Question

name: _________________________ date: _________ section: __
1-54.
spinners – theory vs. reality, part one
your teacher will give your team a spinner. you will need to decide how to color
the spinner so that it meets the following criteria.
40% should be red. 30% should be blue.
$\frac{1}{10}$ should be yellow. the rest should be green.

Explanation:

To determine the percentage of the spinner that should be green, we first convert all the given proportions to percentages and then subtract their sum from 100% (since the total of all sections of the spinner should be 100%).

Step 1: Convert the fraction for yellow to a percentage

The fraction for yellow is \(\frac{1}{10}\). To convert this to a percentage, we multiply by 100:
\[
\frac{1}{10} \times 100 = 10\%
\]

Step 2: Find the sum of the percentages of red, blue, and yellow

We know the percentage of red is \(40\%\), blue is \(30\%\), and yellow is \(10\%\) (from Step 1). The sum of these percentages is:
\[
40\% + 30\% + 10\% = 80\%
\]

Step 3: Calculate the percentage for green

Since the total percentage of the spinner must be \(100\%\), we subtract the sum of the other percentages from \(100\%\) to find the percentage for green:
\[
100\% - 80\% = 20\%
\]

So, the percentage of the spinner that should be green is \(20\%\). If we want to know the fraction, we can convert \(20\%\) to a fraction: \(20\%=\frac{20}{100}=\frac{1}{5}\).

If the spinner is divided into, say, 10 equal parts (to make the fractions easier to visualize with the given \(\frac{1}{10}\) for yellow), we can also calculate the number of sections for each color:

• Red: \(40\%\) of 10 sections is \(0.4\times10 = 4\) sections.
• Blue: \(30\%\) of 10 sections is \(0.3\times10 = 3\) sections.
• Yellow: \(\frac{1}{10}\) of 10 sections is \(1\) section.
• Green: The remaining sections. Total sections accounted for: \(4 + 3+ 1=8\) sections. So green sections: \(10 - 8 = 2\) sections. And \(2\) sections out of \(10\) is \(\frac{2}{10}=\frac{1}{5}\) or \(20\%\), which matches our earlier result.

Answer:

The percentage of the spinner that should be green is \(\boldsymbol{20\%}\) (or the fraction \(\boldsymbol{\frac{1}{5}}\)). If considering the number of sections in a 10 - part spinner, green should occupy 2 sections.