1 / 88

Ch 5 Rate, Ratio and Percent

Ch 5 Rate, Ratio and Percent. 5.1 Relating Fractions, Decimals and Percents. Hundred Grid . To represent a percent, you can shade squares on a grid of 100 squares, called a hundred grid. One completely shaded grid represents 100%.

erica
Download Presentation

Ch 5 Rate, Ratio and Percent

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Ch 5 Rate, Ratio and Percent

  2. 5.1 Relating Fractions, Decimals and Percents

  3. Hundred Grid • To represent a percent, you can shade squares on a grid of 100 squares, called a hundred grid. One completely shaded grid represents 100%. • To represent a percent greater than 100%, shade more than one grid. • To represent a fraction percent between 0% and 1%, shade part of one square. • To represent a fractional percent greater than 1%, shade squares from a hundred grid to show the whole number and part of one square from the grid to show the fraction.

  4. Key Ideas • Fractions, decimals and percents can be used to represent numbers in various situations • Percents can be written as fractions and decimals • ½ % = 0.5% = 0.5/100 = 5/1000= 0.005 • 150% = 150/100 = 1.5 or 1 ½ • 43 ¾ % = 43.75% = 43.75/100 = 4375/10000= 0.4375 • When we have a decimal percent, we express it in fraction form. You add as many zeros as there are decimal places. The example above had two decimal places, so we added 2 zeros. • To get the decimal – remember we divide the numerator by the denominator

  5. Workbook • Page 100-104 • Text pg 240-241 #12-14, 19-20

  6. 5.2 Calculating Percents

  7. Converting Percents to Decimals • Remember that 1% = 1/100 = 0.01 • So 175% = 175/100 = 1.75 • 0.5% = 0.5/100 = 5/1000 = 0.005 • Notice that the decimal is in the place value of the denominator • Another way to look at it is how to move the decimal when converting from percent to decimal move the decimal 2 spots to the left • 230% = 2 3 0 = 2.30 • 0.09% =0 0 0 0 . 0 0 9 = 0.00009

  8. How to convert a fraction to percent • First convert the fraction to a decimal. Once you have a decimal the properties are similar to as converting a percent to a decimal – instead move the decimal 2 spots to the right to get percent. • ½ = 0.5 = 0.5 0 = 50% • 3/2 = 1.5 = 1 . 5 0 = 150% • 3/200 = 0.015 = 0 . 0 1 5 = 1.5%

  9. Complete the chart

  10. Answers to Chart

  11. Calculating percent of a number • Take the percent and convert it to a decimal, than multiply by the number you are calculating the percent of • 200% of 40 = 2.0 x 40 = 80 • 20% of 40 = 0.2 x 40 = 8 • 2% of 40 = 0.02 x 40 = 0.8

  12. Word Problems – Give this a Try • A marathon had 618 runners registered. Of these runners, about 0.8% completed the race in under 2h 15min. How many runners completed the race in under 2h 15min? • 0.8% of 618 runners • 0.008 of 618 runners • 4.94 = 5 runners

  13. Word Problems – Try This One • Twenty boys signed up for the school play. The number of girls who signed up was 195% of the number of boys. At the auditions, only 26 girls attended. What percent of the girls who signed up for the play attended the auditions? • 195% of 20 = 39 • 26 of the girls who signed up attended = 26/39 = 0.6666 = 66.66%

  14. Workbook • Page 105 – 106

  15. 5.3 Solving Percent Problems

  16. You are given a number that equals a certain percent • 40% = 160 • You want to find out what 100% is so first find out what 1% is. • 1% = 160/40 = 4 • To calculate 100% take the number you got for 1% and multiply by 100. This also works if you want 85%, 115%, etc. • 100% = 4 x 100 = 400 • 155% = 4 x 155 = 620

  17. You Try • 6% of a number is 9 • 6% = 9 • 1% = • 100% = • 350% = • 28% of a number is 56 • 28% = 56 • 1% = • 100% = • 350% = • 150% of a number is 36 • 150% = 36 • 1% = • 100% = 1.5 150 525 2 200 700 0.24 24

  18. To Calculate the Percent Increase • Mary had $50 before her birthday in her account. After her birthday she had $300. Calculate the percent increase. • Step 1 – calculate the difference between the two numbers • 300 – 50 = 250 • Step 2 – express the difference over the original (a fraction) • 250/50 • Step 3 – calculate the decimal and than percent • 5 x 100 = 500% • She had a 500% increase after her birthday.

