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Lecture Comments (1)

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Post by Kumar Sandrasegaran on June 6, 2011

Example IV should say "$ 8.50 per hour for the first 40 hours ..."

Rates

  • Rates and Unit Rates are types of ratios. A rate is a ratio that compares quantities measured in different units, such as miles per gallon. A unit rate is the rate for one unit of a quantity.
  • To find a unit rate, divide the denominator by itself, and divide the numerator by the same number.
  • Comparing unit rates can help you find the better buy when comparing different quantities of the same amount.

Rates

A car can go 70 miles on 2 gallons of gas. Find the unit rate.
  • [(70 miles)/(2 gallons)] = [(m miles)/(1 gallon)]
  • [(70 ÷2)/(2 ÷2)] = [35/1]
35 miles per 1 gallon
Unicorns can produce 12 rainbows every 4 hours. Find the unit rate.
  • [(12 rainbows)/(4 hours)] = [(r rainbows)/(1 hour)]
  • [(12 ÷4)/(4 ÷4)] = [3/1]
3 rainbows per 1 hour
A runner can run 21 miles in 3 hours. Find the unit rate.
  • [(21 miles)/(3 hours)] = [(m miles)/(1 hour)]
  • [(21 ÷3)/(3 ÷3)] = [7/1]
7 miles per 1 hour
A train travels 2 miles per chunk of coal. How many chunks of coal does a train need to travel 36 miles?
  • [(2 miles)/(1 chunk of coal)] = [(36 miles)/(c chunks of coal)]
  • [(2 ×18)/(1 ×18)] = [36/c]
c = 18 chunks of coal
Building a fence takes 36 nails. How many fences can be built using 144 nails?
  • [(36 nails)/(1 fence)] = [(144 nails)/(f fences)]
  • [(36 ×4)/(1 ×4)] = [144/f]
f = 4 fences
Every 33 ounces of frozen yogurt costs $ 1. How much frozen yogurt can be bought with $ 0.50?
  • [(33 ounces)/$ 1] = [(y ounces)/$ 0.50]
  • [(33 ÷2)/($ 1 ÷2)] = [(y ounces)/$ 0.50]
y = [33/2] ounces = 16[1/2] ounces
Lisa can type 90 words per minute. How long would it take Lisa to type 450 words?
  • [(90 words)/(1 minute)] = [(450 words)/(m minutes)]
  • [(90 ×5)/(1 ×5)] = [450/m]
m = 5 minutes
One box of 32 - ounce cereal costs $ 3.60. Another box of 45 - ounces cereal costs $ 5.45. Which box of cereal is the better buy?
  • [$ 3.60/(32 ounces)] ≈ [$ 0.11/(1 ounce)]
  • [$ 5.45/(45 ounces)] ≈ [$ 0.12/(1 ounces)]
The 32-ounce box of cereal is the better buy.
Joe went to go buy a tub of ice cream. The tub of ice cream was 7 servings, and each serving was 350 calories. Joe ate the whole tub of ice cream. How many calories did Joe consume?
  • [(1 serving)/(350 calories)] = [(7 servings)/(x calories)]
  • [(1 ×7)/(350 ×7)] = [7/x]
x = 2450 calories
Melissa needs 4 packs of glue for her science project. Should she buy two 2 - packs of glue that cost $ 2.50 each, or should she buy one 4 - pack of glue that costs $ 4.95?
  • [$ 2.50/(2 glue sticks)] = [$ 1.25/(1 glue stick)]
  • [$ 4.95/(4 glue sticks)] ≈ [$ 1.24/(1 glue stick)]
4-pack

*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

Rates

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 0:04
    • Topics Overview
  • Vocabulary 0:18
    • Rate
    • Unit Rate
  • Finding a Unit Rate 1:00
    • Example: Delivery Rate
  • Using a Unit Rate 1:46
    • Example: Miles and Gallon of Gas
  • Comparing Unit Rates 2:52
    • Example: Which is the Better Buy
  • Extra Example 1: Calories 6:30
  • Extra Example 2: Typing Speed 7:22
  • Extra Example 3: Which is the Better Buy 8:23
  • Extra Example 4: Wages 10:48