Ch 7 Ratio and Proportion

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Ch 7 Ratio and Proportion
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A ratio is a comparison of two numbers and can be
written several ways. Each of the following are
ways to write the ratio of 3 to 4.
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If the quantities to be compared include units,
then the units should be the same if possible. To
find the ratio of 1 ft to 15 in, express both
quantities in inches and then find the ratio.
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Express each ratio in lowest terms.
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A rate is a comparison of two quantities that
have different units that do not cancel out. A
unit rate is one in which the denominator is 1.
Rates are often written using a slash (/) which
is read per. Examples
50 miles per hour 50mi/h(mph)
32 miles per gallon 32mi/gal(mpg)
20 dollars per hour 20/h
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Express each rate in lowest terms.
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Unit Price

• A unit price, or unit rate, is the ratio of price
  to the number of units.

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Example

• A baker buys 25 lb of flour for 74.75. What is
  the rate or unit price in dollars per pound?
• Since we are asked for the rate in dollars per
  pound, the monetary amount must be in the
  numerator.

2.99 dollars per pound or 2.99/lb
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• Unit prices often vary with the size of the item
  being sold.
• Many factors can contribute to determining unit
  pricing in food, such as variations in store
  pricing and special discounts.
• Compare unit prices to determine the best buy for
  a certain item that is sold in various size
  containers.

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Example

• Find the unit price of a 32 oz bottle of
  household cleaner and then decide which is the
  best purchase based on the unit price per ounce.

Based on unit price alone the 32-oz size is the
best buy.
19.656 /oz
The unit price for the 32-oz size is given by
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What is the alternator-to-engine drive ratio if
the alternator turns at 1125 rpm when the engine
is idling at 500 rpm?
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The resistance in ohms of a resistor is the ratio
of the voltage drop across the resistor, in
volts, to the current through the resistor in
amperes. A resistor has a voltage drop across it
of 117 V and a current through it of 2.6 A. What
is the resistance in ohms of the resistor?
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Suppose 12 gallons of herbicide concentrate are
used on 28 acres. Find the rate of application in
gallons per acre.
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Over a period of 5 h, 1200 cc of a drug will be
administered intravenously. How many cubic
centimeters per minute is this?
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A common medical practice is to give medication
by IV (intravenous). The number of drops per
minute is related to the equipment being used.
The number of drops per mL is called the drop
factor. Common drop factors are 10 drops/mL, 12
drops/mL and 15 drops/mL.
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A doctor orders 500 mL of glucose to be given by
IV in 6 hours. The drop factor of the equipment
is 15 drops/mL. Determine the number of drops per
minute (flow rate) in order to set up the IV.
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How long should the IV be administered to give
1500 mL of saline solution IV with a drop factor
of 10 drops/mL and a flow rate of 50 drops/min?
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7.2 Proportion
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A proportion states that 2 ratios are equal. A
proportion may be true or false.

• A true proportion

• A false proportion

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A proportion has four terms. In the proportion
the first term is 2, the second term is 5 the
third term is 4, and the fourth term is 10. The
first and fourth terms are called the extremes
and the second and third terms are called the
means.
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If a proportion is true, then the product of the
means must equal the product of the extremes.
These products are referred to as the cross
products.
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To solve a proportion means to find the value of
the missing term. To do this use cross products
to write an equation then solve the
equation.Solve
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Solve each proportion (round to 3 significant
digits when necessary.)
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Since a proportion is 2 equal ratios, they are
often used to solve applications in which we are
given a ratio or rate and then asked to find the
result if one part of the ratio or rate changes.
When setting up the proportion be sure to keep
the 2 ratios (rates) in the same order.
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If 125 bolts cost 7.50, how much do 200 bolts
cost?

• Since 125 and 7.50 are compared, use them to form
  the first rate, then set up the second in the
  same order.

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Suppose 826 bricks are used to build a wall 14 ft
long. How many bricks are needed for a similar
wall 35 ft long?
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A label reads Gantrisin, 1.5g in 20 cc. How
many cubic centimeters are needed to give 10.5 g
of Gantrisin
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Example

• If 5 ounces of a medicine must be mixed with 8
  ounces of water, how many ounces of medicine
  would be mixed with 36 ounces of water?

Thus, 22.5 ounces of medicine would be needed.
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Proportions can be used to work a variety of
percent problems. Since percent literally means
per 100, start by placing the percent () number
over 100. This gives half of the proportion.
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To complete the proportion, we need to identify
the whole (base) amount and the part. The whole
is the amount that follows the phrase of and
the part is usually the amount that precedes or
follows the word is. We then complete the
proportion as follows
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Percent problems generally have one of the
following forms.

• Find 40 of 72(whole)
• What of 80(whole) is 60 (part)?
• 25 (part) is 30 of (whole)

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Set up the proportion used to solve these percent
problems.

• What is 40 of 72?
• What of 80 is 60?
• 25 is 30 of how much?

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When solving applications involving percent,
first set the percent over 100, determine the
whole and then complete the proportion with the
part over the whole.
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A welder makes high quality welds 90 of the
time. Out of 120 welds, how many are expected to
be high quality?
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You need 25 of a 60-mg tablet. How many mg do
you need?
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Find the amount of pure ingredient needed to
prepare 1000 mL of 5 Lysol solution from pure
Lysol.
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Find the amount of pure ingredient needed to
prepare 400 mL of 150 sodium bicarbonate
solution from pure sodium bicarbonate.
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What percent of 2000 ft is 400 yds?
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Some common variations of basic percent problems
and the related proportion are given below

• Discount
• Sales tax

Sale price original price - discount
Total cost price sales tax
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Continued

• Percent increase/decrease
• Interest

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The loan for a new car requires an 8 down
payment. If the car sells for 24,350, how much
is required for the down payment?
If Sam only has 1500, what price car can he get
a loan for?
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A new car is listed at 26,850. The salesperson
offers to sell it to you for 21,000. What
percent discount is he offering you?
If the sales tax rate is 4, what will the total
price be?
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Jill makes 18.40 an hour. If she gets a 5
increase, how much will she be making with the
raise?
If her pay increases to 20.00 per hour, what
percent increase is this?