Understanding Fractions and Percentages: A Comprehensive Guide

When dealing with fractions and percentages, it is essential to understand the relationships and conversions between these numerical concepts. This article will explore how to calculate fractions and percentages, specifically focusing on the fraction 1/10 and its application in different contexts.

What is 1/10 of 800?

To find 1/10 of 800, simply divide 800 by 10:

frac10; of 800 800 ÷ 10 80

This calculation is straightforward and can be verified through different methods, such as converting it to a decimal or using a proportion:

Converting to a Decimal

1/10 can be converted to a decimal, which is 0.1. Multiplying 900 by 0.1 or dividing 900 by 10 provides the same result:

0.1 × 900 90

900 ÷ 10 90

Using Proportions

Alternatively, you can use the concept of proportions to find 1/10 of any number. Here, we want to find the percentage 10 is of 800:

Pecentage Calculation

The percentage 10 is of 800 can be explained by inspection:

Since 10 is 1/80th of 800, express 1/80th as a percentage fraction, which is 0.0125 or 1.25%. So, 10 is 1.25% of 800.

Related Calculations and Conversions

Let's explore how 10 and 800 can be manipulated to find other useful fractions and percentages:

Conversion to Percentage

To convert 10 into a percentage of 800, you can use the method of converting the fraction to a decimal and then to a percentage:

100 ÷ 800 0.125

Multiplying both the numerator and denominator by 0.125:

100 × 0.125/800 × 0.125 1.25/100

This re-writes the result as a percentage, and you find that 10/800 as a percentage is 1.25%.

Algebraic Approach

Using an algebraic approach, let x be the number whose percent is 10:

x of 800 10

x/100 × 800 10

8x 10

x 10/8

x 1.25

Simplification

Another simplified method involves dividing 100 by the denominator and then multiplying the numerator and denominator by this result:

100 ÷ 800 0.125

100 × 0.125/800 × 0.125 1.25/100

Therefore, 10 out of 800 as a percentage is 1.25%.

These calculations and conversions are useful not only for academic purposes but also in practical applications, such as calculating discounts, interest rates, and proportions in various fields.