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

In this article, we will explore the question “**84 is what percent of 105?**” step-by-step and discuss various methods to find the percentage.

Utilizing the “**X is What Percent of Y Calculator**”,we can compute that **84 is 80% of 105**.

Table of Contents

## Step-by-Step Solution: 84 is What Percent of 105?

Now that we know we want to find **84 is what percent of 105? **, 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 “84 is what percent of 105?”.**

### Step1: Write the Ratio as a Fraction

First, we can express “84 is what percent of 105?” as the fraction 84/105.

84 of 105 can be written as: 84 105

### 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 105 into 100

To find this number, divide 100 by 105:

100 105 = 0.9524

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

Multiply both the numerator and denominator by 0.9524:

84105 x 0.95240.9524

= 84 x 0.9524105 x 0.9524

= 80100

### 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 84 : 105 to a fraction and then a percentage with a denominator of 100 allows us to calculate that **84 is 80% of 105**.

## 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:

84 of 105 can be written as: 84 105

### Step 2: Divide the Numerator by the Denominator

Use long division to divide the numerator by the denominator:

84 105 = 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 84/105 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 **84 is 80% of 105**.

## Comparing the Two Methods

Let’s summarize the two methods we used to find the percentage “84 is what percent of 105?”:

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 84 : 105 to an equivalent percentage fraction. The fraction to decimal method indirectly converts the fraction 84/105 to a decimal and then a percentage.**

p>Both methods follow a clear step-by-step procedure to arrive at the same result that 84 is 80% of 105. Understanding multiple approaches builds flexibility in thinking through percentage problems.

## Standard Percentage of 105 Calculation Examples

Now that we have calculated that **84 is 80% of 105**, let’s explore what 5%, 10%, up to 95% of 105 would be.

**5.25 is 5% of 105**

**10.5 is 10% of 105**

**15.75 is 15% of 105**

**21 is 20% of 105**

**26.25 is 25% of 105**

**31.5 is 30% of 105**

**36.75 is 35% of 105**

**42 is 40% of 105**

**47.25 is 45% of 105**

**52.5 is 50% of 105**

**57.75 is 55% of 105**

**63 is 60% of 105**

**68.25 is 65% of 105**

**73.5 is 70% of 105**

**78.75 is 75% of 105**

**84 is 80% of 105**

**89.25 is 85% of 105**

**94.5 is 90% of 105**

**99.75 is 95% of 105**

**105 is 100% of 105**

## 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 “84 is what percent of 105?” 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 84 is 80% of 105.

We also looked at calculating a range of standard percentages from 5% to 95% of the total number 105. Practicing these types of percentage calculations helps improve mathematical proficiency and comfort applying different techniques.