Proportions Meaning | unipolaris academy

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

Last updated : 29 June 2024, Saturday

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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:

Using a double colon (::) : For example, 3:5 :: 6:10.
As fractions: For example, 3/5 = 6/10
Using the equals sign (=): 3:5 = 6:10
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:

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.
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

1 / 23

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?

2 / 23

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?

5 / 23

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?

$3000

$4500

$6000

$7500

7 / 23

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?

10 grams

25 grams

30 grams

20 grams

8 / 23

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?

9 / 23

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

10 / 23

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?

11 / 23

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?

12 / 23

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?

180

500

480

360

13 / 23

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

3/5

15/24

5/8

9/16

14 / 23

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

Calculating the speed of a car.

Finding the actual height of a building using its scale model.

Dividing a pizza among friends

Predicting population growth.

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

Inverting both ratios in a proportion preserves the equality.

The product of means equals the product of extremes.

Adding the same number to the numerator and denominator of a ratio preserves the proportion.

Proportions can be represented as fractions.

16 / 23

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

The scale factor is the ratio of any two corresponding lengths in two similar figures.

Scale factors are always greater than 1.

Scale factors can be used in map reading.

A scale factor of 1 indicates identical sizes.

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

A proportion is an equation that states two ratios are equal.

Proportions are used to solve problems involving scale.

The cross-products of a proportion are always equal.

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

3/4 = 6/8

5/10 = 2/5

7/14 = 1/2

9/3=6/2

19 / 23

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

20 / 23

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

The number of workers on a task and the time taken to complete it.

The speed of a vehicle and the time taken to travel a fixed distance.

The amount of paint used and the area covered.

The volume of gas and its pressure at constant temperature.

21 / 23

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

4.5

22 / 23

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

A ratio is a comparison of two quantities.

All ratios are proportions.

A proportion is a statement that two ratios are equal.

Ratios can be written in fractional form.

23 / 23

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

Calculate the area of triangles.

Determine similar figures.

Find the lengths of missing sides in similar polygons.

Measure angles in right triangles.

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