1. Customary Units of Measure

2. Overview 3 feet numbers 7 miles units 12 yards U.S. Customary System
Set of standard units used in the United States established to simplify trade and commerce.
Set of standard units to describe all units of measure
length, weight, capacity, time, energy, power, etc.
A measurement includes a number and a unit 3 7 12
feet
miles
yards
numbers
units

3. Equivalences between Units of Length in the U.S. Customary System:
U.S. Customary System units of length are:
Inch, foot, yard, and mile
We often need to convert from one unit of measure to another.
For example, you are sewing a garment that calls for 50 in of fabric. The fabric store sells fabric at $2 per yd.
Question: What do we need to know in order to determine how much money you will need to purchase enough fabric to finish your garment?
Equivalences between Units of Length in the U.S. Customary System:
12 inches (in) = 1 foot (ft)
3 ft = 1 yard (yd)
36 in = 1 yd
5280 ft = 1 mile (mi)

4. Length
To figure this out, we need to form Conversion Rates.
Conversion rates???
Relationships between units
Used to change a measurement from one unit to another.
For example, since 3 ft = 1 yd, the conversion rates are:
Note that these are both equivalent to 1. Keep this in mind
Why?
3 ft
1 yd
and
1 yd
3 ft

5. Length Converting between units of measure Steps Examples
Construct the conversion rates.
Multiply the measurement by the appropriate conversion rate.
Note: Make sure you use the conversion rate which has the unit in the numerator that you want in your answer
Examples
Convert 27 ft to yards
Conversion rates are
3 ft/1 yd and 1 yd/3 ft
Which one do we choose?
27 ft x 1 yd/3 ft = 9 yd

6. Length Examples More Examples Convert 5 yards to feet
Conversion rates are 3 ft/1 yd and 1 yd/3 ft
Which one do we choose?
5 yd x 3 ft/1 yd = 15 ft
More Examples
Convert 40 in to feet.
Conversion rates are 12 in/1 ft and 1 ft/12 in
40 in x 1 ft/12 in = 40 ft/12 in = 3 1/3 ft
Convert 3 ¼ yd to feet
3 ¼ yd = 13/4 yd = 13/4 yd x 3 ft/1 yd = 39/4 ft = 9 ¾ ft

7. Length Class Examples Convert 14 ft to yards Convert 10560 ft to miles
Conversion rate: 1 yd/3 ft
14 ft x 1 yd/3 ft = 4 2/3 yd
Convert ft to miles
Conversion rate: 1 mi /5280 ft
10560 x 1 mi/5280 ft = 2 mi

8. Length 3 4 Writing measurements in simplest form Before we had:
40 in = 3 1/3 ft
If we want to convert 40 in to ___ft ___in
Divide 40 by 12 (since there is 12 inches in 1 ft.)
This will tell us how many feet there are.
Any remainder is the number of inches.
Examples
17 in = ___ft ___in
1 ft 5 in
31 ft = ___yd ___ft
10 yd 1 ft 3 4

9. Length Class Examples Convert: 42 in = ___ft ___in
Convert: 14 ft = ___yd ___ft
4 yd 2 ft

10. Length
Arithmetic operations with measurements (Addition)
Steps
Add the quantities of the measurement that have the same units
Write the sum in simplest form
4 ft 4in
+ 1 ft 11 in
5 ft
15 in
5 ft 15 in = 5 ft 12 in 3 in = 6 ft 3 in + =
1 ft

11. Length
Arithmetic operations with measurements (Subtraction)
Steps
Subtract the quantities of the measurement that have the same units . (Borrowing from the ft. may be necessary)
Write the measurement you get for your answer in simplest form
8 ft
12 in
18 in
9 ft 6 in
- 3 ft 8 in
5 ft
10 in
5 ft 10 in

12. Length
Arithmetic operations with measurements (Multiplication)
Steps
Multiply each of the quantities in the measurement by the desired factor. Carry units along
Write the measurement you get for your answer in simplest form
4 ft 5in x
12 ft 15 in
12 ft 15 in = 12 ft 12 in 3 in = 13 ft 3 in

