Question

chapter 4 test a 6.1.7 i can convert between equivalent representations of positive rational numbers. write the percent as a fraction or mixed number in simplest form 1. 15% 2. 240% 3. 2.7%

Explanation:

Problem 1: 15% as a fraction

Step1: Recall percent to fraction rule

To convert a percent to a fraction, we write the percent as a fraction with a denominator of 100. So, \(15\%=\frac{15}{100}\).

Step2: Simplify the fraction

We find the greatest common divisor (GCD) of 15 and 100, which is 5. Then we divide both the numerator and the denominator by 5: \(\frac{15\div5}{100\div5}=\frac{3}{20}\).

Step1: Convert percent to fraction

Using the percent to fraction rule, \(240\% = \frac{240}{100}\).

Step2: Simplify and convert to mixed number

First, simplify \(\frac{240}{100}\) by dividing numerator and denominator by 20: \(\frac{240\div20}{100\div20}=\frac{12}{5}\). Now, convert \(\frac{12}{5}\) to a mixed number. We divide 12 by 5: \(12\div5 = 2\) with a remainder of 2. So, \(\frac{12}{5}=2\frac{2}{5}\).

Step1: Convert percent to fraction

First, write \(2.7\%\) as \(\frac{2.7}{100}\). To eliminate the decimal in the numerator, we multiply both the numerator and the denominator by 10: \(\frac{2.7\times10}{100\times10}=\frac{27}{1000}\).

Step2: Check for simplification

The GCD of 27 and 1000 is 1, so the fraction is already in simplest form.

Answer:

\(\frac{3}{20}\)

Problem 2: 240% as a mixed number