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**Chapter 16 - Math & Measurement Skills**

Workforce Essentials Ms. Baumgartner

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Chapter 16 Objectives Identify occupations requiring math and measurement skills Apply math skills to computation of total purchase amount, trade discount, cash discount, markup, sales tax, and markdown Calculate surface measures and volume measures Convert measures from one unit to another

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Lesson 16.1 Basic Math This lesson explains some common uses of math at work These uses are called ‘business math’ Many occupations require business math skills The following examples show some common ways in which math is used on the job They are total purchase amount, trade discount, cash discount, markup, sales tax, and markdown

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**Lesson 16.1 Basic Math Total Purchase Amount**

Most of your purchases involve single items Ex) You buy a pair of running shoes for $54.95, the total amount of your purchase is easy to figure: 1 x $54.95 = $54.95 (plus tax, in most states) Businesses often buy large numbers of the same item A sporting goods store might buy dozens of pairs of running shoes

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**Lesson 16.1 Basic Math Total Purchase Amount**

To find the total amount of the purchase, multiply the number of items by the price of one item (the unit price) PROBLEM: Figure the total amount of a purchase of 24 pair of shoes at $42.95 each, 15 pairs of socks at $1.85 each, and 3 dozen packages of shoelaces at $0.89 each…

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**Lesson 16.1 Basic Math Total Purchase Amount**

SOLUTION: Quantity x Unit price x = Amount Shoes: 24 x $42.95 = Socks: 15 x $1.85 = Laces: 36 x $0.89 = Total Amount = This skill is important when preparing invoices, a bill for goods, example on page 225

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**Lesson 16.1 Basic Math Trade Discount**

A trade discount is a deduction from the catalog (list or suggested retail) price of an item Trade discounts are usually given to retailers to enable them to sell merchandise at a greater profit In some cases, buyers get special discounts when ordering large quantities

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**Lesson 16.1 Basic Math Trade Discount**

PROBLEM: An office desk is listed in a catalog at $680. Business customers can buy the desk at a trade discount of 30%. How much will a business have to pay for the desk? SOLUTION: 30% = .30 $ $680 x discount Net purchase price

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**Lesson 16.1 Basic Math Cash Discount**

Every sale between a business buyer and seller involves terms, these state the time limit within which the buyer must pay A common term of sale is “net due in 30 days”, this means that the buyer has 30 days in which to pay the bill After 30 days, the buyer must pay the price plus interest

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**Lesson 16.1 Basic Math Cash Discount**

To encourage prompt payment, the seller may offer a cash discount A cash discount is a reduction in price, often several %, often to a buyer to encourage early payment on an account The buyer saves money, while the seller has a paid account

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**Lesson 16.1 Basic Math Cash Discount**

PROBLEM: An invoice for $510 has terms of net due in 30 days with a 3% discount given for payment within 10 days. What is the sale price if the buyer pays within 10 days? SOLUTION: 3% = .03 $ $510 x discount Net amount of payment

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**Lesson 16.1 Basic Math Markup**

A retailer buys good from a supplier to resell Remember the running shoes? The price the store paid is called the ‘cost price’ To make money, the retailer then added an amount, the markup, to the cost price Selling price = cost price + markup

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**Lesson 16.1 Basic Math Markup**

PROBLEM: An item costs $28; its selling price is $45. How much is the markup? SOLUTION: $ Selling price -$ Cost price Businesses mark up merchandise to cover their expenses and make a profit

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**Lesson 16.1 Basic Math Percent Markup**

PROBLEM: Based on the cost price, what is the percent of markup? Percent of markup = markup / cost price SOLUTION: $7 / $28 = (convert answer to %)

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**Lesson 16.1 Basic Math Markup**

Businesses know how much markup will give them enough money to cover expenses and make a fair profit, so they add the markup to an item before trying to sell it PROBLEM: A radio costs $42 and will be sold at a markup of 30% of the cost price. What is the selling price? (reverse the previous problem!)

