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 feet miles yards units numbers

U.S. Customary System units of length are: 1. 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)

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 3 ft 1 yd and

Converting between units of measure Steps 1. Construct the conversion rates. 2. Multiply the measurement by the appropriate conversion rate. 1. Note: Make sure you use the conversion rate which has the unit in the numerator that you want in your answer Examples 1. 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

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. 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 2. 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 Conversion rate: 1 yd/3 ft 14 ft x 1 yd/3 ft = 4 2/3 yd 2. Convert ft to miles Conversion rate: 1 mi /5280 ft x 1 mi/5280 ft = 2 mi

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 in = ___ft ___in 1 ft 5 in ft = ___yd ___ft 10 yd 1 ft 34

Class Examples 1. Convert: 42 in = ___ft ___in 3 ft 6 in 2. 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 2. Write the sum in simplest form 4 ft 4in + 1 ft 11 in 5 ft 5 ft 15 in = 5 ft 12 in 3 in = 6 ft 3 in 1 ft 15 in + =

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) 2. Write the measurement you get for your answer in simplest form 9 ft 6 in - 3 ft 8 in 5 ft 5 ft 10 in 8 ft 12 in 18 in 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. Write the measurement you get for your answer in simplest form 4 ft 5in x 3 12 ft 15 in 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. Convert to inches 2. Do division 3. 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 7 ft 14 in = 7 ft 12 in 2 in = 7 ft 1 ft 2 in = 8 ft 2 in 2. Subtract: 4 ft 2 in – 1 ft 8 in 2 ft 6 in 3. 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 9 ft 14 in = 9 ft 12 in 2 in = 9 ft 1 ft 2 in = 10 ft 2 in yd 1 ft – 2 yd 2 ft. 7 yd 2 ft 3. 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 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 16 oz 1 lb and

Example: 1. Convert 62 oz to pounds 62 oz x 1 lb/16 oz = 62/16 lb = 3 7/8 lb 2. 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 3. 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 Conversion rate: 16 oz/1 lb 3 lbs x 16 oz/1 lb = 48 oz 2. 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 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 2. 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. Find the difference between 14 lb 5 oz and 8 lb 14 oz 5 lb 7 oz 2. Find the sum of 5 lb 8 oz and 4 lb 10 oz 10 lb 2 oz 3. 2 lb 6 oz x 3 7 lb 2 oz lb 2 oz ÷ 6 1 lb 11 oz

Class Examples 1. Find the difference between 7 lb 1 oz and 3 lb 4 oz 3 lb 13 oz 2. Multiply: 3 lb 6 oz x 4 13 lb 8 oz 3. 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) Time (Section 8.4) 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