How to Calculate Ratios and Proportions in Math

Ratios and Proportions are a very important part of math for those just starting off. They describe the relationship between two amounts by a single number.



They are used everywhere in life; how many eggs to cups flour in the cookie recipe and how many miles per gallon does a car consume are two examples.

Difficulty:

Easy

Instructions

Things You'll Need

• Paper
• Pencil or Pen

How to compute ratios and proportions

1. Identify the amounts that are being compared. If comparing apples to oranges, then the amount of apples and the amount of oranges must be known. Express each as a number. For example, let's say I have 20 apples and 10 oranges.

2. Decide which will be the first quantity. Are apples going to be described first, or oranges?

3. Divide the first quantity by the second quantity. If I choose apples, then I would divide as follows:

   number of apples (20) divided by (/) number of oranges (10) equals (=) proportion of apples to oranges (2)

   20/10 = 2

4. Describe the result in words. From the result of step 3, I would have 2 apples for every orange.

Other examples

1. Lets say your car used 10 gallons to go 300 miles. Compute the miles per gallon for your car.

2. Amount of miles (300) divided by amount of gas (10) equals miles per gallon

   300 / 10 = 30 miles per gallon.

3. You and your four friends won 700 dollars. If the five of you get equal shares, how much money does each person get?

4. Amount of money (700) divided by number of people (5) is the money per person.

   700 / 5 = 140 dollars per person.

5. If a batch of cookies needs 3 eggs, how many batches can you cook with 12 eggs?

6. In this problem, we use the ratio given.

   12 eggs divided by 3 eggs per batch = 4 batches.

Tips & Warnings

• Always try to express the problem as an A per B

• In real life, the numbers are not always simple. Use a calculator when needed.

Resources

• Read this Article in Spanish