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Course 1 Unit 2Fractions, Decimals, and PercentsName: ___________________Lesson 2-1 Part 1: Decimals and FractionsRational Number – Example 1: Write the decimal 0.6 as a fraction in simplest form.Draw the place value chart shows that the place value of the last decimal place is tenths.0.6 = 610 = ______________Example 2:Write the decimal 0.45 as a fraction in simplest form.Draw the place value of the last decimal place.0.45 = 45100 = ________________Example 3: Write the decimal 0.375 as a fraction in simplest form.0.375 = 3751000 = _________Got it? Write each decimal as a fraction in simplest form.a) 0.8b) 0.28c) 0.125 Example 4: The average length of a conch shell is 9.85 inches. Express 9.85 as a mixed number in simplest form.9.85 = 98510085100 ÷ 55 = 1720= __________ inchesGot it? It takes approximately 4.65 quarts of milk to make a pound of cheese. Express this amount as a mixed number in simplest form.Example 5Write 912 as a decimal. (Hint: You can also use a ratio table)Got it? a) 35 b) 1425 Guided Practice:Write each decimal as a fraction or mixed number in simplest form. 1. 0.4 = __________ 2. 0.64 = __________3. 2.75 = __________4. 0.225 = __________Write each fraction or mixed number as a decimal. 5. 2775= __________6. 315= __________7. Write a fraction and a decimal (not from the lesson or Guided Practice) that are equivalent. Lesson 2-2 Percents and FractionsPercent - _______________________________________________________Example 1Write 50% as a fraction in simplest form.50% means 50 out of 100.50% = 50100 = ___________Example 2In a recent survey, 55% of cell phone owners said they text message. What fraction of cell phone owners is this?55% = __________= ___________So, _______________ of cell phone owners text message.Got it? Write each percent as a fraction in simplest form.a. 75%b. 90%c. 38%Example 3The table shows the percent of each movie type rented during a month. What fraction of the rentals were action movies?35% = 35100 = __________Action movies were rented __________ of the time.Got it? Write the fraction of rentals that were horror movies.Example 4Write the fraction 68 as a percent. 68 = __________34 = ?10034 = ____________________%Got it? Write the fraction 812 as a percent. (Hint: Use a ratio table to get to 100.)Example 5Mitch made 12 out of 40 shots during the basketball championship game. What percent of his shots did Mitch make?We need to scale back before we can scale forward.1240 = ____________________ = ?100__________= __________=__________%Got it? Alana spelled 19 out of 25 words correctly. What percent of the words did Alana spell correctly? Guided Practice: Write each percent as a fraction in simplest terms. 1. 15%2. 80%3. 33%Write each fraction as a percent. 4. 3105. 3206. 257. Fill in the blanks with the correct number to represent 32%. a. ________ out of 100. b. ________ out of 50Lesson 2-3 Percents and DecimalsExample 1:Write the 56% as a decimal.Method 1: Write the percent as a fraction.Rewrite the percent as a fraction with a denominator of 100. 56% = _________ Write 56 hundredths as a decimal.56% =________Method 2: Move the decimal point.Move the decimal point _______ places to the left. Then remove the percent sign.56% = _________Example 2:Write the 8% as a decimal.Method 1: Write the percent as a fraction.Rewrite the percent as a fraction with a denominator of 100. 8% = __________Write 8 hundredths as a decimal.8% =__________Method 2: Move the decimal point.Move the decimal point 2 places to the left. Then remove the percent sign.8% = __________Example 3:Write the 2% as a decimal.Method 1: Write the percent as a fraction.Rewrite the percent as a fraction with a denominator of 100. 