Math Skills – Week 7

Class project due next weekSample final exams available on websiteReducing fractions, rates, and ratios$500

huh?17/30

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Section 8.1 – LengthSection 8.2 – WeightSection 8.3 – CapacitySection 8.4 – Time

U.S. Customary SystemSet 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

37

12

feetmilesyards

unitsnumber

s

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 yd5280 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 mindWhy?

3 ft 1 yd 3 ft

1 ydand

Converting between units of measureSteps

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

Examples1. 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

Examples1. 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 Examples1. Convert 14 ft to yards

Conversion rate: 1 yd/3 ft 14 ft x 1 yd/3 ft = 4 2/3 yd

2. Convert 10560 ft to miles Conversion rate: 1 mi /5280 ft 10560 x 1 mi/5280 ft = 2 mi

Writing measurements in simplest formBefore we had:

40 in = 3 1/3 ftIf 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

1. 17 in = ___ft ___in1 ft 5 in

2.31 ft = ___yd ___ft10 yd 1 ft

3 4

Class Examples1. 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 in5 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 5inx 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 example1. Find the quotient of 4 ft 3in and 3

Method 1 – Direct Division Method 2 – Convert first

1. Convert to inches 2. Do division3. Write answer in simplest form

17in or 1 ft 5 in

Examples1. 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 Examples1. 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

2. 10 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 oz1 lb 16 oz

1 lband

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

3. 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 formBefore we had:

4200 lb = 2 1/10 tonsIf 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.

Examples1. 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.

Examples1. 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

4. 10 lb 2 oz ÷ 6 1 lb 11 oz

Class Examples1. 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 day7 days = 1 week