Lesson 5.1 Reteach Model Percents A percent is a ratio that compares a number to. It represents part a whole. Model 54% on the 10-by-10 grid. Then write the percent as a ratio. Step 1 The grid represents 1 whole. It has equal parts. To show 54%, shade 54 the equal parts. Step 2 A ratio can be written as a fraction. Write the number shaded parts, 54, in the numerator. Write the total number parts in the whole,, in the denominator. So, 54% is 54 out squares shaded, or 54 _. shaded total 54 _ Model the percent and write it as a ratio. 1. 19% 2. 80% 3. 66% ratio: _ 4. 3% ratio: _ 5. 31% ratio: _ 6. 25% ratio: _ ratio: _ ratio: _ 5-5 Reteach
Lesson 5.1 Enrich Matching Models Write the letter the correct model for each ratio or percent. 1. 48% 2. 70% 3. 52 _ 4. 30 _ 5. 72 _ 6. 36% _ A. B. C. D. E. F. 7. Stretch Your Thinking Describe how you could use one 10-by-10 grid to show that three different percents have a sum %. Then shade the grid to show that 13% 1 24% 1 63% 5 %. 5-6 Enrich
Lesson 5.2 Reteach Write Percents as Fractions and Decimals You can write a percent as a decimal and a fraction. Write 140% as a decimal and as a fraction in simplest form. Step 1 Write 140% as a decimal by changing the percent sign to a decimal point and moving it two places to the left. Step 2 Write 140% as a fraction by removing the percent sign and placing 140 in the numerator. Since percent means out, place in the denominator. Step 3 Simplify. So, 140% 5 1.40 5 7_, or 1 2_ 5 5. 140% 5 140 5 1.40 140% 5 140 _ 140 _ 5 7_, or 1 2_ 5 5 Write the percent as a decimal and as a fraction in simplest form. 1. 75% 2. 44% 3. 128% 4. 5% 5. 464% 6. 38% 7. 7% 8. 0.6% 9. 234% 10. 0.9% 11. 72% 12. 8% 5-7 Reteach
Lesson 5.2 Enrich Percent Pictures Follow the code to find the hidden picture. 0.9 3_ 5 1_ 4 0.06 9 10 0.66 0.32 1.50 5 0.5 16 32 1_ 2 0.77 4.5 0.04 65 77 11 22 9 20 3_ 6 0.06 44 _ 16 31 11 _ 0.500 50 _ 0.50 0.14 1_ 5 50 _ 120 0.12 12 25 0.4 40 60 0.004 0.88 1_ 1 0.400 1 4 10 0.03 6 15 5_ 6 0.07 6.5 8 20 2_ 5 40 _ 0.99 0.43 0.29 0.045 17 20 0.40 0.730 0.83 87 _ 1_ 7 0.15 6 23 0.58 46 _ 0.91 1.11 1. Color numbers equivalent to 50% red. 2. Color numbers equivalent to 45% yellow. 3. Color numbers equivalent to 40% green. What is the hidden picture? _ 5-8 Enrich
Lesson 5.3 Reteach Write Fractions and Decimals as Percents You can write fractions and decimals as percents. To write a decimal as a percent, multiply the decimal by and write the percent symbol. 0.073 5 7.3% To multiply by, move the decimal point two places to the right. To write a fraction as a percent, divide the numerator by the denominator. Then write the decimal as a percent. To write 3_ as a percent, first divide 3 by 8. 8 0.375 8 q w 3.000 224 60 256 40 240 0 So, 3 _ 8 5 0.375. 0.375 5 37.5% To write 0.375 as a percent, multiply by and write the percent symbol. Write the decimal or fraction as a percent. 1. 0.45 2. 0.6 3. 2.34 4. 7 8 5. 19 _ 50 6. 0.03 7. 1 11 _ 16 8. 51 _ 10 5-9 Reteach
Lesson 5.3 Enrich Fraction, Decimal, Percent Soup Use the fractions, decimals, percents, and ratios in the soup bowl below to write the equivalent answers for each square. You will not use all the values in the bowl. RATIO FRACTION 4 out 5 RATIO _ FRACTION 3 8 RATIO FRACTION DECIMAL PERCENT DECIMAL PERCENT 0.74 DECIMAL PERCENT RATIO FRACTION RATIO FRACTION RATIO FRACTION 26 out 40 0.3 out 142% DECIMAL PERCENT DECIMAL PERCENT DECIMAL PERCENT 71 out 50 20% 0.3% 33 1,000 13 20 0.003 1 21 50 0.38 1.42 37 50 7.4% 65% 3 out 8 0.65 3% 4 5 0.375 13 25 37 out 50 0.8 37.5% 74% 80% 140 out 0.25 1. Stretch Your Thinking Write the numbers and ratios that you did not use in order from least to greatest. 2. Explain how to change 86% into an equivalent ratio written in simplest form. 5-10 Enrich
Lesson 5.4 Reteach Percent a Quantity You can use ratios to write a percent a quantity. Find 0.9% 30. Step 1 Write the percent as a rate per. 0.9% 5 _ 0.9 Step 2 Multiply by a fraction equivalent to 1 to get a whole number in the numerator. _ 0.9 3 10 10 5 _ 9 1,000 Step 3 Write the multiplication problem. Step 4 Multiply. So, 0.9% 30 is 0.27. _ 9 3 30 1,000 _ 9 3 30 5 _ 27 5 0.27 1,000 Find the percent the quantity. 1. 8% 90 2. 20% 80 3. 95% 340 4. 33% 28 5. 200% 8.5 6. 125% 70 7. 0.25% 120 8. 0.4% 50 9. 45% 70 10. 155% 30 11. 75% 124 12. 0.8% 1,000 13. James correctly answered 85% the 60 problems on his math test. How many problems did James answer correctly? 14. A basketball player missed 25% her 52 free throws. How many free throws did the basketball player miss? 5-11 Reteach
