Note 2'6 Equivalent Ratios

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Note 2.6 Equivalent Ratios

• Our goals are to
• Read and write ratios in lowest forms
• Find an equivalent ratio
• We need to know how to do this for
• Sports, cooking, shopping

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What is an ANALOGY?

• An analogy compares two things and finds some
  relationship that exists.
• Example
• Dog is to bark as cat is to _____
• Hot is to cold as new is to _____

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What is a Ratio?

• A ratio makes comparisons between two Numbers.
• A ratio can be written in 5 ways
• 1 to 4
• 14
• ¼
• 0.25
• 25

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Example of ratios in sports

• Football
• Football statisticians keep track of the percent
  of successful field goals made by a kicker using
  the following ratio

So, what is a kickers kicking ratio if he
attempted 35 field goals and completed 30 of them?
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Example 1 Write each ratio as a fraction in
simplest form

• 12 c to 96 c
• 65 min 3 h
• 5 m to 2.5 cm

Hint type the numbers into your calculator
using the fraction (a/bc) key. The calculator
will reduce the fraction for you!
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Equivalent Ratios

• Equivalent ratios represent the same numbers.
• If you write both ratios as fractions in simplest
  form, they will be the same!

• Which ratios are equivalent?
• 2 to 3 and 8 to 6
• 5 to 10 and 15 to 30
• 12 2 and 6 1

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Example 2 Find 3 equivalent ratios. Write the
ratios as a fraction.
Answers
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Example 3 Horticulture

• Carlos feeds his houseplants with a mixture of
  liquid plant food and water. This mixture calls
  for 3 parts plant food to 8 parts water.
• What is the ratio of plant food to water?
• How much plant food should he mix with 40 fl oz
  of water?

Answers
Answers
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Example 4 You Try!

• Julio answered 51 out of 60 questions correctly
  on a history test. He answered 17 out of 20
  questions correctly on a math quiz.
• What is the ratio of correct answers to questions
  for the test and the quiz?

Answers
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Work on Homework 2.6Page 76 16-48 even
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Example 2 Find 3 equivalent ratios. Write the
ratios as a fraction.
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Answers to Example 3

• Method 1
• Make a table and extend it to 40 oz.
• So, Carlos should mix 15 fl oz of plant food with
  40 fl oz of water.

• Method 2
• Set up a proportion and cross multiply to solve!

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Answer to Example 4