Question

Write each given percent as a decimal and a fraction in lowest terms Write each given fraction as a decimal and a percent. The number of students in band is about \(115 \%\) of the number in orchestra and about \(\frac{5}{4}\) of the number in choir.

Short answer

115% is 1.15 or \(\frac{23}{20}\); \(\frac{5}{4}\) is 1.25 or 125%.

Step-by-step solution

Title - Convert Percent to Decimal

To convert a percent to a decimal, divide the percent by 100. For the given percent 115%, divide 115 by 100: \(115 \div 100 = 1.15\)

Title - Convert Percent to Fraction

To convert a percent to a fraction, write the percent as a fraction with a denominator of 100 and then simplify. For 115%: \(\frac{115}{100}\). Simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5 in this case: \(\frac{115 \div 5}{100 \div 5} = \frac{23}{20}\). Therefore, 115% is \(\frac{23}{20}\) in its simplest form.

Title - Convert Fraction to Decimal

To convert a fraction to a decimal, divide the numerator by the denominator. For the given fraction \(\frac{5}{4}\), divide 5 by 4: \(5 \div 4 = 1.25\). Therefore, \(\frac{5}{4}\) as a decimal is 1.25.

Title - Convert Fraction to Percent

To convert a fraction to a percent, divide the numerator by the denominator and then multiply by 100. For \(\frac{5}{4}\): \(\left( \frac{5}{4} \right) \times 100 = 1.25 \times 100 = 125\)%.

Key concepts

Converting Fractions

Converting a fraction to other formats like decimals or percents is a foundational skill in math. Here's how to do it easily. Click the bullet points below for helpful tips:

• Change a fraction to a decimal: Simply divide the numerator (top number) by the denominator (bottom number). For example, for \(\frac{5}{4}\), divide 5 by 4 to get 1.25.


• Change a fraction to a percent: Once you have the decimal from dividing the fraction, just multiply by 100. So, \( \frac{5}{4} = 1.25\), and then \(1.25 \times 100 = 125\)%.

Using these simple steps, you can switch between fractions, decimals, and percents with ease.

Simplifying Fractions

Simplifying fractions is all about making them as simple as possible. Here's how to master this:

• Find the greatest common divisor (GCD): The GCD of two numbers is the largest number that can evenly divide both of them. For example, for the fraction \(\frac{115}{100}\), the GCD is 5.


• Divide both the numerator and denominator by the GCD: This reduces the fraction to its simplest form. For instance, \(\frac{115}{100}\) becomes \(\frac{115 \, \div \, 5}{100 \, \div \, 5} = \frac{23}{20}\).

By following these steps, you ensure that your fractions are as simple as possible, which is helpful for calculations and comparisons.

Basic Algebra

Basic algebra involves using variables to represent numbers in equations and expressions. Here are some basics to know:

• Variables: Variables are symbols (often letters) that stand for unknown values. For example, in \(x + 3 = 7\), \(x\) is the variable.


• Solving equations: The goal is to find the value of the variable that makes the equation true. For instance, in \(x + 3 = 7\), subtract 3 from both sides to find \(x = 4\).

Understanding basic algebra helps you solve problems that involve relationships between numbers and unknown values. It makes working with equations and formulas much more manageable.