Utilizing the “What is X Percent of Y Calculator”, we can compute that 20% of 21 equals 4.2.
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Step-by-Step Solution: What is 20% of 21?
Now that we know we want to find 20% of 21, let’s look at two different step-by-step methods we can use to solve this percentage problem. Each approach arrives at the same solution, but understanding different ways to think through the math builds flexibility and deeper learning.
Method 1: Convert the Percent to a Decimal and Multiply
One approach to finding 20 percent of 21 is to convert the percent to a decimal and multiply. Here are the steps:
Step 1: Identify the part and whole
The part is the amount we want as a percentage. In this case, it is 20%.
The whole is the total amount. In this case, the whole is 21.
Step 2: Write the percentage as a decimal by dividing it by 100:
20% = 20/100 = 0.2
Step 3: Multiply the decimal form of percentage by the whole amount:
0.2 * 21 = 4.2
Therefore, 20% of 21 is 4.2.
Let’s look at this visually:
20% * 21 = 20/100 * 21 = 0.2 *21 = 4.2
This approach of converting the percentage to a decimal and multiplying is straightforward and can be applied to any “percent of number” problem. The key is properly converting the percent to a decimal by dividing by 100.
Method 2: Finding Percentages Using Algebraic Equations
Another way to find 20% of 21 is to set up an algebraic equation and solve it. Here are the steps:
A proportion is an equation that states two ratios are equivalent. Here is the proportion formula:
Part/Whole = Percentage/100
Step 1: Define the Unknown Variable
Let’s define an unknown variable x to represent 20% of 21. In algebraic equations, variables are used to represent unknown values.
Step 2: Set Up the Equation
Using the variable x, we can set up an equation with the information given:
- The unknown variable x (Part) is the amount we want to find, which is 20% of 21
- The Whole is 21
- The Percentage is 20
Substitute into the equation:
In this case, we can multiply both sides of the equation by 21
21 *x/21 = 20/100 * 21
x = 20 /100 * 21 = 420/100 = 4.2
Therefore, 20% of 21 is 4.2.
Comparing the Methods
Both methods arrive at the same solution:
- Method 1 gets the solution by converting 20% to 0.2 and multiplying by 21.
- Method 2 sets up an equation, defines a variable, and solves algebraically.
The decimal conversion method is straightforward, avoiding any algebra. But the algebraic method is more flexible for complex problems where defining variables and setting up equations is helpful.
Common Percentage Scenarios
Here are some common percentage scenarios and how to solve them:
Finding the Percentage Given the Part and Whole
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Here is the proportion formula:
Part/Whole = Percentage/100
We will now demonstrate how to utilize proportion formula to calculate the percentage given a part and whole amount through an example determining what percent of 21 is 4.2.
What Percent of 21 is 4.2?
Step 1: Define the Unknown Variable
Let unknown variable x = the unknown percent we want to find..
Step 2: Set Up the Equation
Using the variable x, we can set up an equation with the information given:.
- The unknown variable x (Percentage) is the number we want to find.
- The Part is 4.2
- The Whole is 21
Substitute into the equation:
4.2/21 = x/100
Step 3: Solve the Equation
To isolate x, we can cross multiply as follows:
- Take the numerator of one side of the equation, which is 4.2
- Multiply it by the denominator of the other side of the equation, which is 100
- Set that equal to the numerator of the second half (x) multiplied by the denominator of the first half (21)
When written out, the cross multiplication looks like:
4.2 * 100 = x * 21
x * 21 = 4.2 * 100
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Then we can solve the resulting equation:
x * 21 = 420
x = 20
Therefore, the answer is that 20% of 21 is 4.2.
Finding the Whole Given the Percentage and Part
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Here is the proportion formula:
Part/Whole = Percentage/100
We will now demonstrate how to utilize proportion formula to calculate the whole given the percentage and part through an example determining 4.2 is 20 Percent of What Number.
4.2 is 20 Percent of What Number?
Step 1: Define the Unknown Variable
Let unknown variable x = the unknown number we want to find.
Step 2: Set Up the Equation
Using the variable x, we can set up an equation with the information given:
- The unknown variable x ( Whole) is the number we want to find.
- The Part is 4.2
- The Percentage is 20
Substitute into the equation:
4.2/x = 20/100
Step 3: Solve the Equation
To isolate x, we can cross multiply as follows:
- Take the numerator of one side of the equation, which is 4.2
- Multiply it by the denominator of the other side of the equation, which is 100
- Set that equal to the numerator of the second half (20) multiplied by the denominator of the first half (x)
When written out, the cross multiplication looks like:
4.2 * 100 = 20 * x
x * 20 = 4.2 * 100
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Then we can solve the resulting equation:
x * 20 = 420
x = 21
Therefore, the answer is that 4.2 is 20% of 21.
Common Percentage Calculations
Here is a quick reference table of some typical percentage calculations:
Calculation Formula Example Find what percentage a part is of a whole Part / Whole x 100% 4.2 / 21 x 100% = 20% Find what percentage a part is of a whole Part / Percentage 4.2 / 20% = 21 Find the part given the whole and percentage Whole x Percentage 21 * 20% =4.2
Having these common formulas memorized can make solving a variety of percentage problems quicker. When in doubt, break things down step-by-step into smaller pieces.
Standard Percentage of 21 Calculation Examples
5 Percent of 21 = 5/100 * 21 = 0.05 * 21 = 1.05
10 Percent of 21 = 10/100 * 21 = 0.1 * 21 = 2.1
15 Percent of 21 = 15/100 * 21 = 0.15 * 21 = 3.15
20 Percent of 21 = 20/100 * 21 = 0.2 * 21 = 4.2
25 Percent of 21 = 25/100 * 21 = 0.25 * 21 = 5.25
30 Percent of 21 = 30/100 * 21 = 0.3 * 21 = 6.3
35 Percent of 21 = 35/100 * 21 = 0.35 * 21 = 7.35
40 Percent of 21 = 40/100 * 21 = 0.4 * 21 = 8.4
45 Percent of 21 = 45/100 * 21 = 0.45 * 21 = 9.45
50 Percent of 21 = 50/100 * 21 = 0.5 * 21 = 10.5
55 Percent of 21 = 55/100 * 21 = 0.55 * 21 = 11.55
60 Percent of 21 = 60/100 * 21 = 0.6 * 21 = 12.6
65 Percent of 21 = 65/100 * 21 = 0.65 * 21 = 13.65
70 Percent of 21 = 70/100 * 21 = 0.7 * 21 = 14.7
75 Percent of 21 = 75/100 * 21 = 0.75 * 21 = 15.75
80 Percent of 21 = 80/100 * 21 = 0.8 * 21 = 16.8
85 Percent of 21 = 85/100 * 21 = 0.85 * 4.2 = 17.85
90 Percent of 21 = 90/100 * 21 = 0.9 * 21 = 18.9
95 Percent of 21 = 95/100 * 21 = 0.95 * 21 = 19.95
100 Percent of 21 = 100/100 * 21 = 1 * 21 = 21
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