Review of Customary Units, Fractions, and Dimensional

Analysis.

By Ms. Dewey-Hoffman

February 23, 2020

Chapter 5, Section 5

(if you must know)

Example of Conversion Factors

To find a COMMON DENOMINATOR

between Two Fractions,

you MULTIPLY one or both

fractions by a Conversion Factor.

A Conversion Factor is always equal to 1.

This is the Same with Conversion Factors in Converting Units!

Use Equivalent Units To Write A Conversion Factor.

Like: 12 inches = 1 foot.They Are Equivalent!

Also: 4 quarts = 1 gallon.They Are Equivalent!

Also: 24 hours = 1 day.They Are Equivalent!

Turn The Conversions Into Fractions…They’re Equivalent

• Just Write These Equivalents to Make a Fraction that is Equal to 1.

12 inches = 11 foot

2 cups = 18 Fluid Ounces

Dimensional AnalysisThe process of analyzing units to decide

which conversion factors to use.When you are looking at the Legend on your

handout, that’s Dimensional Analysis!

This is a Fraction Bar

These Bars mean

Multipl-ication and

separate fractions or Conversion

Factors.

10 quarts = ? gallons

10 Quarts ? Gallons

Conversion Factor Goes Here

4 Quarts

1 Gallon

Now turn it into a Fraction/Multiplication Problem

10 ¼ = 2 ½ gallons

10 quarts = 2 ½ gallons

This is a Fraction Bar

These Bars mean

Multipl-ication and

separate fractions or Conversion

Factors.

Dealing with Mixed Numbers and Conversions?

3 3/16 yards = ? inches

1) Change Mixed Number to an Improper Fraction, then Convert.

51 Yards

1 Yard

3 Feet

1 Foot

12 Inches

16

2) Take the answer and Change to a Mixed Number.

Notice how the IMPROPER Fraction looks like a Fraction

on the T graph.

(51 3 12) (16 1 1) = 114.75 or 114 ¾

To Compare Different Units…

Change ONE Unit into the other and see which is bigger, less, or equal.

Inequalities Anyone?

10 Gallons ____ 42 Quarts

1) 42 Quarts is how many gallons?

2) 4 Quarts for every 1 Gallon. (42/4 = 10 ½ Gallons)

3) Which is bigger? 42 Quarts or 10 Gallons?

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