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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