Math Skills – Week 7
 Class project due next week
 Sample final exams available on website
 Reducing fractions, rates, and ratios
 $500
 huh?
 17/30
 hmmmmmmm
 Section 8.1 – Length
 Section 8.2 – Weight
 Section 8.3 – Capacity
 Section 8.4 – Time
 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
numbers
3 feet
7 miles
12 yards
units
 U.S. Customary System units of length are:
1.
Inch, foot, yard, and mile
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)

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?
 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:
3 ft
1 yd
and
1 yd
3 ft
 Note that these are both equivalent to 1. Keep this in mind
 Why?
 Converting between units of measure
 Steps
1. Construct the conversion rates.
2. 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
1.

Examples
Convert 27 ft to yards
1.
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

Examples
1.
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
1.
Convert 40 in to feet.


2.
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


Conversion rates are 3 ft/1 yd and 1 yd/3 ft
3 ¼ yd = 13/4 yd = 13/4 yd x 3 ft/1 yd = 39/4 ft = 9 ¾ ft

Class Examples
1.
Convert 14 ft to yards


2.
Conversion rate: 1 yd/3 ft
14 ft x 1 yd/3 ft = 4 2/3 yd
Convert 10560 ft to miles


Conversion rate: 1 mi /5280 ft
10560 x 1 mi/5280 ft = 2 mi
 Writing measurements in simplest form
 Before we had:
 40 in = 3 1/3 ft
3 ___in
4
 If we want to convert 40 in to ___ft
 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
1.
17 in = ___ft ___in

1 ft 5 in
31 ft = ___yd ___ft
2.

10 yd 1 ft
 Class Examples
1.
Convert: 42 in = ___ft ___in

2.
3 ft 6 in
Convert: 14 ft = ___yd ___ft

4 yd 2 ft
 Arithmetic operations with measurements (Addition)
 Steps
1. Add the quantities of the measurement that have the same
units
4 ft 4in
+ 1 ft 11 in
5 ft
2.
15 in
Write the sum in simplest form
5 ft 15 in = 5 ft 12 in 3 in = 6 ft 3 in
+
1 ft
=
 Arithmetic operations with measurements
(Subtraction)
 Steps
1. Subtract the quantities of the measurement that have the
same units . (Borrowing from the ft. may be necessary)
8 ft
12 in
9 ft 6 in
- 3 ft 8 in
5 ft
2.
18 in
10 in
Write the measurement you get for your answer in simplest
form
5 ft 10 in
 Arithmetic operations with measurements
(Multiplication)
 Steps
1. Multiply each of the quantities in the measurement by the
desired factor. Carry units along
4 ft 5in
x
3
12 ft 15 in
1.
Write the measurement you get for your answer in simplest
form
12 ft 15 in = 12 ft 12 in 3 in = 13 ft 3 in
 Arithmetic operations with measurements (Division)
 Division is a little trickier…best illustrated by an example
1. Find the quotient of 4 ft 3in and 3
Method 1 – Direct Division
Method 2 – Convert first


1.
2.
3.

Convert to inches
Do division
Write answer in simplest form
17in or 1 ft 5 in
 Examples
1.
Find the sum of 3 ft 5 in and 4 ft 9 in

2.
Subtract: 4 ft 2 in – 1 ft 8 in

3.
7 ft 14 in = 7 ft 12 in 2 in = 7 ft 1 ft 2 in = 8 ft 2 in
2 ft 6 in
Multiply 4 yd 1 ft x 8

32 yd 8 ft
4. Find the quotient of 7 yd 1 ft and 2
 3 yd 2 ft
 Class Examples
1.
5 ft 9 in + 4 ft 5 in

2.
10 yd 1 ft – 2 yd 2 ft.

3.
9 ft 14 in = 9 ft 12 in 2 in = 9 ft 1 ft 2 in = 10 ft 2 in
7 yd 2 ft
2 ft 7 in x 5

10 ft 35 in = 10 ft 2 ft 11 in = 12 ft 11 in
4. 5 ft 9 in ÷ 3
 1 ft 11 in
 U.S. Customary System units of Weight are:

Ounce, Pound, and ton
Equivalences between Units of Weight in the U.S. Customary System:
16 ounces (oz) = 1 pound (lb)
2000 lb = 1 ton

We can use these equivalences to construct conversion
rates

Example: What are the conversion rates for ounces and
pounds?
16 oz
1 lb
and
1 lb
16 oz
 Example:
1.
Convert 62 oz to pounds

2.
Convert 3 ½ tons to pounds.


3.
62 oz x 1 lb/16 oz = 62/16 lb = 3 7/8 lb
Conversion rate: 2000 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
 Class Examples:
1.
Convert 3 lbs to ounces


2.
Convert 4200 pounds to tons.


3.
Conversion rate: 16 oz/1 lb
3 lbs x 16 oz/1 lb = 48 oz
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


Conversion rate: 1 ton/2000 lb
5000 lb x 1 ton/2000 lb = 25/10 tons = 2 ½ tons
 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
1.
Convert: 4200 lb = ___tons ___lb

2 tons 200 lb
Convert: 62 oz = ___lb ___oz
2.

3 lb 14 oz
 Arithmetic operations with weight (any)
measurements are done using the same techniques as
with length measurements.
 Examples
1.
Find the difference between 14 lb 5 oz and 8 lb 14 oz

2.
Find the sum of 5 lb 8 oz and 4 lb 10 oz

3.
5 lb 7 oz
10 lb 2 oz
2 lb 6 oz x 3

7 lb 2 oz
4. 10 lb 2 oz ÷ 6
 1 lb 11 oz
 Class Examples
1.
Find the difference between 7 lb 1 oz and 3 lb 4 oz

2.
Multiply: 3 lb 6 oz x 4

3.
3 lb 13 oz
13 lb 8 oz
7 lb 14 oz ÷ 3

2 lb 10 oz
4. Find the sum of 10 lb 2 oz and 6 lb
 16 lb 2 oz
 Everything discussed here can be done with any types
of measurements including:
 Capacity (Section 8.3)
8 fluid ounces (fl oz) = 1 cup (c)
2 c = 1 pint
2 pt = 1 quart (qt)
4 qt= 1 gallon (gal)
 Time (Section 8.4)
60 seconds (s) = 1 minute (min)
60 min = 1 hour (hr)
24 h = 1 day
7 days = 1 week