  19. Cross Multiply • Mary had $50 before her birthday in her account. After her birthday she had $300. Calculate the percent increase. • Step 1 – calculate the difference between the two numbers • 300 – 50 = 250 • Step 2 – express the difference over the original (a fraction) and make it equal to your unknown % over 100% • 250 = x__ 50 100 • Step 3 – cross multiply and divide to solve 50(x) = 250(100) 50x = 25000 50 50 x = 500 The percent increase is 500%

  20. You Try • The width of the rectangle increased from 8cm to 12cm • Step 1 – calculate the difference between the two numbers • 12 – 8 = 4 • Step 2 – express the difference over the original (a fraction) • 4/8 • Step 3 – calculate the decimal and than percent • 0.5 x 100 = 50%

  21. Cross Multiply • The width of the rectangle increased from 8cm to 12cm • Step 1 – calculate the difference between the two numbers • 12 – 8 = 4 • Step 2 – express the difference over the original (a fraction) and make it equal to your unknown % over 100% • 4 = _x_ 8 100 • Step 3 – cross multiply and divide to solve 4(100) = 8(x) 400= 8x 8 8 x = 50 The percent increase is 50%

  22. Another one • The price of a hotel room increased from $90 to $120 • Step 1 – calculate the difference between the two numbers • 120 – 90 = 30 • Step 2 – express the difference over the original (a fraction) • 30/90 • Step 3 – calculate the decimal and than percent • 0.333 x 100 = 33.33%

  23. Cross Multiply • The price of a hotel room increased from $90 to $120 • Step 1 – calculate the difference between the two numbers • 120 – 90 = 30 • Step 2 – express the difference over the original (a fraction) and make it equal to your unknown % over 100% • 30 = _x_ 90 100 • Step 3 – cross multiply and divide to solve 30(100) = 90(x) 3000= 90x 90 90 x = 33.33 The percent increase is 33.33%

  24. To Calculate the Percent Decrease • Susie made a pitcher of punch that was 56L, after her party she had 12L left. Calculate the percent decrease. • Step 1 – calculate the difference between the two numbers • 56 – 12 = 44 • Step 2 – express the difference over the original (a fraction) • 44/56 • Step 3 – calculate the decimal and than percent • 0.7857 x 100 = 78.57% • The pitched decreased in volume for 78.57%

  25. Cross Multiply • Susie made a pitcher of punch that was 56L, after her party she had 12L left. Calculate the percent decrease. • Step 1 – calculate the difference between the two numbers • 56 – 12 = 44 • Step 2 – express the difference over the original (a fraction) and make it equal to your unknown % over 100% • 44 = _x_ 56 100 • Step 3 – cross multiply and divide to solve 44(100) = 56(x) 4400= 56x 56 56 x = 78.57 The percent decrease is 78.57%

  26. You Try • The volume of water in the tank decreased from 40L to 32L. • Step 1 – calculate the difference between the two numbers • 40L – 32L = 8L • Step 2 – express the difference over the original (a fraction) • 8/40 • Step 3 – calculate the decimal and than percent • 0.2 x 100 = 20%

  27. Cross Multiply • The volume of water in the tank decreased from 40L to 32L. • Step 1 – calculate the difference between the two numbers • 40L – 32L = 8L • Step 2 – express the difference over the original (a fraction) and make it equal to your unknown % over 100% • 8_ = _x_ 40 100 • Step 3 – cross multiply and divide to solve 8(100) = 40(x) 800= 40x 40 40 x = 20 The percent decrease is 20%

  28. You Try • The number of students in the class decreased from 30 – 27 • Step 1 – calculate the difference between the two numbers • 30 – 27 = 3 • Step 2 – express the difference over the original (a fraction) • 3/30 • Step 3 – calculate the decimal and than percent • 0.1 x 100 = 10 %

  29. Cross Multiply • The number of students in the class decreased from 30 – 27 • Step 1 – calculate the difference between the two numbers • 30 – 27 = 3 • Step 2 – express the difference over the original (a fraction) and make it equal to your unknown % over 100% • 3_ = _x_ 30 100 • Step 3 – cross multiply and divide to solve 3(100) = 30(x) 300= 30x 30 30 x = 10 The percent decrease is 10%

  30. Workbook • Try questions 5 – 10 on page 108 - 109

  31. 5.4 Sales Tax and Discount

  32. Discount • When an item is sold at a reduced price – it is said to be sold at a discount. • There are 2 ways to calculate discount

  33. Discount Calculations – Method 1 (A Review) • 20% off $129 • Step 1 – calculate how much the discount is • 0.2 x $129 = $25.8 • Step 2 – calculate how much the cost is after you subtract the discount • $129 - $25.8 = $103.2

