Embark on an enthralling mathematical journey as we unravel the mystery of “what percent is 20 of 36?” Delve into a world of proportions, calculations, and alternative methods, where the intricacies of percentage unfold before your very eyes.
Prepare to witness a symphony of numbers as we establish proportions, solve equations, and uncover the hidden relationships that govern the enigmatic realm of percentages.
Introduction: What Percent Is 20 Of 36
Percentage, denoted by the symbol “%”, is a mathematical concept that represents a fraction of 100. It is widely used in various fields, such as mathematics, science, economics, and everyday life, to express proportions and compare quantities.
In this particular problem, we aim to determine what percentage 20 is of 36. To solve this, we will utilize the formula: Percentage = (Part / Whole) x 100, where “Part” represents 20 and “Whole” represents 36.
Solution
Setting up a Proportion
To solve for the unknown value (x), we can set up a proportion:“`
/x = 36/100
“`This proportion states that the ratio of 20 to x is equal to the ratio of 36 to 100.
Solving the Proportion using Cross-Multiplication
We can solve for x by cross-multiplying the terms in the proportion:“`
- 20
- 100 = x
- 36
“`This gives us:“`
= 36x
“`Dividing both sides by 36, we get:“`x = 2000 / 36“`Therefore, x = 55.56.
Calculation
To calculate the value of x using the solved proportion, we need to set up an equation based on the proportion.
Solving for x, What percent is 20 of 36
The proportion we solved earlier is: 20/36 = x/100
To solve for x, we can cross-multiply the terms:
20 – 100 = 36 – x
Simplifying the equation:
2000 = 36x
Dividing both sides by 36:
x = 2000/36
x = 55.56
Therefore, 20 of 36 is approximately equal to 55.56.
Example
To illustrate the proportion and its solution, we can create an HTML table:
The table shows the proportion as a fraction and as a percentage, and it also includes the solution to the proportion.
HTML Table
| 20 | x | 36 | 100 |
|---|---|---|---|
| Part | Unknown | Whole | Percentage |
| 20 | x | 36 | 100 |
The table shows that 20 is part of the whole, which is 36. The percentage is 100. The unknown, x, can be solved by setting up a proportion:
/36 = x/100
Solving for x, we get:
x = (20
100) / 36 = 55.56
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But don’t forget to come back and figure out what percent 20 is of 36!
Therefore, 20 is 55.56% of 36.
Alternative Method
An alternative method to solve the problem is by using a fraction.
A fraction is a mathematical expression that represents a part of a whole. In this case, we can express 20 of 36 as a fraction as follows:
Fraction Representation
20 of 36 can be expressed as the fraction 20/36.
To simplify this fraction, we can divide both the numerator and the denominator by their greatest common factor, which is 4.
20/36 = (20 ÷ 4)/(36 ÷ 4) = 5/9
Therefore, 20 of 36 can be expressed as the fraction 5/9.
Comparison with Proportion Method
The alternative method using a fraction is similar to the proportion method in that both methods involve finding an equivalent fraction.
However, the fraction method can be more straightforward in some cases, especially when the numbers involved are small.
FAQ Compilation
What is the formula for calculating percentages?
Percentage = (Part / Whole) x 100
How do I solve proportions?
Cross-multiply the values diagonally: a/b = c/d, then ad = bc.
