What is 8 of 30? Unlocking the Key to Proportions!

Proportions is a mathematical concept that deals with the relationships between quantities. Understanding the concepts of proportions is essential to solving problems in real-life situations. In this digital age, most of us rely heavily on technology, which has made life easier for everyone. However, it is essential to keep in mind that we must also have a basic understanding of mathematics, including proportions. So, what is 8 of 30? How can we use this concept in day-to-day life? Let’s explore the answers to these questions and much more.

The Basics of Proportions

Proportions are the comparison of two ratios. Ratios describe the relationship between two quantities, and this relationship is expressed as a fraction. A proportion is a mathematical statement that two ratios are equal. The general form of a proportion is:

a:b = c:d

where ‘a’ and ‘c’ are called the first terms, and ‘b’ and ‘d’ are called the second terms. For example, if 5 apples cost $6, then the ratio of the cost of apples to the number of apples is 6/5 or 1.2. Now let’s see its proportion:

Cost: Number of apples = 6:5

What is 8 of 30?

‘8 of 30’ means that 8 is a part of 30. It can be expressed as a ratio in the form of 8/30, which may be simplified as 4/15. In other words, 8 out of 30 is equivalent to 4 out of 15. We can also express it as a percentage, which is approximately 26.67%.

Application of 8 of 30

Understanding ‘8 of 30’ is essential because it allows us to solve various real-life problems that involve proportions. For example, suppose a company conducted a survey of 3000 online shoppers and found that only 800 of them were satisfied with the service. Now, the company wants to estimate how many of the 30,000 customers will be satisfied. Here, we can use the concept of ‘8 of 30’ to estimate the number of satisfied customers. Since 800 customers are satisfied out of 3000, the proportion of satisfied customers is:

800 : 3000 = x:30000

By calculating the above proportion, we get ‘x’ as 8000. Therefore, we can conclude that 8000 of the 30,000 customers will be satisfied. This is a simple example, but the applications of the concept of proportions are endless.

This is How to Solve Proportions

  • Step 1: Identify the two ratios and write them in fraction form.
  • Step 2: Determine the unknown value ‘x’ in the proportion.
  • Step 3: Cross-multiply the fractions.
  • Step 4: Solve for ‘x’.

Example

Suppose it costs $6 for 5 gallons of petrol. How much will it cost for 8 gallons?

Cost of 5 gallons: Cost of 8 gallons = 6: x

Cross-multiplying yields:

5x = 48

Divide both sides by 5 to find the value of ‘x’:

x = 9.6

Therefore, the cost of 8 gallons of petrol is $9.6.

Direct Proportions

In a direct proportion, the two quantities increase or decrease at the same rate. If we double one quantity, the other quantity will also be doubled. The general form of a direct proportion can be represented as:

y = kx

Here, ‘y’ and ‘x’ are the two quantities, and ‘k’ is the constant of proportionality.

Example

Suppose a person walks 4 miles in 1 hour. How much time will he need to travel 12 miles?

We can use the formula y = kx, where y is distance, x is time, and k is the constant of proportionality.

Substituting the values into the formula yields:

4 = k * 1

k = 4

Now we can determine the time required to travel 12 miles:

y = k * x

12 = 4 * x

x = 3

Therefore, the person will take 3 hours to travel 12 miles.

Inverse Proportions

In an inverse proportion, the two quantities vary inversely to each other. In other words, if we increase one quantity, the other quantity decreases, and vice versa. The general formula of an inverse proportion is:

y = k/x

Here, ‘y’ and ‘x’ are the two quantities, and ‘k’ is the constant of proportionality.

Example

Suppose a machine can produce 10 units per hour. How much time will it take to produce 40 units?

We can use the formula y = k/x, where y is the total production, x is the time, and k is the proportionality constant.

Substituting the values, we get:

10 = k/1

k = 10

To find the time required to produce 40 units, we can use the same formula:

y = k/x

40 = 10/x

x = 2.5

Therefore, the machine will take 2.5 hours to produce 40 units.

Bonus Tip: Cross Multiplication

Cross Multiplication is a shortcut method that can be used to find out the value of an unknown quantity ‘x’ by multiplying the numerator of one ratio with the denominator of the other ratio. This method can be used to solve a variety of proportionality problems. Let’s understand it with an example:

Example

Suppose, x and y are in a direct proportion. If x = 3 when y = 5, what is x when y = 7?

We can use cross-multiplication to find the value of ‘x’.

5/3 = 7/x

Cross multiplying the above equation gives:

5x = 21

Divide both sides by 5 to find the value of ‘x’:

x = 4.2

Therefore, when y = 7, x is equal to 4.2.

Conclusion

The concept of proportions is fundamental in mathematics, and it is used in various fields such as science, engineering, and finance. In this guide, we explored the basics of proportions and how to solve them. We also discussed the different types of proportions, including direct and inverse proportions. Understanding proportions is essential because it helps us make estimates and predictions based on known quantities. The formulae and methods described in this guide can be applied to a wide range of real-life problems.

FAQs

  • What is a proportion?

    A proportion is a statement that two ratios are equal.

  • What is the formula for a proportion?

    The general form of a proportion is a:b = c:d.

  • What is 8 of 30?

    ‘8 of 30’ means that 8 is a part of 30. It can be expressed as a ratio in the form of 8/30 or simplified to 4/15.

  • What is cross multiplication?

    Cross multiplication is a shortcut method to solve proportionality problems.

References

  • https://www.mathsisfun.com/algebra/proportions.html
  • https://www.splashlearn.com/math-vocabulary/algebra/proportionality
  • https://www.math-only-math.com/proportion.html
  • https://www.purplemath.com/modules/ratio.htm

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