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K. Academy TopicsWarm-Up: (0 Questions)Ratios/Rates/Unit Rates
Measurement Ratios
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Khan Academy Topics
1. Ratio Word Problems2. Rate Problems .53. Rates & Proportional RelationshipsTopics are due by December 20 for on-line and Alt.Khan.**Waaaaay too many people have a grade of zero for their homework grade (Khan), which is 20% of your overall grade.
Solving Unit Rate Problems
Unit rates are rates in which the second quantity is 1.
Unit rate:
30 miles,1 hour
or 30 mi/(1)h
The ratio903
can be simplified by dividing:903
= 301
Finding the Unit Rate1. A 64 oz. Apple Juice costs $1.35. Find the unit rate.
2. A 12 slice pizza costs $9.00. Find the unit rate.3. Which is the better buy: A 12 oz. bottle of juice for $0.85, or an 8 oz. can of juice for $0.50?
Which unit, (oz. or $) do we want to reduce to 1?
Unit Conversions
Liquid Measures:
8 ounces (oz.) = 1 Cup16 ounces = 1
Pint32 ounces = 1
Quart64 ounces = ½
Gallon128 ounces = 1
Gallon
Dry Measures:16 ounces (oz.) = 1
pound (lb.)2000 lbs. = 1 Ton
Distance:
12 inches= 1 Foot3 Feet = 1 Yard5280 Feet= 1 Mile
Ratios Involving Measurement
WHEN A RATIO INVOLVES MEASUREMENTS, BOTH QUANTITIES MUST HAVE THE SAME UNIT OF MEASURECONVERT LARGER UNIT (FT) TO THE SMALLER UNIT (IN).
1. Express the ratio 6 feet to 15 inches as a fraction in simplest form.
2. SIMPLIFY AS A FRACTION: 3 PINTS TO 2 CUPS
*Change the larger unit to the smaller one. 3 pints = 6cups. The ratio is now 6 cups to 2 cups. Simplify to: 3/1
Six feet = 72 in. Simplify 72/15; the answer is 24/5
1. Rates Involving Two Different Measures: 10 ft./ sec. = miles/hour *Convert one unit at a time* The process is the same as finding equivalent fractions. 1st: How many seconds are in an hour? 3600Next: Set up a proportion:2. 30 yards/ minute = how many feet/secondChange yards to feet: 30 yds. = 90 ft.
Converting Rates & Measurement
Change minutes to seconds: 60 seconds. The ratio is now:90 ft./60 seconds. Reduce to the final answer: 1.5 ft./sec
8
The shadow of a 4 ft. tall mailbox is 3 ft. long. If the shadow of a tree is 36 ft. long, how tall is the tree?
heightshadow
heightshadow
=
You must be careful to place the same quantities in corresponding positions in the proportion
Proportions
144 = 3HH = 48The tree is 48 ft. tall
H 36
4 3 =
Comparing Unit Rates
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