13. Length Arithmetic operations with measurements (Division)
Division is a little trickier…best illustrated by an example
Find the quotient of 4 ft 3in and 3
Method 1 – Direct Division
Method 2 – Convert first
Convert to inches
Do division
Write answer in simplest form
17in or 1 ft 5 in

14. Length Examples Find the sum of 3 ft 5 in and 4 ft 9 in
7 ft 14 in = 7 ft 12 in 2 in = 7 ft 1 ft 2 in = 8 ft 2 in
Subtract: 4 ft 2 in – 1 ft 8 in
2 ft 6 in
Multiply 4 yd 1 ft x 8
32 yd 8 ft
Find the quotient of 7 yd 1 ft and 2
3 yd 2 ft

15. Length Class Examples 5 ft 9 in + 4 ft 5 in 10 yd 1 ft – 2 yd 2 ft.
9 ft 14 in = 9 ft 12 in 2 in = 9 ft 1 ft 2 in = 10 ft 2 in
10 yd 1 ft – 2 yd 2 ft.
7 yd 2 ft
2 ft 7 in x 5
10 ft 35 in = 10 ft 2 ft 11 in = 12 ft 11 in
5 ft 9 in ÷ 3
1 ft 11 in

16. Weight U.S. Customary System units of Weight are:
Ounce, Pound, and ton
We can use these equivalences to construct conversion rates
Example: What are the conversion rates for ounces and pounds?
Equivalences between Units of Weight in the U.S. Customary System:
16 ounces (oz) = 1 pound (lb)
2000 lb = 1 ton
16 oz
1 lb
and
1 lb
16 oz

17. Weight Example: Convert 62 oz to pounds Convert 3 ½ tons to pounds.
62 oz x 1 lb/16 oz = 62/16 lb = 3 7/8 lb
Convert 3 ½ tons to pounds.
Conversion rate: lb/1 ton
3 ½ tons = 7/2 tons = 7/2 tons x 2000 lbs/1 ton = 7000 lbs
Convert 42 oz to pounds
Conversion rate: 1 lb/16 oz
42 oz x 1 lb/16 oz = 42/16 lb = 2 5/8 lb

18. Weight Class Examples: Convert 3 lbs to ounces
Conversion rate: 16 oz/1 lb
3 lbs x 16 oz/1 lb = 48 oz
Convert 4200 pounds to tons.
Conversion rate: 1 ton/2000 lb
4200 lbs x 1 ton/2000 lb = 4200/2000 tons = 21/10 tons = 2 1/10 tons
5000 lb = ______ tons
5000 lb x 1 ton/2000 lb = 25/10 tons = 2 ½ tons

19. Weight Writing weight measurements in simplest form Before we had:
4200 lb = 2 1/10 tons
If we want to convert 4200 lb to ___tons ___lb
Divide 4200 by 2000 (since there are 2000 lb in 1 ton)
Tells us how many tons there are.
Remainder is the number of pounds.
Examples
Convert: 4200 lb = ___tons ___lb
2 tons 200 lb
Convert: 62 oz = ___lb ___oz
3 lb 14 oz

20. Weight
Arithmetic operations with weight (any) measurements are done using the same techniques as with length measurements.
Examples
Find the difference between 14 lb 5 oz and 8 lb 14 oz
5 lb 7 oz
Find the sum of 5 lb 8 oz and 4 lb 10 oz
10 lb 2 oz
2 lb 6 oz x 3
7 lb 2 oz
10 lb 2 oz ÷ 6
1 lb 11 oz

21. Weight
Class Examples
Find the difference between 7 lb 1 oz and 3 lb 4 oz
3 lb 13 oz
Multiply: 3 lb 6 oz x 4
13 lb 8 oz
7 lb 14 oz ÷ 3
2 lb 10 oz
Find the sum of 10 lb 2 oz and 6 lb
16 lb 2 oz

22. Other Types of Measurements
Everything discussed here can be done with any types of measurements including:
Capacity
Time
8 fluid ounces (fl oz) = 1 cup (c)
2 c = 1 pint
2 pt = 1 quart (qt)
4 qt= 1 gallon (gal)
60 seconds (s) = 1 minute (min)
60 min = 1 hour (hr)
24 h = 1 day
7 days = 1 week