Changing Percents to Fractions

Transcription

1 Math 604, Lesson Lesson pp. 0- Lessons 2, Write the ratios as percents. 2. a. 8 out of 00 8% b. 8:00 8% c. 00 % Answer the question. 26. If 2% of the fish in a pond are bluegills, what percent are not bluegills? 28% Changing Percents to Fractions The Studyrite Publishing Company sold 0% of the books it displayed at the homeschool convention. What fraction was this? To change a percent to a decimal, write it as a two-place decimal. To change it to a fraction, write it with a denominator of 00, and reduce to simplest form % = 0.0 = reduces to 0 The Studyrite company sold 0 of the books displayed. Here is another example. % = 0.0 = cannot be simplified. Write each percent as a two-place decimal.. a. 2% 0.2 b. 80% 0.80 c. 60% 0.60 Write each decimal as a fraction with a denominator of a b c Teaching the Lesson Changing Percents to Fractions To change a percent to a decimal, remove the percent sign and move the invisible decimal point two places to the left to make a two-place decimal.to change a percent to a fraction, write it as a fraction with a denominator of 00. Reduce it to simplest form if necessary. Board Work for this lesson is found on page 229. IOptional Activity on page. 228

2 Math 604, Lesson Lesson Write each percent as a fraction with a denominator of 00.. a. 40% b. 29% c. 6% 6 00 Change each percent to a fraction showing hundredths. Then reduce to simplest form. 4. a. 60% = 60 b. 2% = 2 0 We R emember Write the ratios as percents.. a. 64 out of 00 64% b. :00 % c % Answer the question. 6. If 99% of the students like milk, what percent do not like milk? % = Divide. Write remainders with R. 6R242 8 R42 6 R28. a. 600),842 b. 400),42 c. 00), I Find the sum without adding each number. Look for patterns. No calculators! = 26 IOptional Activity.?... M ental M ath 9. of = Board Work è Change to decimals: 6% % 8% 99% % 44% 2% 4% 6% 2% è Change to fractions in simplest form:

3 Math 604, Lesson Lesson + - x 2 = = S kill B uilders a. + 2 b = 4 = 2 c. 9 4 = = = = a = b. = 9 c Round to the nearest hundredth ) M astery D rill 2. a. millennium =,000 years b. decade = 0 years. a. century = 00 years b. kilometer =,000 meters 4. a. 2 = 9 b. 6 2 = 6 c. 2 = 2 d. 4 2 = 96. An equilateral triangle has congruent sides. 6. A scalene triangle has 0 congruent sides.. An isosceles triangle has 2 congruent sides. Answer the question. 8. What is the volume of a drawer 0 inches long, 8 inches wide, and inches deep? 240 inches

4 Math 604, Lesson Lesson 9. Six mobile homes on half-acre lots are for rent at the following costs per month: $60, $62, $90, $6, $62, and $642. What is the average cost of renting these mobile homes? Round to the nearest dollar. $62.00 ( ) 6 = Randy s new home is near Big Whaley Lake, shown below. Estimate the area of the lake, if each square in the picture measures mi 2. Hint: Put parts of the squares together in your mind to count the squares that are not whole. OR 6 mi 2 Match the words and expressions. 2. c six minus two times four a. 6(2) 22. a six times two b. 6n 2. b six times a number c d six times four d. 6 4 Write the formulas without using multiplication symbols. 2. Area of a square A=s Circumference of a circle C=πd 2. Area of a triangle 28. Area of a rectangle A= bh A=lw Euclid, a famous Greek thinker, developed the basic rules of geometry that are still in use today. Change each percent to a fraction showing hundredths. Then reduce to simplest form. 29. a. 6% = b. 90% = a. 4% = 4 0 b. 8% =

5 Math 604, Lesson 4 Lesson 4 pp G raphs and S tatistics Choosing Suitable Graphs Graphs are one of the ways to show collected information (called statistics) in an organized form. You have learned to recognize, use, and create three different kinds of graphs: pictographs, bar graphs, and line graphs. Key: = day Jan Feb Mar April pictograph Days 9 Jan Feb Mar April bar graph Days Jan Feb Mar April line graph These three graphs show the same basic information. Usually, however, there is a reason to choose a particular kind of graph for a particular kind of information. Pictographs work best to display information that can be easily shown with a picture or symbol. It is hard to show exact values with pictures, especially if the numbers are large. But a pictograph can show small numbers of items, or rounded numbers. This pictograph shows information gathered about a small number of students (2 students.) Class Survey: Favorite Breakfast Foods Cereal Toast Eggs Pancakes represents 2 students 4 Teaching the Lesson Graphs and Statistics: Choosing Suitable Graphs This lesson explains the reasons for choosing particular kinds of graphs for particular kinds of data. Students will be tested on this knowledge. You may use the oral quiz under Helpful Hints below to help them retain the facts. However, encourage them to also use logical thinking when doing the review exercises for this graph increment. There may be more than one correct answer for some situations. Give credit to students for using good thinking skills if they can supply logical reasons for answers that differ from the answer key. Teacher Aide Checks on page 9. IOptional Activity on page 9. 22