  34. Discount Calculations – Method 2 • 20% off $129 (means you are paying 80% of $129) • Step 1 – calculate the cost of what you are paying (in this case 80% of $129) • 0.8 x $129 = $103.2 • You are done – this method allows you to calculate in one step – you don’t have to do the subtraction – less steps, means less chance of making a silly mistake

  35. Another Example – Both Methods Shown • Calculate the sale price on a $92 watch, 30% off • Method 1 • 0.3 x $92 = $27.60 • $92 - $27.60 = $64.40 • Method 2 • 0.7 x $92 = $64.40

  36. Note • Only use method 2 if you are calculating the sale price – not if you are asked to calculate the discount only.

  37. Sales Tax • Sales tax is added to the final cost of you bill – in BC we currently have HST which is 12%. • Again there are 2 methods

  38. Sales Tax Calculations – Method 1 (A Review) • 12% tax on $288 • Step 1 – calculate how much the tax is • 0.12 x $288 = $34.56 • Step 2 – calculate how much the cost is after you add the tax • $288 + $34.56 = $322.56

  39. Discount Calculations – Method 2 • 12% tax on $288 (means you are paying 112% of $288) • Step 1 – calculate the cost of what you are paying (in this case 112% of $288) • 1.12 x $288 = $322.56 • You are done – this method allows you to calculate in one step – you don’t have to do the addition – less steps, means less chance of making a silly mistake

  40. Another Example – Both Methods Shown • Calculate the sale price on a $92 watch, 12% • Method 1 • 0.12 x $92 = $11.04 • $92 + $11.04 = $103.04 • Method 2 • 1.12 x $92 = $103.04

  41. Note • Only use method 2 if you are calculating the final price – not if you are asked to calculate the tax only.

  42. Another Example – Both Methods Shown with discount and tax • Calculate the sale price on a $476 TV, 15% off, 12% tax • Method 1 • 0.15 x $476 = $71.40 • $476 - $71.4 = $404.6 • 0.12 x $404.6 = $48.55 • $404.6 + $48.55 = $453.15 • Method 2 • 0.85 x $476 = $404.60 • 1.12 x $404.60 = $453.15 • Or • 0.85 x 1.12 x $476 = $453.15

  43. Note about multiply discounts • If a company offers multiple discounts – you cannot add them together – you must calculate each one • Example • Macy’s offers 30% off all 7 jeans, because you are a Canadian citizen, you get an additional 15% off using your WOW card. If your mom sign’s up for a Macy’s card, you will get an additional 10% off. You cannot add 30% + 15% + 10%, because you get 15% off the price after the 30% is taken and the 10% off after the other two are taken • $300 x 0.7 = $210 • $210 x 0.85 = $178.5 • $178.5 x 0.9 = $160.65 • $300 x 0.45 = $135 • $160.65 ≠ $135

  44. Sports R Us vs. Sports Galore • Sports R Us offers a 2 day discount where you get 10% off on day 1 and an additional 10% off on day 2. Sports Galore is offing a one day sale of 20% off. Who has the better sale if the object that you want is $200? • Sports R Us would be $200 x 0.9 = $180 x 0.9 = $162 • Sports Galore would be $200 x 0.8 = 160 • Sports Galore has the better sale. • What is the total discount that Sports R Us Offers • The selling price after two 10% discounts is $162. Find the difference - $38. Express the difference over the original $38/$200. Convert to a decimal 0.19 than to a percent 19%.

  45. Workbook • Page 110 - 111

  46. 5.5 Exploring Ratios

  47. Ratio Definitions • Part to Whole Ratio: How many of one item to all items • Part to Whole Ratios can be written as follows • Circles to all shapes • 4 to 12 or 4:12 or 1/3 or 33.33% • Part to Part Ratio: How many of one item to another item • Part to Part Ratios can be written as follows • Circles to squares • 4 to 5 or 4:5 • Part to Part Ratios cannot be written in Fraction or Percent form, as it is not comparing one part to the whole. You can do a 3 term ratio for part to part – 3 to 4 to 5 or 3:4:5

  48. Write each ratio • A pencil case contains 7 yellow, 3 red, 1 black and 5 green pencil crayons. Write Each Ratio • Red: green • 3:5 • Black: total pencil crayons • 1:16 • Yellow: red: green • 7:3:5 • Yellow: red • 7:3 • Yellow: total pencil crayons • 7:16

  49. Workbook • Page 112 – 114 together

  50. 5.6 Equivalent Ratios

More Related