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## Welcome to the guide on Ratios

Please note this topic is a big differentiator in getting a high score

There are no prerequisites for this lesson, but it may help to review the percentages lesson first.

First, let’s understand what a ratio/proportion is. Visit any of these links to better understand the fundamentals:

• How To Solve Ratios And Proportions (Very good for basics, visit this first if you have no previous experience with ratios)

• Cross products (Gives a good background, as well as an introduction to cross products)

• Types of problems (Moves on to proportions, gives a basic understanding of problems you might see)

• Advanced knowledge  (Here’s a very advanced cover - so don’t feel pressured into understanding everything here.)

If you’re here, you should now have a good understanding of the above concepts. If not, or if you have any questions, don’t be afraid to go back and review! However, if you want to practice and warm up, use some of the links below:

• Guided Practice (The question is in green and the answer is explained below that)

1. Ammonia is a compound consisting of a 1 : 3 ratio of nitrogen and hydrogen atoms. If a sample of ammonia contains 156 nitrogen atoms, how many atoms of hydrogen are present?​​

2. Ammonia is a compound consisting of a 1 : 3 ratio of nitrogen and hydrogen atoms. If a sample of ammonia contains 1425 hydrogen atoms, how many nitrogen atoms are present?

3. Methane is a compound consisting of a 1 : 4 ratio of carbon and hydrogen atoms. If a sample of methane contains 1565 atoms, how many carbon and hydrogen atoms are present?

4. Methane is a compound consisting of a 1 : 4 ratio of carbon and hydrogen atoms. Can a sample of methane contain a total of 1566 atoms?

5. The length of a violin string varies inversely as the frequency of its vibrations. A violin string 14 inches long vibrates at a frequency of 480 cycles per second. Find the frequency of a 12 -inch violin string.

6. A backyard pond has 12 sunfish and 30 rainbow shiners. Write the ratio of sunfish to rainbow shiners in simplest form.

7. Ms. Ekpebe's class has 32 students, of which 20 are girls. Write the ratio of girls to boys.

8. CHALLENGE: If a varies inversely with the square root of b, and a = 7 when b = 36, find a when b = 289.