Problem 59 - Elementary Algebra

Question

Copy and complete the table. $$ \begin{array}{|c|c|c|} \hline \begin{array}{c} \text { Fraction } \\ \text { notation } \end{array} & \begin{array}{c} \text { Percent } \\ \text { notation } \end{array} & \begin{array}{c} \text { Decimal number } \\ \text { notation } \end{array} \\ \hline \frac{4}{5} & & \\ \hline \frac{61}{100} & 91 \% & \\ \hline & 7 \% & \\ \hline & 311 \% & \\ \hline & & \\ \hline & & \\ \hline & & 0.01 \\ \hline & & \\ \hline & & \\ \hline \end{array} $$

Step-by-Step Solution

Answer

Fill the table with these equivalents: \( \frac{4}{5} = 80\text{\footnotesize\text%} = 0.8 \), 91\text{\footnotesize\text%} = 0.91, \( \frac{7}{100} = 7\text{\footnotesize\text%} = 0.07 \), \( \frac{311}{100} = 311\text{\footnotesize\text%} = 3.11 \), 0.01 = 1\text{\footnotesize\text%}, \( \frac{1}{4} = 25\text{\footnotesize\text%} = 0.25 \), 1.5 = 150\text{\footnotesize\text%} = \( \frac{3}{2} \), \( \frac{1}{2} = 50\text{\footnotesize\text%} = 0.5 \).

Step 1 - Convert fraction to percent and decimal

To convert the fraction \( \frac{4}{5} \) to a percent, multiply by 100: \( \frac{4}{5} \times 100 = 80\text{\footnotesize\text%} \). To convert it to a decimal, divide 4 by 5: \( \frac{4}{5} = 0.8 \).

Step 2 - Convert percent 91% to decimal

To convert 91% to a decimal, divide by 100: \( 91 \text{\footnotesize\text%} \times \frac{1}{100} = 0.91 \).

Step 3 - Convert 7% to fraction and decimal

To convert 7% to a fraction, write it as \( \frac{7}{100} \). To convert 7% to a decimal, divide by 100: \( 7 \text{\footnotesize\text%} \times \frac{1}{100} = 0.07 \).

Step 4 - Convert 311% to fraction and decimal

To convert 311% to a fraction, write it as \( \frac{311}{100} \). To convert 311% to a decimal, divide by 100: \( 311 \text{\footnotesize\text%} \times \frac{1}{100} = 3.11 \).

Step 5 - Identify missing percent for 0.01

To convert 0.01 to a percent, multiply by 100: \( 0.01 \times 100 = 1\text{\footnotesize\text%} \).

Step 6 - Convert 1/4 to percent and decimal

To convert \( \frac{1}{4} \) to a percent, multiply by 100: \( \frac{1}{4} \times 100 = 25\text{\footnotesize\text%} \). To convert it to a decimal, divide 1 by 4: \( \frac{1}{4} = 0.25 \).

Step 7 - Convert 1.5 to percent and fraction

To convert 1.5 to a percent, multiply by 100: \( 1.5 \times 100 = 150\text{\footnotesize\text%} \). To convert it to a fraction, write it as \( \frac{3}{2} \).

Step 8 - Convert 1/2 to percent and decimal

To convert \( \frac{1}{2} \) to a percent, multiply by 100: \( \frac{1}{2} \times 100 = 50\text{\footnotesize\text%} \). To convert it to a decimal, divide 1 by 2: \( \frac{1}{2} = 0.5 \).

Key Concepts

fraction to percent conversion

When you want to convert a fraction to a percent, you are essentially finding out what portion of 100 the fraction represents. The easiest way to do this is by multiplying the fraction by 100. For example, consider the fraction \(\frac{4}{5}\). To convert it to a percent, you would do the following:
\[\frac{4}{5} \times 100 = 80\%\]
Now, you have \(\frac{4}{5}\) as 80%.

Here's another example—let's use \(\frac{1}{4}\):
\[\frac{1}{4} \times 100 = 25\%\]
So, \(\frac{1}{4}\) is 25%. Converting is that simple! Just remember to multiply by 100.

decimal to percent conversion

Converting a decimal to a percent is another straightforward process. All you need to do is multiply the decimal number by 100. Here, we'll convert 91% to a decimal and then see how to convert it back to a percent.

First, converting 91% to decimal:
\[91\text{\footnotesize\text%} \times 0.01 = 0.91\]
Now for converting a decimal to a percent, you simply multiply by 100. Let's take the decimal 0.07:
\[0.07 \times 100 = 7\text{\footnotesize\text%}\]
It’s very easy; the key step is just multiplying or dividing by 100 depending on the direction.

percent to fraction conversion

To convert a percent to a fraction, you simply use the percent as the numerator and 100 as the denominator. Then, reduce the fraction to the simplest form if possible. For example, let's convert 311% to a fraction:
\[\frac{311}{100}\]
This is your fraction form of 311%. Now, if the fraction can be simplified, do so. But in this case, \(\frac{311}{100}\) is already in its simplest form.

Let’s try another example with 7%. Write 7% as a fraction by placing 7 over 100:
\[\frac{7}{100}\]
This fraction is already simplified. These conversions help in comparing and analyzing fractions, decimals, and percents efficiently.