Exercises

1. Write each fraction as an equivalent fraction with a denominator of \(100\). Then, write each fraction as a percent.
   1. \(\dfrac{6}{10}\)
   2. \(\dfrac{13}{20}\)
   3. \(\dfrac{13}{25}\)
   4. \(\dfrac{3}{4}\)
   5. \(\dfrac{6}{5}\)
2. Since \(8\) is not a divisor of \(100\),  when we write the fraction \(\dfrac{3}{8}\) as a percent, the percent will have to have a tenths digit. One way to write \(\dfrac{3}{8}\) as a percent is to notice that \(\dfrac{3}{8}\) is half way between \(\dfrac{2}{8}\) and \(\dfrac{4}{8}\), which means that the decimal equivalent of \(\dfrac{3}{8}\) is half way between \(0.25\) and \(0.50\), which is \(0.375\). Therefore, as a percent \(\dfrac{3}{8}\) is \(37.5\%\). Use this strategy to write each of the following fractions as a percent.
   1. \(\dfrac{5}{8}\)
   2. \(\dfrac{14}{16}\)
   3. \(\dfrac{11}{40}\)
   4. \(\dfrac{12}{32}\)
   5. \(\dfrac{15}{24}\)
3. All of the percents in question 2) can be expressed using only one decimal place. This is certainly not the case for every fraction. How might you express the fractions \(\dfrac{2}{3}\) and \(\dfrac{2}{7}\) as percents?
4. Looking at the fractions in the table, you will notice that each represents a percent that is reasonably small, which we can conclude by comparing the numerator and the denominator. Using what you already know about how fractions can be converted to percents, complete the table using mental math! The first row has been done for you as an example.

   	Starting Fraction	\(\dfrac{\boxed{\phantom\square}}{100}\)	Decimal Value	Percent
   a.	\(\dfrac{1}{20}\)	\(\dfrac{5}{100}\)	\(0.05\)	\(5\%\) (not \(50\%\))
   b.	\(\dfrac{3}{50}\)
   c.	\(\dfrac{2}{25}\)
   d.	\(\dfrac{3}{40}\)
   e.	\(\dfrac{6}{200}\)
   f.	\(\dfrac{36}{400}\)
   g.	\(\dfrac{9}{360}\)

5. Consider the following set of shapes, which consist of rectangles and ovals. Notice that some shapes are small and some are tall.

   

   1. 1. What percent of the shapes are small?
      2. What percent of the shapes are tall?
      3. Find the sum of the percents in part i) and part ii). Explain why this sum makes sense.
   2. 1. What percent of the shapes are shaded?
      2. What percent of the shapes are not shaded?
      3. Find the sum of the percents in part i) and part ii). Explain why this sum makes sense.
   3. 1. What percent of the shapes are small and shaded?
      2. What percent of the shapes are tall and not shaded?
      3. Find the sum of the percents in part i) and part ii). Explain why the sum is not equal to \(100\%\).
6. Ahmad has just received the results of three assignments that he completed last week. His marks were
   • \(34\) out of \(40\) on his science fair project,
   • \(64\) out of \(80\) on his geography presentation, and
   • \(21\) out of \(25\) on his French oral dictation.
   1. Calculate each of Ahmad's marks as a percent.
   2. To summarize his results, Ahmad decides to calculate two average percentages:
      • First, he calculated the mean of the three percents in part a).
      • Second, he calculated the percent of total marks awarded out of total marks available for all three scores.
      Explain whether these two percents should be the same. If not, which value should be higher. Then calculate both values and compare.
7. 1. The side length of a regular hexagon is \(2\) cm. This side length is what percent of the perimeter of this hexagon? Round your answer to one decimal place.
   2. A line is drawn connecting two diametrically opposite vertices of a regular hexagon of side length \(2\) cm. This line, along with three sides of the hexagon, form an isosceles trapezoid, as shown. This line is what percent of the perimeter of the trapezoid?
8. Rod wants to put down new laminate flooring in his family room. Each box of flooring will cover \(1.3\) m\(^2\). Rod's room has an area of \(20\) m\(^2\).
   1. What is the minimum number of boxes of flooring Rod needs to purchase?
   2. It is suggested that you buy \(10\%\) more flooring than what you need to account for waste from pieces that need to be cut. What is the suggested minimum number of boxes that Rod should purchase?
9. Each time Kim pours water from a jug into a glass, exactly \(10\%\) of the water remaining in the jug is used. What is the minimum number of times that she must pour the water into a glass so that less than half of the water remains in the jug?
10. The graph shows styles of music on a playlist. The playlist is currently composed of \(35\%\) Pop music and \(65\%\) Hip Hop music. Country music songs are added to the playlist so that now \(40\%\) of the songs are Country. If the ratio of Hip Hop songs to Pop songs remains the same, what percent of the total number of songs are now Hip Hop?