Problem 66 - Prealgebra

Question

Change each fraction or mixed number to a percent. $$2 \frac{1}{8}$$

Step-by-Step Solution

Answer

The percent form of \(2 \frac{1}{8}\) is 212.5\%.

Step 1: Convert Mixed Number to Improper Fraction

To convert a mixed number into an improper fraction, multiply the whole number by the denominator of the fractional part and then add the numerator. For the mixed number \(2 \frac{1}{8}\), multiply 2 by 8 (denominator) and add 1 (numerator). This gives \(\frac{2 \times 8 + 1}{8} = \frac{17}{8}\).

Step 2: Convert Fraction to Decimal

To convert the improper fraction \(\frac{17}{8}\) into a decimal, perform the division 17 divided by 8. This results in 2.125 as the decimal equivalent.

Step 3: Convert Decimal to Percent

To convert a decimal to a percent, multiply the decimal by 100. Therefore, multiply 2.125 by 100, which results in 212.5. Thus, the percent form of \(2 \frac{1}{8}\) is 212.5\%.

Key Concepts

Mixed Numbers

When dealing with mixed numbers, you are combining a whole number with a fraction. For example, if you have the mixed number \(2 \frac{1}{8}\), the number 2 is the whole number, and \(\frac{1}{8}\) is the fraction.

• Mixed numbers are helpful for representing quantities that fall between whole numbers.
• They make it easier to visualize measurements like lengths or weights that aren't whole.
• Mixed numbers are common in everyday situations, like measuring ingredients in recipes.

If you need to convert a mixed number to an improper fraction, it's a straightforward process. Multiply the whole number by the denominator of the fraction, then add the numerator. This combined value becomes the new numerator, with the original denominator staying the same. In our example, calculating \(2 \times 8 + 1 = 17\) gives you the improper fraction \(\frac{17}{8}\).

Improper Fractions

Improper fractions are types of fractions where the numerator is larger than or equal to the denominator, such as \(\frac{17}{8}\). They are called "improper" because their value is greater than or equal to 1.

• Improper fractions are useful in calculations because they enable easy operations like addition or multiplication.
• They provide an alternative and simplified representation of mixed numbers.
• Improper fractions are essential when converting to decimals.

To convert the improper fraction \(\frac{17}{8}\) to a decimal, you will perform a simple division: divide 17 by 8. This division gives you 2.125. Working through improper fractions, this way can streamline calculations and make them more manageable.

Decimal Conversion

Decimal conversion is a method used to express fractions in a base-10 format, which is understandable and commonly used in everyday contexts. By converting \(\frac{17}{8}\) into a decimal, you get 2.125.

• Decimals are easy to read and use in both spoken and written communication.
• They allow for straightforward comparisons and calculations.
• Decimals simplify the process of converting to percentages.

Once you have a decimal representation, turning it into a percentage is simple. Multiply the decimal by 100. In the case of 2.125, this calculation becomes \(2.125 \times 100 = 212.5\). Therefore, \(2 \frac{1}{8}\) is equivalent to 212.5\% when expressed as a percentage. Understanding decimal conversion is crucial for handling different numerical representations efficiently.