Lesson 5.4 Enrich Percent Wheels Choose from the numbers below to complete the percent wheels. The first one in Wheel 1 has been done for you. Percent Wheel 2 10% 2% 5% 6% 8% 6005 10% 15% 20% 50% 75% 150% 30% 60 5 500 16 32 48 120 480 Percent Wheel 1 5% 8% 10% 12% 15% 20% 22% 24% 25% 26% 50% 1,2005 24 200 240 250 750 1. Stretch Your Thinking Write a percent problem where the answer is 80. 2. Is 150% 25 equal to 25% 150? Explain your answer. 5-12 Enrich
Lesson 5.5 Reteach Problem Solving Percents Use a model to solve the percent problem. Lucia is driving to visit her parents, who live 240 miles away from her house. She has already driven 15% the distance. How many miles does she still have to drive? Read the Problem What do I need to find? I need to find the difference between the total distance and the distance already driven. What information do I need to use? The total distance is 240 miles and she has already driven 15% the total distance. How will I use the information? I will draw a model to find the number miles already driven and subtract that amount from the total distance. total distance distance driven? 15% Solve the Problem Use a bar model to help. Draw a bar to represent the total distance. Then draw a bar that represents the distance driven plus the distance left. % 240 miles The model shows that % 5 so 1% 240 5 240 _ 5 miles. 15% 240 5 15 3 5 So, Lucia has already driven She still has to drive 240 2 5 204 miles. 2.4 2.4 36 36 240 36 miles, miles. 1. At a deli, 56 sandwiches were sold during lunchtime. Twenty-five percent the sandwiches sold were tuna salad sandwiches. How many the sandwiches sold were not tuna salad? 42 sandwiches 2. Mr. Brown bought a TV for $450. He has already paid 60% the purchase price. How much has he already paid and how much does he have left to pay? $270; $180 5-13 Reteach
Lesson 5.5 Enrich Time to Shop! Use the items in the sports store to solve the problems. $ 35 $ 10 $ 15 $ 40 $ 50 $ 260 1. Mariah wants to buy two cans tennis balls and a tennis racket. If she has 35% the money saved, how much more does she need? 2. The director an athletic club wants to buy two new soccer goals. His budget accounts for 75% the money needed, and he receives another 10% in donations. How much more money does the director need? 3. Aaron and Kendall both want a hockey stick. Aaron has 60% the money saved. Kendall has 45% the money saved. How much more does Aaron have saved than Kendall? 4. Megan bought two baseball gloves and one baseball bat. She paid for 40% with her birthday money and her uncle paid the remaining amount. How much did Megan pay and how much did her uncle pay? 5. Stretch Your Thinking Describe a different method than the one you used to solve Problem 1. 5-14 Enrich
Lesson 5.6 Reteach Find the Whole from a Percent You can use equivalent ratios to find the whole, given a part and the percent. 54 is 60% what number? Step 1 Write the relationship among the percent, part, and whole. The percent is 60%. The part is 54. The whole is unknown. Step 2 Write the percent as a ratio. Step 3 Simplify the known ratio. percent 5 _ part whole 60% 5 54 _ 60 5 54 Find the greatest common factor (GCF) the numerator and denominator. 60 5 2 3 2 3 3 3 5 GCF 5 2 3 2 3 5 5 20 5 2 3 2 3 5 3 5 Divide both the numerator and 60 4 20 5 54 denominator by the GCF. 4 20 3_ 5 54 5 Step 4 Write an equivalent ratio. Look at the numerators. Think: 3 3 18 5 54 Multiply the denominator by 18 to find the whole. 3 3 18 5 54 5 3 18 54 5 54 90 90 5 So, 54 is 60% 90. Find the unknown value. 1. 12 is 40% 2. 15 is 25% 3. 24 is 20% 4. 36 is 50% 5. 4 is 80% 6. 12 is 15% 7. 36 is 90% 8. 12 is 75% 9. 27 is 30% 5-15 Reteach
Lesson 5.6 Enrich A Whole Lotta Game In a recreational basketball league, the Lions are playing the Bears. The number points scored from free throws and the percentage total points that are scored from free throws are given. Find the total number points scored in each quarter. Lions Bears 1ST 4 points is 25% 1ST 1 point is 10% 2ND 8 points is 40% 2ND 5 points is 20% 3RD 15 points is 50% 3RD 9 points is 45% 4TH 3 points is 20% 4TH 12 points is 75% 1. How many total points did the Lions score? How many total points did the Bears score? 2. In basketball, the team with the most points wins the game. Which team won? By how many points? 3. Explain how to use multiplication instead ratios to find the number points the Lions scored in the 3rd quarter. 5-16 Enrich