120 is What Percent of 150? = 80% [With 2 Solutions]

Determining percentages is an important mathematical skill used in many real-world situations.

In this article, we will explore the question “120 is what percent of 150?” step-by-step and discuss various methods to find the percentage.

Utilizing the “X is What Percent of Y Calculator”,we can compute that 120 is 80% of 150.

Step-by-Step Solution: 120 is What Percent of 150?

Now that we know we want to find 120 is what percent of 150? , 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 “120 is what percent of 150?”.

Step1: Write the Ratio as a Fraction

First, we can express “120 is what percent of 150?” as the fraction 120/150.

120 of 150 can be written as: 120 / 150

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 150 into 100

To find this number, divide 100 by 150:

100 /150 = 0.6667

Step 3: Multiply the Fraction by the Number from Step 2

Multiply both the numerator and denominator by 0.6667:

120/150 x 0.6667/0.6667
= 120 x 0.6667/150 x 0.6667
= 80/100

Step 4: The Numerator is Now the Percentage

Since our new denominator is 100, the numerator 80 represents the percentage

This step-by-step method of converting the ratio 120 : 150 to a fraction and then a percentage with a denominator of 100 allows us to calculate that 120 is 80% of 150.

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:

120 of 150 can be written as: 120 / 150

Step 2: Divide the Numerator by the Denominator

Use long division to divide the numerator by the denominator:

120 / 150 = 0.8

Step 3: Multiply the Decimal by 100

To convert the decimal to a percentage, multiply it by 100:

0.8 x 100 = 80%

Therefore, by dividing 120/150 to 0.8 and then multiplying by 100, the result is 80%

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 120 is 80% of 150.

Comparing the Two Methods

Let’s summarize the two methods we used to find the percentage “120 is what percent of 150?”:

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 120 : 150 to an equivalent percentage fraction. The fraction to decimal method indirectly converts the fraction 120/150 to a decimal and then a percentage.

p>Both methods follow a clear step-by-step procedure to arrive at the same result that 120 is 80% of 150. Understanding multiple approaches builds flexibility in thinking through percentage problems.

Standard Percentage of 150 Calculation Examples

Now that we have calculated that 120 is 80% of 150, let’s explore what 5%, 10%, up to 95% of 150 would be.

7.5 is 5% of 150

15 is 10% of 150

22.5 is 15% of 150

30 is 20% of 150

37.5 is 25% of 150

45 is 30% of 150

52.5 is 35% of 150

60 is 40% of 150

67.5 is 45% of 150

75 is 50% of 150

82.5 is 55% of 150

90 is 60% of 150

97.5 is 65% of 150

105 is 70% of 150

112.5 is 75% of 150

120 is 80% of 150

127.5 is 85% of 150

135 is 90% of 150

142.5 is 95% of 150

150 is 100% of 150

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 “120 is what percent of 150?” 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 120 is 80% of 150.

We also looked at calculating a range of standard percentages from 5% to 95% of the total number 150. Practicing these types of percentage calculations helps improve mathematical proficiency and comfort applying different techniques.