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1 - Ratios & Proportions

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This powerpoint reviews ratios and proportions for the GED Test.

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1 - Ratios & Proportions

1. 1. RATIOS & PROPORTIONS LESSON 1 TENNESSEE ADULT EDUCATIONThis curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in any way without written permission. ©
2. 2. RATIOSRatios are comparisons made between two setsof numbers. For example:There are eight girls and seven boys in a class. The ratio of girls to boys is 8 to 7.
3. 3. Ratios are used everyday. They are used for:Miles per hourThe cost of items per pound, gallon, etc.Hourly rate of pay 80 miles to 1 hour = 80mph
4. 4. THERE ARE 3 WAYS TO WRITE RATIOS.1. Write the ratio using the word “to” between the twonumbers being compared. For example: There are 8 girls and 5 boys in my class. What is the ratio of girls to boys? The ratio is: 8 girls to 5 boys 8 to 5
5. 5. 2. Write a ratio using a colon between the two numbers being compared.For example: There are 3 apples and 4 oranges in the basket. What is the ratio of apples to oranges? The ratio is: 3 apples to 4 oranges. 3:4
6. 6. 3. Write a ratio as a fraction.For example: Hunter and Brandon were playing basketball. Brandon scored 5 baskets and Hunter scored 6 baskets. What was the ratio of baskets Hunter scored to the baskets Brandon scored?The ratio of baskets scored was: 6 baskets to 5 baskets 6 5
7. 7. GUIDED PRACTICE:Directions: Write the ratio in three different ways.There are 13 boys and 17 girls in sixth grade.Find the ratio of boys to the girls in sixth grade. 13 13 to 17 13 : 17 17
8. 8. RULES FOR SOLVING RATIO PROBLEMS. 1. When writing ratios, the numbers should be written in the order in which the problem asks for them. For example: There were 4 girls and 7 boys at the birthday party. What is the ratio of girls to boys?Hint: The question asks for girls to boys; therefore, girlswill be listed first in the ratio. 4 girls 4 girls to 7 boys 4 girls : 7 boys 7 boys
9. 9. GUIDED PRACTICE:Directions: Solve and write ratios in all three forms.1. The Panthers played 15 games this season. They won 13 games. What is the ratio of games won to games played? The questions asks for Games won to Games played. 13 13 to 15 13:15 15
10. 10. 2. Amanda’s basketball team won 7 games and lost 5. What is the ratio of games lost to games won?THE QUESTION ASKS FOR GAMES LOST TO GAMESWON. THEREFORE, THE NUMBER OF GAMES LOSTSHOULD BE WRITTEN FIRST, AND THE GAMES WONSHOULD BE WRITTEN SECOND. Games lost = 5 to Games won = 7 5 to 7 5:7 5 7
11. 11. REDUCING RATIOSRatios can be reduced without changing their relationship. 2 boys to 4 girls = 1 boy to 2 girls =
12. 12. REDUCING RATIOSIs this relationship the same? 2 boys to 4 girls = 1 boy to 3 girls =
13. 13. 2. ALL RATIOS MUST BE WRITTEN IN LOWEST TERMS.Steps: 1. Read the word problem. 2. Set up the ratio. For example: You scored 40 answers correct out of 45 problems on a test. Write the ratio of correct answers to total questions in lowest form. Step 1: Read the problem. What does it want to know? 40 to 45 40 : 45 40 45
14. 14. 3. Reduce the ratio if necessary. Reduce means to break down a fraction or ratio into the lowest form possible. Reduce = smaller number; operation will always be division.HINT: When having to reduce ratios, it is better to set up the ratio in thevertical form. (Fraction Form) 40 40 to 45 = 45 Look at the numbers in the ratio. What ONE number can you divide BOTH numbers by? Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40 Factors of 45: 1, 3, 5, 9, 15, 45 40 ÷ 5 = 8 45 ÷ 5 = 9
15. 15. Guided Practice:Directions: Solve each problem. Remember to reduce. 1. There are 26 black cards in a deck of playing cards. If there are 52 cards in a deck, what is the ratio of black cards to the deck of cards? Step 1: Read the problem. (What does it want to know?) Step 2: Set up the ratio. 26 black cards to 52 cards Step 3: Can the ratio be reduced? If so, set it up like a fraction. 26 ÷ 26 = 1 52 ÷ 26 = 2 What is the largest number that will go into both the top number and the bottom number evenly? (It can not be the number one!)