2% = __________Write 2 hundredths as a decimal.2% =__________Method 2: Move the decimal point.Move the decimal point 2 places to the left. Then remove the percent sign.2% = __________Got it? 1Write each percent as a decimal.32% b. 6%c. 93%Example 4:Write 0.38 as a percent.Method 1: Write the decimal as a fraction.0.38 = __________38100 = __________Method 2: Move the decimal point. 0.38 = __________Example 5Write 0.2 as a percent.Method 1: Write the decimal as a fraction.0.2 = __________210 = __________Method 2: Move the decimal point. 0.2 = __________Got it? Write each decimal as a percent.d. 0.47e. 0.73f. 0.5Example 6The United States produces more corn than any other country, producing 0.4 of the total corn crops. Write 0.4 as a percent.0.4 x __________ = _____________________%Got it? About 0.7 of the human body is water. What percent is equivalent to 0.7? (Example 6)Guided Practice:Write each percent as a decimal. 1. 27%2. 15%3. 4%Write each decimal as a percent. 4. 0.35. 0.826. 0.517. What method do you use to convert a percent to a decimal? Give an example using different numbers than this lesson. 8. What method do you use to convert a decimal to a percent? Give an example using different numbers than this lesson.Lesson 2-4 Percents Greater Than 100% and Percents Less Than 1%Example 1:Write 0.2% as a decimal and as a fraction.Decimal: Move the decimal 2 places to left.= _________Fraction: Change decimal to fraction.2 is in the thousandths place.21,000 or ___________Got it? Write 0.25% as a decimal and a fraction.Example 2:Write 170% as a mixed number in simplest form and as a decimal.Mixed Number: 170% = ___________= 1710= ___________Decimal: Move the decimal 2 places to left.= _________Got it? Write 325% as a decimal and as a mixed number.Example 3:Jimmy’s savings increased by 250%. Write 250% as a mixed number in simplest form and as a decimal.Fraction: 250% = _________= ________Decimal: Move the decimal 2 places to left.= _________Got it? 3Write 530% as a decimal and as a mixed number in simplest form.Example 4:Write 114 as a percent.14 is one of those fractions to have memorized…it equals _________. So, 114 is _________%.Got it? Write 325 as a percent.Example 5Write 1.68 as a percent.Move the decimal point ______ places to the right.1.68 = _________%Example 6Write 0.0075 as a percent.Move the decimal point ______ places to the right.0.0075 = __________%Got it? a. Write 1.92 as a percent.b. Write 0.0094 as a percent.Example 7The cheetah is the fastest land mammal in the world. The peregrine falcon is the fastest bird in the world. Its speed is 2.1 times as fast as the cheetah. Write this number as a percent.2.1 = _______%The falcon’s speed is ________% of the cheetah’s.Got it? The slowest land mammal is the sloth. Its speed is about 0.0016 that of a cheetah. Write this number as a percent.Guided Practice:Write each percent as a decimal and as a mixed number or fraction in simplest form. 1. 325% 2. 480%3. 0.6%Write each mixed number or decimal as a percent. 4. 1455. 0.00156. 2.757. Fill in the blank. A manufacturing company finds that ________________ or 0.19% of all light bulbs are defective. (The blank is a decimal). 8. What is one mistake someone can make when converting a decimal into a percent? Lesson 2-5 Compare and Order Fractions, Decimals, and PercentsLeast common denominator (LCD) –________________________________________________________________________________________________________________________________________________3 Steps to Comparing Fractions: 1. Find the _________ of the fractions.2. Write an _____________________ fraction for each using the LCD.3. Compare the _______________________Example 1:Which is bigger 310 or 56?1. What is the LCD? (circle it)10: 10, 20, 30, 40, 50, 60…6: 6, 12, 18, 24, 30, 36…2. Write each fraction with a denominator of _________.310 = __________ 56 = __________3. Since ________ is bigger than ________, _________ < __________Got it? 50504272530931345424708110553703673923 492. 512 783. 