Problem 9 - Elementary Algebra

Question

For the following problems, convert each fraction to a percent. $$ \frac{27}{55} $$

Step-by-Step Solution

Answer

Question: Convert the fraction 27/55 into a percentage. Answer: 49.09%

Step 1: Divide the numerator by the denominator

First, we need to perform the division of the numerator (27) divided by the denominator (55). $$ \frac{27}{55} $$ Perform the division to get: $$ \frac{27}{55} = 0.4909 $$

Step 2: Convert the decimal to a percentage

Now that we have the decimal value, we need to convert it into a percentage. To do this, simply multiply the decimal by 100. $$ 0.4909 \times 100 $$ Calculate the result: $$ 0.4909 \times 100 = 49.09 $$

Step 3: Write the final answer

Now that we have converted the fraction to a percentage, we can write the final answer: $$ \frac{27}{55} = 49.09\% $$

Key Concepts

basic arithmetic

When working with numbers, basic arithmetic is foundational. It includes four essential operations: addition, subtraction, multiplication, and division. These operations help us solve everyday problems and are crucial in handling more complex math concepts.
In the context of converting a fraction to a percentage, arithmetic helps you move through the process efficiently. For instance, division transforms fractions into decimals, and multiplication turns those decimals into percentages. Each step relies on understanding and performing these basic operations.

• Addition combines numbers together.
• Subtraction finds the difference between them.
• Multiplication increases a number by a factor.
• Division splits a number into smaller, equal parts.

Knowing these fundamentals allows you to tackle various mathematical challenges with ease.

fractions

Fractions represent parts of a whole. They consist of two numbers: a numerator and a denominator. The numerator is the top part and indicates how many pieces we have, while the denominator is the bottom part and shows how many pieces make up a whole.
For example, in the fraction \(\frac{27}{55}\), 27 is the numerator, and 55 is the denominator. This fraction indicates 27 parts of a 55-part whole. Understanding fractions is crucial as it helps in dividing quantities and comparing parts of different wholes.
Fractions can be converted into decimals and percentages through division and multiplication, which makes them versatile for various applications like calculating discounts, proportions, and data interpretation.

percentages

Percentages are a way of expressing numbers as parts of 100. They are helpful in comparing portions of different wholes on an equal basis. For example, if you say 49.09\%, that means 49.09 out of every 100 parts, which is easier to understand for comparisons than fractions or decimals.
To convert a decimal to a percentage, you multiply the decimal by 100. So, with the decimal 0.4909, you multiply by 100 to get a percentage: 0.4909 \(\times\) 100 = 49.09\%. This makes being familiar with percentages essential in fields like finance, statistics, and everyday calculations like determining a sale discount or interest rate.

division process

The division process is the mathematical operation of dividing a number into several equal parts. It helps in breaking down numbers to understand proportions, ratios, and other comparative measures.
In our exercise, dividing 27 by 55 is the first step to convert a fraction to a decimal. This division gives us a decimal value which can then be transformed into a percentage. Performing division:- Write the numerator inside the division bracket and the denominator outside.- Divide the numbers as you would in simple arithmetic division.- The result will give you a decimal.For example, \(\frac{27}{55} = 0.4909\). This decimal can then proceed to further conversion for more applications.