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Magazine Chapter 8: Problem 68
Convert to fraction notation. $$ 16 \frac{2}{3} \% $$
Short Answer
Expert verified
The fraction notation is \( \frac{1}{6} \).
Step by step solution
01
Understand the Percentage
A percentage is a ratio expressed as a fraction of 100. For example, 50% means 50 out of 100, or \( \frac{50}{100} \).
02
Separate the Mixed Number
In the given percentage, \( 16 \frac{2}{3} \% \), split it into its whole number and fraction parts: \( 16 \% \) and \( \frac{2}{3} \% \).
03
Convert Whole Number Percentage to Fraction
Convert \( 16 \% \) to a fraction: \( 16 \% = \frac{16}{100} \).
04
Convert Fractional Percentage to Fraction
Convert \( \frac{2}{3} \% \) to a fraction: \( \frac{2}{3} \% = \frac{2}{3} \times \frac{1}{100} = \frac{2}{300} \).
05
Combine the Fractions
Combine the two fractions: \( \frac{16}{100} + \frac{2}{300} \).
06
Find a Common Denominator
The denominators are 100 and 300. The least common multiple is 300. Convert \( \frac{16}{100} \) to have a denominator of 300: \( \frac{16}{100} = \frac{16 \times 3}{100 \times 3} = \frac{48}{300} \).
07
Add the Fractions
Add \( \frac{48}{300} \) and \( \frac{2}{300} \): \( \frac{48}{300} + \frac{2}{300} = \frac{50}{300} \).
08
Simplify the Fraction
Simplify \( \frac{50}{300} \): Both the numerator and the denominator can be divided by their greatest common divisor, which is 50: \( \frac{50 \div 50}{300 \div 50} = \frac{1}{6} \).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Percentage Conversion
When you hear the term 'percentage', think of it as 'per 100'. A percentage is a way to express a number as a fraction of 100. For example, 25% means 25 out of 100, which can be written as \( \frac{25}{100} \). This makes comparison easy, as all percentages have the same denominator: 100.
To convert percentages to fractions, remember these steps:
To convert percentages to fractions, remember these steps:
- Identify the percentage value.
- Write it over 100 (e.g., 20% becomes \( \frac{20}{100} \)).
- Simplify the fraction if possible.
Mixed Number
A mixed number consists of a whole number and a fraction combined. For example, in \( 16 \frac{2}{3} \), 16 is the whole number and \( \frac{2}{3} \) is the fractional part.
Let's break it down:
For instance, 16% becomes \( \frac{16}{100} \) and \( \frac{2}{3} \% \) becomes \( \frac{2}{3} \times\frac{1}{100} = \frac{2}{300} \). You then add \( \frac{16}{100} \) and \( \frac{2}{300} \) after finding a common denominator.
Let's break it down:
- First, handle the whole number (in this case, 16%).
- Then handle the fraction (in this case, \( \frac{2}{3} \% \)).
For instance, 16% becomes \( \frac{16}{100} \) and \( \frac{2}{3} \% \) becomes \( \frac{2}{3} \times\frac{1}{100} = \frac{2}{300} \). You then add \( \frac{16}{100} \) and \( \frac{2}{300} \) after finding a common denominator.
Simplifying Fractions
Simplifying fractions makes them easier to understand and work with. To simplify a fraction, you divide the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD).
Here's how to do it:
\( \frac{50 \div 50}{300 \div 50} = \frac{1}{6} \), giving you the simplified fraction \( \frac{1}{6} \). This step ensures your answers remain accurate and easy to interpret.
Here's how to do it:
- Find the GCD of the numerator and the denominator.
- Divide both the numerator and denominator by this number.
- Write down the simplified fraction.
\( \frac{50 \div 50}{300 \div 50} = \frac{1}{6} \), giving you the simplified fraction \( \frac{1}{6} \). This step ensures your answers remain accurate and easy to interpret.
