Determining percentages is an important mathematical skill used in many real-world situations.
In this article, we will explore the question “40 is what percent of 320?” step-by-step and discuss various methods to find the percentage.
Utilizing the “X is What Percent of Y Calculator”,we can compute that 40 is 12.5% of 320.
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Step-by-Step Solution: 40 is What Percent of 320?
Now that we know we want to find 40 is what percent of 320? , 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 Ratio to Percentage
Fractions consist of a numerator and denominator. Fractions consist of a numerator and denominator. The numerator represents the number of pieces being considered, while the denominator is the total number of pieces that make up the whole.
“Percent” means “per hundred”. So percent is another way to express a fraction where the denominator is always 100.
For example, the percentage 50% indicates we have 50 out of a total of 100 pieces. 50% can be rewritten as the fraction 50/100, since we have 50 parts out of 100 total parts.
In summary, to convert a fraction to a percentage, we multiply the numerator and denominator by the same value so that the denominator becomes 100. Once we have a fraction with a denominator of 100, the numerator gives us the percentage amount. This allows any fraction to be converted to an equivalent percentage based on the concept of “out of 100”.
Let’s apply this understanding to calculate “40 is what percent of 320?”.
Step1: Write the Ratio as a Fraction
First, we can express “40 is what percent of 320?” as the fraction 40/320.
40 of 320 can be written as: 40 320
Step 2: Find the Number to Multiply to Get a Denominator of 100
We want the denominator to be 100, so need to multiply by a number that makes 320 into 100
To find this number, divide 100 by 320:
100 320 = 0.3125
Step 3: Multiply the Fraction by the Number from Step 2
Multiply both the numerator and denominator by 0.3125:
40320 x 0.31250.3125
= 40 x 0.3125320 x 0.3125
= 12.5100
Step 4: The Numerator is Now the Percentage
Since our new denominator is 100, the numerator 12.5 represents the percentage
This step-by-step method of converting the ratio 40 : 320 to a fraction and then a percentage with a denominator of 100 allows us to calculate that 40 is 12.5% of 320.
Method 2: Converting Fractions to Decimals and Percents
You can also use division to convert a fraction to a decimal and then to a percentage.
Step 1: Write the Fraction
Start with the original fraction:
40 of 320 can be written as: 40 320
Step 2: Divide the Numerator by the Denominator
Use long division to divide the numerator by the denominator:
40 320 = 0.125
Step 3: Multiply the Decimal by 100
To convert the decimal to a percentage, multiply it by 100:
0.125 x 100 = 12.5%
Therefore, by dividing 40/320 to 0.125 and then multiplying by 100, the result is 12.5%
Following this process carefully of dividing the fraction, multiplying the decimal by 100, and interpreting the result as a percentage provides us another method to find that 40 is 12.5% of 320.
Comparing the Two Methods
Let’s summarize the two methods we used to find the percentage “40 is what percent of 320?”:
Method | Description | Steps |
---|---|---|
Convert Ratio to Percentage | Converts the ratio to a fraction, then multiplies to make the denominator 100 | 1. Write ratio as fraction 2. Multiply to make denominator 100 3. Numerator is the percentage |
Convert Fraction to Decimal and Percentage | Divides the fraction to a decimal, then multiplies the decimal by 100 | 1. Write the fraction 2. Divide numerator by denominator 3. Multiply decimal by 100 4. Result is the percentage |
The ratio to percentage method directly converts the ratio 40 : 320 to an equivalent percentage fraction. The fraction to decimal method indirectly converts the fraction 40/320 to a decimal and then a percentage.
p>Both methods follow a clear step-by-step procedure to arrive at the same result that 40 is 12.5% of 320. Understanding multiple approaches builds flexibility in thinking through percentage problems.
Standard Percentage of 320 Calculation Examples
Now that we have calculated that 40 is 12.5% of 320, let’s explore what 5%, 10%, up to 95% of 320 would be.
16 is 5% of 320
32 is 10% of 320
48 is 15% of 320
64 is 20% of 320
80 is 25% of 320
96 is 30% of 320
112 is 35% of 320
128 is 40% of 320
144 is 45% of 320
160 is 50% of 320
176 is 55% of 320
192 is 60% of 320
208 is 65% of 320
224 is 70% of 320
240 is 75% of 320
256 is 80% of 320
272 is 85% of 320
288 is 90% of 320
304 is 95% of 320
320 is 100% of 320
Conclusion
Finding percentages is an essential mathematical skill used in daily life for calculations of discounts, taxes, tips, interest rates, test scores, and more. In this article, we explored the specific question “40 is what percent of 320?” and discussed two methods to solve it – converting a ratio to a percentage and converting a fraction to a decimal and percentage. Both methods carefully followed arrive at the solution that 40 is 12.5% of 320.
We also looked at calculating a range of standard percentages from 5% to 95% of the total number 320. Practicing these types of percentage calculations helps improve mathematical proficiency and comfort applying different techniques.