16. 16. 2. Kelsey has been reading Hunger Games for class. She read 15chapters in 3 days. What is the ratio of chapters read to thenumber of days she read? 15 chapters to 3 days 15 ÷÷ 3 = 5 3 3 = 1 Hint: When a one is on the bottom, it must remain there. If the one is dropped, there is no longer a ratio.
17. 17. PROPORTIONSProportions are two ratios of equal value. 1 girl 4 girls 4 boys 16 boysAre these ratios saying the same thing?
18. 18. PROPORTIONSProportions are two ratios of equal value. 1 girl 5 girls 4 boys 16 boysAre these ratios proportions?
19. 19. DETERMINING TRUE PROPORTIONS: To determine a proportion true, cross multiply. If the cross products are equal, then it is a true proportion. 4 = 20 5 25 20 x 5 = 4 x 25 100 = 100The cross products were equal, therefore 4 And 20 makes a true proportion. 5 25
20. 20. Guided Practice:Directions: Solve to see if each problem is a true proportion.1. 3 = 15 5 252. 6 = 57 8 763. 7 = 37 12 60
21. 21. Guided Practice:Directions: Solve to see if each problem is a true proportion. 3 15 6 57 1. 5 = 25 2. = 3. 7 = 37 8 76 12 6015 x 5 = 3 x 25 57 x 8 = 6 x 76 7 x 60 = 37 x 12 456 = 456 75 = 75 420 = 444 true true false
22. 22. SOLVING PROPORTIONS WITH VARIABLES What is a variable? A variable is any letter that takes place of a missing number or information.Eric rode his bicycle a total of 52 miles in 4 hours. Riding atthis same rate, how far can he travel in 7 hours? Next, the problem states “how far can he travel in 7 hours.Look for the two sets of You have 52 miles in 4 The problem is missing theratios to make up a hours. This is the first miles. Therefore, the milesproportion. ratio. becomes the variable. Set 1 52 miles n miles Set 2 4 hours 7 hours The proportion should be 52 = n 4 7 set equal to each other. HINT: The order of the ratio does matter!
23. 23. SOLVING THE PROPORTION:When solving proportions, follow these rules:1. Cross multiply.2. Divide BOTH sides by the number connected to the variable.3. Check the answer to see if it makes a true proportion.Problem: 52 n = 4 7 4 x n = 52 x 7 Which number is connected to the variable? 4n = 364 n = 91 miles 4 4Since the 4 is connectedto the variable, DIVIDEboth sides by the 4. 4 ÷ 4 = 1; 364 ÷ 4 = 91 therefore you are left with “n” on one side.
24. 24. If it comes out even, then the answer is correct. Check your answer! 52 91 = 4 7 52 x 7 = 91 x 4 364 = 364
25. 25. GUIDED PRACTICEDirections: Solve each proportion.1.For every dollar Julia spends on her MasterCard, she earns 3 frequent flyer miles withAmerican Airlines. If Julia spends \$609 dollars onher card, how many frequent flyer miles will sheearn?
26. 26. GUIDED PRACTICEDirections: Solve each proportion.1. For every dollar Julia spends on her Master Card, sheearns 3 frequent flyer miles with American Airlines. If Juliaspends \$609 dollars on her card, how many frequent flyermiles will she earn?Step 1: Set up the proportion. \$1.00 = \$609.00 3 miles d milesStep 2: Cross multiply. 1d = 1827Step 3: Divide 1 1Step 4: Check answer. d = 1827
27. 27. 1. Justin’s car uses 40 gallons of gas to drive 250 miles. At this rate, approximately, how many gallons of gas will he need for a trip of 600 miles.2. If 3 gallons of milk cost \$9, how many jugs can you buy for \$45?3. On Thursday, Karen drove 400 miles in 8 hours. At this same speed, how far can she drive in 12 hours?
28. 28. 1. Justin’s car uses 40 gallons of gas to drive 250 miles. At this rate, approximately, how many gallons of gas will he need for a trip of 600 miles. 40 gal x gal 40 x = = 250 mi 600mi 250 600 250x = 24000 250x = 24000 Check: 250 250 40 96 = x = 96 250 600 24000 = 24000
29. 29. 2. If a 3 gallon jug of milk cost \$9, how many 3 gallon jugs can be purchased for \$45? 1 n = 9 45 Check: 1= n 9 45 1 5 9 = 451x45 = 9n 45 = 4545 = 9n 9 95=n5 jugs of milk can bepurchased for \$45
30. 30. 3. On Thursday, Karen drove 400 miles in 8 hours. At this same speed, how far can she drive in 12 hours? 400 miles = x miles 8 hours 12 hours 400 x_ = 8 12 400 x_ = 8 12 8x = 4800 x = 600 miles
31. 31. 4. Susie has two flower beds in which to plant tulips anddaffodils. She wants the proportion of tulips to daffodils to bethe same in each bed. Susie plants 10 tulips and 6 daffodils inthe first bed. How many tulips will she need for the second bedif she plants 15 daffodils?10 tulips = x tulips 10 x_ = 6 daffodils 15 daffodils 6 1510 x x = 25 tulips = 6 156x = 150 10 25 =6x 150 6 15 = 6 6 150 = 150 x = 25