16 518Example 2:Order the fractions from least to greatest:12????914????34?????571. Find the LCD:2: All even numbers4: 4, 8, 12, 16, 20, 24, 28…14: 14, 28…7: 7, 14, 21, 28…. Write all 4 fractions with the denominator of ______.12??= _____________?914=_______________?34=_____________??57 = ________________3. _____________28<______________28<______________28<_______________28?so ________________________________Got it? 1 & 2Order the fractions from least to greatest:12????56????23????35Steps to Compare Fractions, Decimals, and Percents1. Write them all as __________________.2. Start at the ______________.3. Annex (add) ____________ until they all have the same # of digits.Put into Memory:-984255080000118110274955Example 3:34 0.734 = ________Annex (add) a zero so 0.7 = 0.70Which is bigger? _______ or 0.70?So ________________Got it? 27051012700.6 23Example 4:Lucita made 85% of her free throws. Henri made 78 of his free throws. Who has the better average? Explain by showing work.85% = 0.85078 = 0.8750.85 < 0.875Since 0.85 is less than 0.875, ____________had the better average.Got it? -304800444500Example 5:403860029981100The table shows the school carnival attendance. Which grade has the greatest part of the class attending the carnival?58 = _________0.5 = _________58.3% = ___________Since ___________ is the greatest, _______ grade had the best attendance.Got it? Hiroshi found that 35 of his class prefers vanilla ice cream, 26% prefers chocolate, and 0.14 prefers strawberry. Which kind of ice cream do students prefer least?What if……you were asked to write three fractions with different denominators, but all had a LCD of 32? Step 1: Think of numbers that have a multiple of 32.2, 4, 8, 16Step 2: Choose three of those numbers and make that number the denominator. I’m going to choose 2, 4, and 8. 2???4????8Step 3: Make up any numerator that makes sense. Sample?Answer?12???34????58Guided Practice:1. Order the fractions 45, 12, 910, and 34 from least to greatest. 2. Cora spends 25 of her free time blogging. Leah spends 65% of her time blogging. Who spends more time blogging? 4211955269240003. The table shows the wins for some middle school football teams. Which team has the greatest fraction of wins? Lesson 2-6 Estimate with PercentsFinding a Fraction of a Number540756915430500Step 1: Divide by the denominatorStep 2: Multiply by the numerator.Example : Find 23 of 60Step 1: Divide 60 ÷ 3 = 20Step 2: Multiply 20 x 2 = 40So, 23 of 60 is 40.Example 1:Estimate 47% of 692.Step 1: Round 47% up to 50 %Step 2: Round 692 up to 700.Step 3: Solve.50% of 700 = ?12 of 700 = ____________So, 47% of 700 is about ___________. Example 2:Estimate 60% of 27.Step 1: Convert 60% to a fraction.60100 = ____________Step 2: Round 27 to ________.Step 3: Solve 35 of 25.25 ÷5 = 55 x 3 = 15So, 60% of 27 is about __________Got it? Estimate. a. 48% of 76b. 18% of 42c. 73% of 41 Example 3:Polar bears can eat as much as 10% of their body weight in less than one hour. If an adult male polar bear weighs 715 pounds, about how much food can he eat in one hour?Step 1: Convert 10% to a fraction10% = 110Step 2: Round 715 down to 700.Step 3: Solve110 of 700 =700 ÷10=70So, a polar bear can eat about ___________ lbs of food in 1 hour.Got it? Kayleigh decided to donate 30% of her savings. If she has $238 in her savings account, about how much will she donate?Example 4Estimate 17% of 198 using a rate per 100.198 ≈ ___________17% is 17 out of ________.Since 200 = 100 + 100, add 17 + 17 to estimate.≈_________Example 5An airline records the snack orders of passengers. Last year 9 % of all passengers ordered ginger ale to drink. There are 408 passengers on the flight to Houston. About how many passengers does the airline expect to order ginger ale on this flight?Estimate 9% of 408.408 ≈ ___________9 x _________ = 36About ___________ people will order ginger ale.Got it? Estimate using a rate per 100.a. 27% of 307b. 76% of 192Guided Practice:Estimate each percent. 1. 19% of $532. 21% of 963. 