6 This pictograph uses large numbers that are rounded. United States Japan Germany Oral Drill è Quiz the students orally by having them answer pictograph, bar graph, or line graph for the following: (Some answers may vary.). Compares small numbers pictograph 2. Can be vertical or horizontal bar graph. Can show information that is quite exact bar graph 4. Shows a relationship between numbers line graph. Compares large, rounded numbers pictograph 6. Shows changes in data over time line graph. Is used to show comparisons bar graphs 8. Could be used to show favorite books pictograph 9. Could be used to show grades for a year line graph è Have students tell whether a vertical bar graph or a horizontal bar graph would be best for each set of data:. Comparison of tall buildings vertical bar graph 2. Comparison of the lengths of major roads horizontal bar graph Top Users of Cell Phones represents,000 cell phone users Lesson 4 Bar graphs show comparisons. They can be vertical or horizontal. They are usually more exact than pictographs. The following bar graphs compare the lengths of rivers (rivers run horizontally, so the bars are horizontal) and the heights of mountains (mountains are vertical, so the bars are vertical). Limpopo Niger Nile African Rivers,000 2,000,000 4,000 Length in miles Line graphs are most often used to show a relationship between the numbers. They involve information (data) that changes. For instance, a line graph might show the rainfall changes from month to month in a tropical country with a rainy season and a dry season. Rainfall in Inches Height in Feet,000,000 0,000,000 0 North American Peaks McKinley Walsh Columbia 0 0 J F M A M J J A S O N D Month Math 604, Lesson 4 2

7 Math 604, Lesson 4 Lesson 4 Or a line graph might show how the temperature changes each hour of a summer day, from cool at 2 a.m. to warmer after sunrise, to hot at noon, to cool again after sunset. F Temperatures on July 22 2a.m. 4a.m. 6a.m. 8a.m. 0 a.m. noon 2p.m. 4p.m. 6p.m. 8p.m. 0 p.m. Time Match the kind of data with the best kind of graph to display it.. b comparisons of heights, distances, and measurements 2. a data for a small number of items or for large rounded numbers. c a relationship between numbers a. pictograph b. bar graph c. line graph We R emember Change each percent to a fraction showing hundredths. Then reduce to simplest form. 4. a. % = b. 6% = 6. a. 84% = b. % = 4 Divide mentally a. 600) 8,000 b. 8,000) 64,000 c. 60)

8 Math 604, Lesson 4 Lesson x S kill B uilders 2 2. a. 8 2 = 8 b = 64 c = = Divide. Round each quotient to the nearest......tenth....hundredth....thousandth. 8. a ) b ) c ) Use the commutative properties to finish the equations. 9. a. o + n = n + o b. a 4= 4 a c. 9 =9 Use the associative properties to finish the equations. 0. a. (p + q) +r = p +(q + r) b. ( ) = ( ) Write the ratios as percents.. a. out of 00 % b. 6:00 6% c % Answer the question. 2. If % of the people are believers, what percent are unbelievers? 6% 00 = 6 2

9 Math 604, Lesson 4 Lesson 4 Complete the sentence.. The figure is a trapezoid because It has only one pair of parallel sides. Use the formula to find the circumference. Use 4. 4B in 2 4 in C=π d 22 2 C = C = 44 C = 2 C = 4 Match the words and expressions. 22 for pi.. b eight divided by two, times seven a. 4n 6. a four times a number b d three times two c. 8. c seven times three d. 2 Our decimal number system originated in India and was translated and preserved by the Arabs. It wasn t used widely by Europeans until the Middle Ages. Write the formulas without using multiplication symbols. 9. Area of a rectangle. Area of a triangle A=lw A= bh 2. Circumference of a circle 22. Area of a square A=s 2 C=πd Rewrite each decimal as a fraction or mixed number with a denominator of 0, 00, or,000. Reduce to simplest form. 2. a. 4. = 4 4 b.. = 0 = 2 c. 0.0 = 8 26

10 Math 604, Lesson 4 Lesson 4 M astery D rill 24. a. The fraction we use for π is 22. b. A straight angle measures An obtuse angle measures between 90 and An acute angle measures between 0 and A scalene triangle has 0 congruent sides. 28. An equilateral triangle has congruent sides. 29. An isosceles triangle has 2 congruent sides. 0. millennium =,000 years. century = 00 years 2. decade = 0 years I Complete the pattern.. 9, 02, 8, 68,, 4,, 0 Subtract from each number to complete the pattern. Work backwards if that s easier. IOptional Activity. Round to the nearest dollar. 4. a. $2.6 $.00 b. $6.0 $.00 c. $2.6 $24.00 Substitute for a and for b. Simplify the expressions.. a. 9 b a b. (b + ) a c. a 4 d. a b 9 (+) If you were constructing a pictograph, what symbol might you use to show the following? 6. Prices of various kinds of fruits. Number of people in several cities 8. Number of trees logged in various states Answers will vary. Example: coins or dollar bills Answers will vary. Example: stick figures of people Answers will vary. Example: trees 9 Teacher Aide Checks: (Nos. 6-8) Make sure students answers make sense. The Answer Key gives suggested answers. 2

11 Math 604, Lesson Lesson p. Lesson Preparation Quiz for each student Quiz pp. 6, 64 Teacher Check. When student is ready for the quiz, initial circle and administer quiz. è Assign Quiz. è Fascinating Discoveries: Toothpick Puzzles Tell your teacher when you are ready to take Quiz. Fascinating D iscoveries Toothpick Puzzles Arrange toothpicks like this. Quiz Other possible arrangements.. Remove 4 toothpicks to leave only 4 squares. 2. Set up the toothpicks again like before. Now remove 4 toothpicks to leave only squares. Teaching the Lesson Toothpick Puzzles This optional activity encourages logical thinking. Teacher Check on page. 28