Math 80 Lecture - Chapter 7 Merced College; Don Power

7.1 Metric System

Know basic units

Length: meter

Mass: gram (equivalent to weight for ordinary purposes)

Volume (capacity): liter

Know prefixes, and the fact that they refer to powers of 10

Kilo * 1000 m

Hecto 100 m

Deca 10 m

(Basic unit) * 1 m

Deci 1/10 m

Centi * 1/100 m

Milli * 1/1000 m

Conversions: I recommend use of a metric conversion line

See bottom of page 438, top of pg 439

7.2 Ratios and Rates

Obj: Write ratios as fractions [in lowest terms]

Ex: 300 books to 425 books

Obj: Solve ratio problems involving decimals or mixed numbers

Ex: $.08 to $.06

Ex: 1 1/4 to 1 1/2

Obj: Solve ratio problems after converting units

Ex: 8 ft to 4 yards

Ex: 4 pints to 6 cups

Ex: 16 hours to 1 1/2 days

Ex: 4 gallons to 12 quarts

Tasks

Finding ratios based on tables

Find ratios of sides in geometric figures

Find the ratio of an increase (or decrease) in price to the original price

Def: Rate: comparison/fraction using nrs with diff units (so keep the units)

Write rates as fractions

Find unit rates

Find the best buy based on cost per unit

7.3 U.S. Measurement

Know conversion factors listed in the textbook, on page 449, for:

Length: in, ft, yd, mi

Weight: oz, lb, ton

Capacity (volume): fl oz, C, pt, qt, gal

Area: square inches, square feet, square yards

Also: Time: sec, min, hr, day, wk

Methods

Simple cases:

From large unit to small unit, multiply

From small unit to large unit, divide

Harder cases:

Unit analysis using "picket fence" technique

7.4 Proportions

Def: equality of two ratios or rates (or fractions)

Obj: Write proportions

Obj: Deciding whether proportions are true or false:

Cross products must be equal

or -- reduced fractions must be equal

Obj: Find the unknown number in a proportion:

Cross-mult, then div

Alternately: unk = known cross-prod / factor across from unk

7.5 Variation

Set up variation problems:

Direct: y = k x

x and y both change at the same rate (when one doubles, so does the other)

Indirect (or inverse): y = k / x

x and y go in opposite directions (when one is doubled, the other is cut in half)

First, use matched numbers to solve for k

Then, use the new k to find an unknown number

Return to:  Merced College; Don Power               Updated 11/13/06 by Don Power