Lesson 1.3
Core Focus on
Ratios, Rates and Statistics
Customary Conversions
Warm-Up
Write the first four terms of a geometric sequence with the
given first term and ratio.
1. first term: 1
ratio: 3
1, 3, 9, 27, …
2. first term: 10,000
ratio: 101
10,000, 1,000, 100, 10
3. Determine whether or not the sequence is a geometric
sequence. Explain why or why not.
5, 10, 15, 20, 25, …
Not a geometric sequence. The terms have a difference
of 5 but not a ratio between them of 5.
Complete each blank.
4. 1 foot = ____
12 inches
5. 1 hour = ____
60 minutes
Lesson 1.3
Customary Conversions
Convert customary measurements.
Vocabulary
Conversion
The process of renaming a measurement using different units.
Good to Know!
 Customary units are units of measure that include inches,
feet, yards and miles for measuring length, ounces, tons
and pounds for weight and cups, pints, quarts and gallons
for volume.
 The customary system of measurement is used in the
United States.
 Sometimes it is necessary to convert from one unit to
another. Smaller units can be converted to larger units,
like inches to feet. Larger units can be converted to
smaller units, like days to hours.
Example 1
Choose a reasonable estimate. Explain your reasoning for each
choice.
a. amount of water in a personal water bottle: 1 quart or 1 gallon
1 quart. Think about a gallon of milk. That is larger than a
personal water bottle.
b. length of a couch: 6 yards or 6 feet
6 feet. People are measured in feet. A 6 foot person could lay
on a couch. Think about yards on a football field. Six yards
would make a very long couch.
c. weight of an elephant: 2 pounds or 2 tons
2 tons. Elephants are quite large. Most human babies weigh
more than 2 pounds when they are born.
Example 2
Using the information in the conversion table, find the number
of yards in 36 feet.
Feet
3
6
9
12
24
36
Yards
1
2
3
4
8
?
Each pair of feet and yard values
shows the ratio of feet to yards.
Choose any ratio and write it as
a fraction. Simplify the ratio, if
needed.
Find an equivalent ratio with 36 feet.
There are 12 yards in 36 feet.
3 feet
1 yards
Unit Conversions
When converting to smaller units, MULTIPLY ( ).
When converting to larger units, DIVIDE ( ).
Example 3
Complete the conversion.
a. 2 miles = _______ feet
Find the conversion factor.
1 mile = 5,280 feet
Multiply 2 miles by 5,280.
2  5280 = 10560
2 miles = 10,560 feet.
When converting to a
smaller unit, multiply.
Example 3 Continued…
Complete the conversion.
b. 280 days = _______ weeks
Find the conversion factor.
1 week = 7 days
Divide 280 by 7.
280  7 = 40
280 days = 40 weeks.
When converting to a
larger unit, divide.
Example 3 Continued…
Complete the conversion.
c. 18 inches = _______ feet
Find the conversion factor.
1 foot = 12 inches
Divide 18 by 12.
18  12 = 1.5
18 inches = 1.5 feet.
Communication Prompt
Explain a situation where you would want to change
units from inches to feet or feet to yards. How would
you change the units?
Exit Problems
Complete each conversion.
1. 3 weeks = _____
21 days
2. 90 minutes = _____
1.5 hours
3. 4 yards = _____
12 feet