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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