Utilizing the “What is X Percent of Y Calculator”, we can compute that 70% of 30 equals 21.
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Step-by-Step Solution: What is 70% of 30?
Now that we know we want to find 70% of 30, 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 70 percent of 30 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 70%.
The whole is the total amount. In this case, the whole is 30.
Step 2: Write the percentage as a decimal by dividing it by 100:
70% = 70/100 = 0.7
Step 3: Multiply the decimal form of percentage by the whole amount:
0.7 * 30 = 21
Therefore, 70% of 30 is 21.
Let’s look at this visually:
70% * 30 = 70/100 * 30 = 0.7 *30 = 21
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 70% of 30 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 70% of 30. 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 70% of 30
- The Whole is 30
- The Percentage is 70
Substitute into the equation:
In this case, we can multiply both sides of the equation by 30
30 *x/30 = 70/100 * 30
x = 70 /100 * 30 = 2100/100 = 21
Therefore, 70% of 30 is 21.
Comparing the Methods
Both methods arrive at the same solution:
- Method 1 gets the solution by converting 70% to 0.7 and multiplying by 30.
- 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 30 is 21.
What Percent of 30 is 21?
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 21
- The Whole is 30
Substitute into the equation:
21/30 = 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 21
- 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 (30)
When written out, the cross multiplication looks like:
21 * 100 = x * 30
x * 30 = 21 * 100
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Then we can solve the resulting equation:
x * 30 = 2100
x = 70
Therefore, the answer is that 70% of 30 is 21.
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 21 is 70 Percent of What Number.
21 is 70 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 21
- The Percentage is 70
Substitute into the equation:
21/x = 70/100
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 21
- 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 (70) multiplied by the denominator of the first half (x)
When written out, the cross multiplication looks like:
21 * 100 = 70 * x
x * 70 = 21 * 100
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Then we can solve the resulting equation:
x * 70 = 2100
x = 30
Therefore, the answer is that 21 is 70% of 30.
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% 21 / 30 x 100% = 70% Find what percentage a part is of a whole Part / Percentage 21 / 70% = 30 Find the part given the whole and percentage Whole x Percentage 30 * 70% =21
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 30 Calculation Examples
5 Percent of 30 = 5/100 * 30 = 0.05 * 30 = 1.5
10 Percent of 30 = 10/100 * 30 = 0.1 * 30 = 3
15 Percent of 30 = 15/100 * 30 = 0.15 * 30 = 4.5
20 Percent of 30 = 20/100 * 30 = 0.2 * 30 = 6
25 Percent of 30 = 25/100 * 30 = 0.25 * 30 = 7.5
30 Percent of 30 = 30/100 * 30 = 0.3 * 30 = 9
35 Percent of 30 = 35/100 * 30 = 0.35 * 30 = 10.5
40 Percent of 30 = 40/100 * 30 = 0.4 * 30 = 12
45 Percent of 30 = 45/100 * 30 = 0.45 * 30 = 13.5
50 Percent of 30 = 50/100 * 30 = 0.5 * 30 = 15
55 Percent of 30 = 55/100 * 30 = 0.55 * 30 = 16.5
60 Percent of 30 = 60/100 * 30 = 0.6 * 30 = 18
65 Percent of 30 = 65/100 * 30 = 0.65 * 30 = 19.5
70 Percent of 30 = 70/100 * 30 = 0.7 * 30 = 21
75 Percent of 30 = 75/100 * 30 = 0.75 * 30 = 22.5
80 Percent of 30 = 80/100 * 30 = 0.8 * 30 = 24
85 Percent of 30 = 85/100 * 30 = 0.85 * 21 = 25.5
90 Percent of 30 = 90/100 * 30 = 0.9 * 30 = 27
95 Percent of 30 = 95/100 * 30 = 0.95 * 30 = 28.5
100 Percent of 30 = 100/100 * 30 = 1 * 30 = 30
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