Algebraic Ratios
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Algebraic Ratios

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Algebraic Ratios Algebraic Ratios Presentation Transcript

  • ALGEBRAIC RATIOS
    • The number of boys =
    • The number of girls =
    • If we compare boys to girls we get
    • ___ boys to _____ girls.
  • WHAT DO WE CALL A COMPARISON BETWEEN TWO OR MORE QUANTITIES? RATIO We just found the RATIO of boys to girls. Is the ratio of girls to boys the same ? No, when writing a ratio, ORDER matters.
  • AIM:
    • What is a ratio?
  • IT’S FRIDAY NIGHT AND YOUR FRIENDS ARE HAVING A PARTY……
    • The ratio of girls to guys is 2 to 12.
    Would you want to attend the party?
  • HOW MANY BASKETBALLS TO FOOTBALLS ARE THERE?
    • For every 4 basketballs there are 6 footballs.
    • The ratio is 4 to 6.
  • WHAT ARE SOME OTHER WAYS WE CAN WRITE THE RATIO OF BASKETBALL TO FOOTBALLS?
    • 4 to 6
    • 4 : 6
    • 4
    • 6
    First quantity to Second quantity First quantity : Second quantity First quantity divided by the second quantity (as a fraction ). Every ratio can be written in 3 ways: Careful!! Order matters in a ratio. 4 to 6 Is NOT the same as 6 to 4
  • WRITE THE RATIO OF SANDWICHES TO COKE BOTTLES 3 DIFFERENT WAYS.
    • 6:8 , 6 to 8, and 6
            • 8
    Since a fraction can be simplified, We can simplify the ratio 6/8 to 3/4. The ratio of sandwiches to coke bottles can also be expressed as 3 : 4 or 3 to 4. In other words, ratios can be simplified to form equivalent ratios.
  • EQUIVALENT RATIOS
    • Simplify the following ratios:
      • 4 to 8
      • 10 to 8
      • 8 to 10
    Step 1 – Write the ratio as a fraction Step 2 – Simplify the fraction (Find the greatest common factor (GCF) of both numbers and divide the numerator and denominator by the GCF). Step 3 – Write the equivalent ratio in the same form as the question
    • = 4 / 4 = 1 = 1 to 2
    • 8 8 / 4 2
    GCF = 4
  • EQUIVALENT RATIOS CAN BE FORMED BY MULTIPLYING THE RATIO BY ANY NUMBER.
    • For example, the ratio 2 : 3 can also be written as
      • 4 : 6 (multiply original ratio by by 2)
      • 6 : 9 (multiply original ratio by by 3)
      • 8 : 12 (multiply original ratio by by 4)
      • The ratio 2 : 3 can be expressed as
      • 2x to 3x (multiply the original ratio by any number x )
  • COMPOUND RATIOS
    • A ratio that compares more than 2 quantities is called a compound ratio.
    • Example:
      • A cake recipe says the ratio of cups of milk , sugar , and batter are 1 : 2 : 4 .
        • This means that there is one cup of milk for every two cups of sugar and four cups of batter.
  • A BAG CONTAINS 18 YELLOW, BLUE, AND RED MARBLES. THE RATIO OF YELLOW TO BLUE TO RED MARBLES IS 4 : 2 : 3 .
    • Write the ratio of yellow to blue marbles in simplest form.
    • What is the ratio of yellow to red marbles?
    • How many yellow marbles are there?
    4 : 2 can be simplified to 2 : 1 4 : 3 Yellow : Blue : Red is 4 : 2 : 3 Since any multiple of this is an equivalent ratio, this can also be written as 4x : 2x: 3x Let 4x = yellow, 2x = blue , 3x = red 4x + 2x+ 3x = 18 9x = 18 X= 2 Since the question asks for yellow marbles, there are 4 x or 4 ( 2 ) = 8 yellow marbles.
  • PRACTICE PROBLEM # 1
    • It takes Max ¼ of an hour to ride his bike to school, and it takes Riley 21 minutes to walk to school.
    • Write a ratio comparing Max’s time to Riley’s time.
  • PRACTICE PROBLEM #2
    • A TV normally sells for $400 is on sale for $340. The tax on the reduced price is $23.80, so the total cost with tax is $363.80.
    • What is the discount rate?
    • What is the tax rate?
    • Including tax, how much would a customer save by buying the TV on sale?
  • PRACTICE WORD PROBLEMS
    • You go to a party where the ratio of boys to girls is 28 to 56. Express the ratio of boys to girls in simplest form.
    • Explain what this ratio tells us.
    • 28 / 56 = 1 / 2
    • The ratio of boys to girls is 1 to 2
    • (2) For every 1 boy there are 2 girls at the party.
  • PRACTICE WORD PROBLEMS
    • Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy.
    • Explain what this ratio tell us.
  • CHALLENGE QUESTION
    • Suppose a team has won 15 of it’s first 38 games. How many games must it win in a row to bring its winning percentage to at least .500?