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**Lesson 16.1 Basic Math Percent Markup SOLUTION: $42 cost price**

x .30 markup markup selling price

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**Lesson 16.1 Basic Math Sales Tax**

Most states and cities have sales tax on goods and services Sales tax usually range between 1-7 % The sales tax is added on to the purchase price of goods and services

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**Lesson 16.1 Basic Math Sales Tax**

PROBLEM: Someone buys a sweater for $38 and a pair of slacks for $46. a 5% sales tax is added to the purchase price. What is the total amount of the purchase? SOLUTION: $38 + $46 purchase price

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**Lesson 16.1 Basic Math Markdown**

Most retail stores have periodic sales to move slow-selling merchandise, clear out end-of-season goods, or attract customers to the store A reduction in the selling price of a product is called a markdown, it is usually expressed as a percent (25% off all women’s dresses)

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**Lesson 16.1 Basic Math Markdown**

PROBLEM: A merchant is having a sale on all summer swimwear at 40% off (markdown). What is the sale price of a swimsuit that was originally priced at $55? SOLUTION: $55 original price x markdown

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**16.1 Checkpoint Why are these formulas called “business math?”**

How does a cash discount benefit a buyer? How does it benefit a seller? A company is billed $1,850 with a cash discount of 5% if they pay within 10 days. How much will they save? Explain the difference between cost price and selling price. What is the selling price of a dress that costs $60 and marked up 40%? Later, that same dress is put on sale for 25% off, what is price then?

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**Lesson 16.2 Basic Measurement**

Measurement is the act of determining the dimensions, quantity, or degree of something The object can be volume, area, distance, temperature, time, energy, or weight Measurement answers the question ‘how much?’

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**Lesson 16.2 Basic Measurement**

The perimeter of an object is the distance around it Perimeter is measured in standard linear units, including miles, feet, inches, km, meters, cm, and mm You find the perimeter by adding together the lengths of the outer edges of the figure for most shapes The perimeter of a circle is called the circumference

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**Lesson 16.2 Basic Measurement**

To determine the circumference, you must use a formula, the formula is as follows: Circumference = 3.14 x diameter or C = 3.14 x D Using Figure 16-3, how wide of a piece of sheet metal will you need to roll it into a cylinder that is 16 inches in diameter? C = 3.14 x D C = 3.14 x 16 inches C =

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**Lesson 16.2 Basic Measurement**

The area is the number of square units of space on the surface of a figure enclosed by the perimeter Area = length x width or A = l x w For example, the area of a rectangular room that is 8 feet long and 12 feet wide is… A = 8 x 12 =

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**Lesson 16.2 Basic Measurement**

To find the area of a circle, you again use a formula that contains the constant 3.14, as well as the value of the radius The formula is written as follows: A = 3.14 x r² A = 3.14 x 8² A = 3.14 x 64 A =

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**Lesson 16.2 Basic Measurement**

Like perimeters and areas, volume measures are often used on the job Volume is the amount of space an object takes up It can be expressed in units of cubic measure such as cubic inches, cubic yards, and cubic feet It can also be given in units such as gallons, quarts, ounces, and bushels

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**Lesson 16.2 Basic Measurement**

Volume = length x width x height or V = l x w x h For example, to find the volume of a rectangular box that is 4 feet long, 2 feet wide, and 1 foot high, you multiply 4x2x1=8 If the dimensions are in different units, they will have to be converted to the same unit of measurement before multiplying…

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**Lesson 16.2 Basic Measurement**

Example) Let’s say that you are going to lay a 6 inch gravel base in a ditch before installing a sewer pipe, the ditch is 30 inches wide and 150 feet long… V = l x w x h V = 150 feet x 30 inches x 6 inches Convert all measures to the same units, in this case, use feet (12 inches = 1 foot) V = 150 feet x 2.5 feet x 0.5 feet V =

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**Lesson 16.2 Basic Measurement**

To be effective on the job, you should be able to work with the basic units of measure in the conventional (or English) and metric systems You should be familiar with procedures for converting measures from 1 unit to another within the same system You also need to be able to convert measures from the conventional system to the metric system and vice versa

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**Lesson 16.2 Basic Measurement**

Most of the world, except for the United States, uses the metric system of measure Congress passed a trade bill in 1988 that required all federal agencies to convert to the metric system by 1992 This means, if the Dept. of Defense wants to buy gasoline, it must do so in liters, not gallons This law will not force private companies to convert to the metric system See conversion chart in Figure 16-6 on p 234

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