59% of 164. A purse that originally cost $29.99 is on sale for 50% off. About how much would you pay for the purse after the sale? 5. Mr. Marcucci received a bonus of $496 from his employer. He has to pay 33% of his bonus to taxes. How much will Mr. Marcucci pay in taxes? Lesson 2-7 Percent of a NumberExample 1: 392430028575000Suppose there are 300 students at York Middle School. Find the number that has cheese as a snack.Write the percent as a decimal. 15% = 0.15Then multiply: 0.15 x 300 = _________So, ________ students have cheese as a snack.Example 1 – Another WayStep 1: Make 15% a fraction.15% = 15100Step 2: Multiply that by 300.15100?x?3001Simplify: = _________Got it? Find the number of students at York Middle School that have chips as a snack.Example 2:Find 145% of 320. Step 1: Write the percent as a decimal.145% = 1.45Step 2: Multiply.1.45 x 320 = 464Got it? Find 220% of 65.Example 3:Find 0.25% of 58.Step 1: Write 0.25% as a decimal.0.25% = ____________Step 2: Multiply.0.0025 x 58 = ____________So, 0.25% of 58 is ___________Got it? Find 0.3% of 200.Example 4:In a recent state Special Olympics meet, Franklin County sent a team of 70 players. Twenty percent of the team competed in soccer. How many athletes competed in soccer?Step 1: Write 20% as a decimal.20% = ________Step 2: Multiply.0.2 x 70 = __________So, __________ athletes competed in soccer.Got it? Troy wants to buy a jersey of his favorite MLS team. The jersey is 30% off the original price. If the original price is $35, what is the amount Troy will save?Guided Practice:Find the percent of each number. 1. 32% of 60 = ___________2. 0.55% of 220 = ___________3. 275% of 4 = ____________4. A sandwich shop sold 75 sandwiches at lunchtime. Twelve percent of the sandwiches were grilled cheese. How many grilled cheese sandwiches did the shop sell? 5. Is 15% of 10 the same as 10% of 15? Explain by showing your work. Lesson 2-8 Solve Percent ProblemsProportion – ___________________________________________________________________________________________________________________________________Percent proportion – __________________________________________________________________________________________________________________________partwhole=partwholeExample 1:10 is 25% of what number?Set up a percent proportion:10? = 2510025 ÷ 2 = 12.5100 ÷ 12.5 = ___________So, 10 is 25% of __________. Example 2:Country music makes up 45% of Landon’s music library. If he has downloaded 90 country music songs, how many songs does Landon have in his music library?90? = 45100Since 45 x 2 is 90, 100 x 2 = ___________So, Landon has ____________ songs in his music library.Got it? 1. 30 is 50% of what number?2. Peyton spent 60% of his money to buy a new television. If the television cost $300, how much money did he have?Example 315 is 30% of what number?407035374015172529535877540703518478501725295179641543922951986915751649519869152944495296481515? = 30100Divide each by ______.=___________4190728771163Example 4:32194526543000225 is 75% of what number?1397000165105080001841513970002260605080002260605232400-508003200400-5080050800032321522225002952750Got it? a. 75 is 15% of what number?b. 9 is 36% of what number?c. 7 is 70% of what number?Example 5Before 1982, pennies were 95% zinc and 5% copper. If 100 pennies minted in 1980 have an approximate mass of 15 grams of copper, what is the total mass of 100 pennies?The percent is 5 and the part is 15. You need to find the whole.15? = ______________The total mass of 100 pennies is __________ grams.Got it? In the first year of ownership, a new car can lose 20% of its value. If a car lost $4,200 of value in the first year, how much did the car originally cost?Guided Practice:1. 120 is 30% of what number? 2. 60 is 15% of what number? 3. An advertisement announced that 95% of doctors approve of this new medication. Why is this misleading? ................
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