DIMENSIONAL ANALYSIS

WARM-UP

Four more than three times a number is one less than four times the number. What is the number?

5

5

4143

1434

n

n

nn

nn

Dimensional Analysis• Dimensional Analysis is a procedure used to convert from

one unit of measurement to a different unit of measurement.

• To do dimensional analysis, you must understand what is meant by a unit fraction.

Unit Fraction• A unit fraction is any fraction in which the numerator and

denominator contain different units and the value of the fraction is 1.

• The table on the next slide shows many unit fractions involving U.S. customary units.

Examples of Unit Fractions

Example: How many inches are in 5 feet?

.60.1

.125 in

ft

inxft

8 oz is how many pounds? (Hint: 1 pound = 16 oz)

poundsoz

poundxoz

2

1

16

8

16

18

15 yards to feet

ftftxyard

feetxyards 45)315(1

315

4 feet to inches

inft

inxft 481

124

6 pints to cups (Hint: 1 pint = 2 cups)

cupspt

cupsxpts 121

26

42 inches to feet

ftin

ftxin 5.3

12

42

12

142

John drives on the interstate 60 miles per hour. How many feet per second is he traveling?

sec88sec3600

316800

sec60

min1

min60

1

1

528060 ftft

xhr

xmi

ftx

hr

mi

Kim can scan 20 items per minute. How many can she scan in 15 seconds?• Find how many she can scan per second:• Multiply by 15 seconds.

sec3

1

60

20

sec60

120 itemsMinute

xMinute

items

itemsx 5153

1

Jared can work 54 math problems in 1 hour. How many problems can he work in 10 minutes?

• Figure the amount per minute first:• Now multiply that amount by 10 minutes.

Minproblemstoduces

Min

hrx

hr

problems

10

9Re

60

54

60

154

problemsMinxMinproblems 910

10

9

A machine makes 360 gadgets every 24 hours. How many gadgets does it make every 20 minutes.

• Find the # of gadgets per minute first:• Next, multiply by 20 minutes to get the # of gadgets.

Min

gadgets

Min

hourx

hours

gadgets315.

60

1

24

360 gadgetsMinx

Min

gadgets3.620315.

Perry’s car can travel an average of 22 miles on 1 gallon of gas. How many miles can his car travel on 1 quart of gas? (Hint: 1 gallon = 4 quarts)

quartmiles

or

quartmilesquarts

gallonx

gallon

miles

5.5

/4

22

4

122