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Lecture Comments (1)

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Post by Giri Iyer on November 20, 2011

my dad is making me watch this

Ratios

  • A ratio is a comparison of two quantities by division. It can be written in three ways: a/b, a:b, and a to b.
  • Equivalent ratios are ratios that name the same quantity and are the same as equivalent fractions.
  • To write a ratio in simplest form, divide the numerator and denominator by their greatest common divisor.

Ratios

Write two different ratios equivalent to 3:9.
  • [(3 ÷3)/(9 ÷3)] = [1/3] = 1:3
  • [(3 ×2)/(9 ×2)] = [6/18]
Possible answers: 1:3, 6:18, 9:27, 12:36, 15:45, and more.
Write two different ratios equivalent to 4:8.
  • [(4 ÷2)/(8 ÷2)] = [2/4]
  • [(4 ÷4)/(8 ÷4)] = [1/2]
Possible answers: 1:2, 2:4, 8:16, 6:12, 12:24, and many more.
Write two different ratios equivalent to 7:28.
  • [(7 ÷7)/(28 ÷7)] = [1/4]
  • [(1 ×2)/(4 ×2)] = [2/8]
Possible answers: 1:4, 2:8, 3:12, 4:16, 5:20, and many more.
There are 5 red balls and 10 blue balls. Write the ratio of blue to red balls in simplest form.
  • blue balls : red balls
    10:5
  • [(10 ÷5)/(5 ÷5)] = [2/1]
2:1
There are 12 poodles and 30 golden retrievers. Write the ratio of poodles to golden retrievers in simplest form.
  • poodles : golden retrievers
    12:30
  • [(12 ÷6)/(30 ÷6)] =
  • [2/5]
2:5
There are 15 white flowers, 30 yellow flowers, and 5 purple flowers. Write the ratio of yellow to purple to white flowers in simplest form.
  • yellow : purple : white
    30 : 5 : 15
  • 30 ÷5 = 6
    5 ÷5 = 1
    15 ÷5 = 3
6:1:3
You have 3 pencils, 4 pens, and 2 highlighters. Write the ratio of pens to highlighters and the ratio of pencils to pens in simplest form.
  • pens : highlighters = 4 : 2 =
  • [(4 ÷2)/(2 ÷2)] =
  • [2/1] =
  • 2 : 1
pencils : pens = 3 : 4
A recipe needs 3 cups of flour for 12 cookies. How many cups of flour do you need to make 36 cookies?
  • The recipe's ratio of flour to cookies is 3:12. The ratio of flour to cookies must remain the same, regardless of how many cookies you make
  • So, flour:cookies for 12 cookies = flour:cookies for 36 cookies.
    [(3 cups of flour)/(12 cookies)] = [(f cups of flour)/(36 cookies)]
  • [3/12] = [f/36]
  • You want to multiply the numerator and denominator of [3/12] by the same number, and you want to choose that number so you get 36 as the new denominator.
    [(3 ×?)/(12 ×?)] = [f/36]
  • That number is 3, because 12 ×3 = 36.
    [(3 ×3)/(12 ×3)] = [f/36]
  • [9/36] = [f/36]
  • f = 9 cups of flour
  • Or, if you have already learned cross multiplication, you may do that instead (both methods give the same answer):
    12f = 3(36)
  • 12f = 108
f = 9 cups of flour
A recipe needs 1 cup of sugar for 6 macaroons. How many cups of sugar do you need to make 24 macaroons?
  • sugar : macaroons = sugar : macaroons
    [(1 cup of sugar)/(6 macaroons)] = [(s cups of sugar)/(24 macaroons)]
  • [1/6] = [s/24]
  • [(1 ×4)/(6 ×4)] = [s/24]
  • [4/24] = [s/24]
  • s = 4 cups of sugar
  • Or, use cross multiplication:
    6s = 1(24)
  • 6s = 24
s = 4 cups of sugar
A recipe calls for 6 teaspoons of salt for 12 muffins. How many muffins could you make with 2 teaspoons of salt?
  • salt : muffins = salt : muffins
    [(6 teaspoons of salt)/(12 muffins)] = [(2 teaspoons of salt)/(m muffins)]
  • [6/12] = [2/m]
  • [(6 ÷3)/(12 ÷3)] = [2/m]
  • [2/4] = [2/m]
  • m = 4 muffins
  • Or, use cross multiplication:
  • 6m = 2(12)
  • 6m = 24
m = 4 muffins

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

Ratios

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • What You'll Learn and Why 0:06
    • Topics Overview
  • Vocabulary 0:22
    • Ratio
    • Equivalent Ratios
  • Writing a Ratio 1:18
    • Write the Ratio in Three Ways
  • Writing an Equivalent Ratio 2:07
    • Different Ratios Equivalent to 10:12
  • Writing a Ratio in Simplest Form 2:47
    • Write the Ratio in Simplest Form
  • Extra Example 1: Write the Ratio 3:32
  • Extra Example 2: Ratio in Simplest Form 4:38
  • Extra Example 3: Write the Ratio 5:08
  • Extra Example 4: Ratio in Simplest Form 5:48