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 7 12

feet miles yards units

 U.S. Customary System units of length 1.

Inch, foot, yard, and mile are: 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.

2.

Construct the conversion rates.

1.

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  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

  1.

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 1.

2.

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 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

 1.

2.

Class Examples   Convert 14 ft to yards 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     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.

2.

 17 in = ___ft ___in 1 ft 5 in  31 ft = ___yd ___ft 10 yd 1 ft

 Class Examples 1.

2.

 Convert: 42 in = ___ft ___in 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 15 in 2.

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

18 in

- 3 ft 8 in

5 ft 10 in 2.

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 1.

4 ft 5in x 3

12 ft 15 in 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   1.

2.

3.

Method 2 – Convert first Convert to inches Do division Write answer in simplest form 17in or 1 ft 5 in

 Examples 1.

2.

3.

4.

 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

 Class Examples 1.

2.

3.

4.

 5 ft 9 in + 4 ft 5 in 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

 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.

2.

3.

 Convert 62 oz to pounds 62 oz x 1 lb/16 oz = 62/16 lb = 3 7/8 lb   Convert 3 ½ tons to pounds.

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.

2.

3.

  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 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.

2.

 Convert: 4200 lb = ___tons ___lb 2 tons 200 lb  Convert: 62 oz = ___lb ___oz 3 lb 14 oz

 Arithmetic operations with weight (any) measurements are done using the same techniques as with length measurements.

 Examples 1.

2.

3.

4.

 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

 Class Examples 1.

2.

3.

4.

 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

 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