps average draw per leg at 30Hp. What is the actual Hp when the draw is 36 amps?

Answers:

1. (6 gallons) / (? gallons):(45,000 gpd) / (62,000 gpd)

(6 gal X 62,000 gpd) = (? gal X 45,000 gpd)

? gal = (6 gal X 62,000 gpd) / (45,000 gpd) = 8.3 gal

2. (41 amps) / (36 amps) = (30 Hp) / (? HP)

(41 amps X ? Hp) = (36 amps X 30 Hp)

? Hp = (36 amps X 30 Hp) / (41 amps) = 26.3 Hp