Learn about proportions, how they are used, attempt quiz on proportions

Last updated : 30 April 2024, Tuesday

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What is a proportion ?

A proportion is a mathematical statement that two ratios are equal.

Proportions can be written in various ways, including:

  1. Using a double colon (::) : For example, 3:5 :: 6:10.
  2. As fractions: For example, 3/5 = 6/10
  3. Using the equals sign (=): 3:5 = 6:10
  4. In words: “Three to five is equal to six to ten.”

How are Proportions Used ?

Proportions are used in many different areas of mathematics, including geometry, algebra, and trigonometry. They are also used in many real-world applications, such as cooking, construction, and finance.

Here are some examples of how proportions are used:

  • Cooking: A recipe may call for a certain proportion of ingredients, such as 1 part flour to 2 parts milk. This means that for every 1 cup of flour, you need to use 2 cups of milk.
  • Construction: Architects and engineers use proportions to design buildings and other structures.For example, the Golden Ratio is a specific proportion that is often used in architecture to create visually pleasing designs.
  • Finance: Investors use proportions to compare the performance of different investments. For example, a mutual fund may have a return of 10% per year, while a stock market index may have a return of 5% per year. This means that the mutual fund is outperforming the stock market index by a proportion of 2:1.

How to Solve Proportions Problems?

There are two main ways to solve proportion problems:

  1. Using cross-multiplication: This method involves multiplying the numerator of one ratio by the denominator of the other ratio, and vice versa. For example, to solve the proportion “3:5 = 6:10,” you would multiply 3 by 10 and 5 by 6. This gives you the equation 30 = 30, which is true.
  2. Using the unit rate: This method involves dividing both sides of the proportion by the same number. For example, to solve the proportion “3:5 = 6:10” you would divide both sides by 5. This gives you the equation 3=3, which is also true.

Proportions practice

Proportions Questions

Questions 1-5 are short text

Questions 6-13 have single answer correct

Questions 14-23 have one or more answers correct

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Problem: Coffee Bean Blend

A company has two types of coffee beans:

Type A costs $10 per pound, and Type B costs $15 per pound.

The company wants to mix the two types of beans to create a new blend that costs $12 per pound.

What is the ratio of Type A to Type B beans in the new blend?

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Problem : Train Meeting Time

A train leaves New York at 10:00 AM and travels west at a speed of 60 mph.

Another train leaves Chicago at 11:00 AM and travels east at a speed of 70 mph.

The distance between New York and Chicago is 900 miles.

At what time will the two trains meet?

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Problem: Pool Filling Time

A swimming pool has a volume of 10,000 gallons of water.

A hose is turned on and fills the pool at a rate of 50 gallons per minute, while a drain is opened and empties the pool at a rate of 25 gallons per minute.

How long will it take to fill the pool?

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A container is filled with a mixture of two liquids, P and Q, in the ratio 7:5. If 8 liters of liquid Q are added to the mixture, the ratio becomes 7:9. What was the initial volume of the mixture?

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In a mixture , the ratio of alcohol to water 3:4 . If the amount of water is increased by 10 litres , the ratio becomes 3:5 . What is the original amount of alcohol in the mixture?

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In a Certain business partnership , the profit sharing ratio between three partners X , Y and Z is 4:5:6 . If partner Y receives $500 more than X , what is the total profit?

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A chemical solution contains substances A,B, and C in the ratio 5:3:2 . If there are 15 grams of substance B , how many grams of substance A are there?

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In a school , the ratio of students studying Arts to Science to Commerce is 3:5:7 . If the difference between the number of Science and Commerce students is 40 , how many students study Arts?

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The ratio of boys to girls in a class is 3:4 . If there are 21 boys , how many girls are there?

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A mixture contains water and juice in the ratio 3:5 . If there are 9 litres of water , how many litres of juice are there?

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The ratio of the number of apples to oranges in a basket is 4:6 .If there are 16 apples , how many oranges are there?

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The gears of a machine are in the ratio 5:3 . If the smaller gear makes 300 rotations , how many rotations does the larger gear makes?

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If a:b = 3:4 and b:c = 5:6, what is the ratio a:c?

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Real-World Applications
Question: In which of the following scenarios can proportions be used?

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Properties of Proportions
Question: Which of these properties are true for all proportions?

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Scale Factors
Question: Which statements are true regarding scale factors in proportions?

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Basic Proportion Concept
Question: Which of the following statements are true about proportions?

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Identifying Proportions
Question: Identify which of the following are examples of proportions:

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Solving Proportions
Question: If 4/5 = x/10, what are the possible values of x?

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Direct and Inverse Proportion:
Question: Identify the type of proportion (direct or inverse) in each scenario:

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Complex Proportions
Question: If 3/x = 4/6, what are the possible values for x?

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Ratios and Proportions
Question: Which statements are true about ratios and proportions?

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Proportionality in Geometry
Question: In geometry, proportions are used to:

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