RSPT 1325 Sciences: unit 1 lecture/homework page 1

RSPT 1325 Scienceslecture

Part I of Unit 1: Math Key

By Elizabeth Kelley Buzbee AAS, RRT-NPS, RCP

  1. [pp.42-53] Be able to calculate percentages

A fraction is a way of comparing two numbers. One number represents the content [what we actually have] while the other number is the capacity [the total number of items]

Complete this table

The fraction / The relationship
10/20 / You have 10 out of a possible 20.
3/4 / You have 3 out of a possible 4
4/2 * / You have 4 out of a possible 2

*Please note that the last fraction has more in the content than in the capacity. Oddly enough, in nature we will sometimes end up with a content that is larger than the capacity.

For example a person with a fast heart rate [tachycardia] has more heartbeat/min [content] than normal heart/beat [capacity]. If normal high HR is 100 bpm and your patient has a heart rate of 120, he has 120 parts out of a possible 100.

A percent is a fraction based on 100 parts. 50% is 50/100, 3% is 3/100 and .25% is .25/100.

  1. Obviously, when we discuss numbers, they are rarely in groups of 100, so we need to convert a percentage of a number into an actual number.
  2. To work with a percent, we need to change the percent to a decimal. To do this we take the fraction created by the percent and divide:

You do these:

Percent / fraction / Decimal
.25% / .25/100 / .0025
75% / 75/100 / .75
6% / 6/100 / .06
1.25% / 1.25/100 / .0125
5% / 5/100 / .05
.5% / .5/100 / .005
  1. If you need to find 25% of a number, you would multiply that number by .25 because as we know 25/100 is .25.
  2. Example: Tires are on sale for 33% off. The ticket price is $250.

(33/100) x 250 =

.33 x 250

=82.5.

You have saved $82.5 and only have to pay $167.5.

You do these:

  1. Based on the above example: you have to pay 8% tax on these tires based on their sale price.
  2. How much tax will you pay?

Sales price = $167.5

8% of 167.5 =

8/100 x 167.5

.08 x 167.5 =13.4 tax

167.5 + 13.40 = $180.9

  1. Based on the above example: you have a coupon that will give you 10% off the original [ticket] price.
  2. How much more money have you saved?

Original price = $250

10% of 250 = 10/100 x 250=

.1x 250 = $ 25

We have saved $25 on tires with coupon

  1. What do you pay now?

$250 – $25 = $225 sale price

$225 x .08 [tax] = $18 tax

$225 + $18 = $ 243

  1. After you start him on oxygen mask, your patient has a heart rate that has dropped 25% from his base line of 125 bpm.
  2. How many beat/minute has the heart rate dropped?

125 x .25 = 31.25 the HR has dropped 31 bpm

  1. What is the current heart rate?

125 + 31 = 156 bpm

  1. One way of measuring lung function is to measure the speed of exhaled gases. After inhaling some medicine, your patient’s peak flow rate rises 70% from the baseline of 300 ml/minute.
  2. By how many ml/minute has the peak flow risen?

300 x .70 = 210 ml/minute increase

  1. What is the new peak flow?

300 + 210 = 510 ml/minute

  1. Another way to use percentages is to figure out what percent a number is of another number.
  2. To do this calculation, we turn the percentage into a decimal and multiply by the number [capacity] then multiply by 100.

Do these:

problem / Turn into a fraction: / Turn the fraction into a decimal / Multiply the decimal by 100 to get the percent.
30 is what percent of 60? / 30/60 / .5 / 50%
18 is what percent of 180 / 10/180 / .055 / 5.5%
25 is what percent of 30 / 25/30 / .833 / 83.3%
120 is what percent of 100* / 120/100 / 1.2 / 120%

* Note that the last problem results in a number higher than 100%

i. Another way to work with percentages is to figure out what the capacity is when we know what percent a given content is of the unknown capacity.

In other words, if 80 is 40% of a number, what is that number?

  1. To solve this problem we do the following:

Problem: / Turn percent into decimal / Turn the word “of” into multiplication / Solve for X by dividing both sides by the decimal
80 is 40% of what number?
or
80 = 40% of X / 80 = .4 of X / 80 = .40 ( X) / 80 /. 40 = .40 ( X)
.40
80/.40 = X
X = 200
80 is 40% of 200
450 is 2% of what number? / 450=.02 of X / 450 = .02 X / 450 = .02 X
.02 .02
450 is 2% of 22,500
3.5 is 75% of what number? / 3.5 = .75 of X / 3.5 = .75 X / 3.5 = .75 X
.75 .75
3.5 is 75% of 4.66
.3 is 12.5% of what number? / .3 = .125 of X / .3 = .125 X / .3 = .125 X
.125 .125
.3 is 12.5 % of 2.4
50 is 125% of what number? / 50 = 1.25 of x / 50 = 1.25 x / 50 = 1.25 x
1.25 1.25
50 is 1.25% of 40

For further practice on percentages, go to the book at page 57-59 to answer the following questions: 68-72, 76-78, & 80-82.

Key on handout

  1. [pp. 18-21, 25-32 ] Be able to calculate ratio problems.
  2. When we use ratios we are comparing two numbers with the same units. 1:2 is easy to understand, but most of us find it harder to understand a relationship of 120:2450.
  3. Because most of us need to compare something to one in order to understand the relationship, it is better to reduce the ratio so that one of the numbers equals 1.
  4. This action is accomplished by dividing both sides of the ratio by the lower number.

Example:

25: 75

25 : 75

25 25

1: 3

You do these:

ratio / 1 : x
33:66 / 33 : 66 =
33 33
1:2
25.4: 100.5 / 25.4: 100.5
25.4: 25.4
1: 3.9
30:30,000 / 30: 30,000
30 :30
1:1000

If the lower number happens to be to the right of the “:”, we still do the formula the same way:

ratio / x : 1
88:44 / 88 : 44
44 44
2:1
18: 9.7 / 18: 9.7
9.7 9.7
1.855: 1
350:30 / 350 :30
30 30
11.666: 1

How would we use this skill in Respiratory Care?

If a person is breathing 10 breaths /minute, each breath lasts about 6 seconds [6 seconds x 10 = 60 seconds.]

If the inspiratory phase lasts 2 seconds, what is the ratio of inspiratory to expiratory phase?

[Part I] Inspiratory phase + expiratory phase = 6 seconds

So 2 seconds + x = 6 seconds

6 seconds-2 seconds = x seconds

Expiratory time is 4 seconds

[Part II] the ratio of inspiratory:expiratory would be

2 seconds:4 seconds

To reduce this would be:

1:2

You solve the following questions:

  1. If the patients inspiratory time was 1 second and his expiratory time was 3 seconds, what is his I:E ratio?

I + E = 1:3

  1. If the patients inspiratory time is 1 second and the total breath lasts 2 seconds, what is the I:E ratio?

I + E = total breath

1 second + x = 2 seconds

1 second + x -1 = 2 seconds -1 second

X = 1

Inspiratory time = 1 second

Expiratory time = 1 second

I + E = 1:1

  1. Your patient is a newborn baby with an inspiratory time of .25 second and a respiratory rate of 60 bpm [entire breath is 1 second.. What is the I:E?

I:E = X

X = 1 second

1 second = .25 + E

1 second -25 = .25 + E -.25

E = .75

I:E = .25 : .75

I:E = .25 :.75

.25 : .25

I:E ratio = 1:3

Each breath has a measurable volume which we call the VT. Part of this VT is considered ‘wasted’ or ‘dead space’ [VD] because it doesn’t come in contact with the blood stream. A normal VD/VT ranges between .30 to .40 or 30-40% of a person’s VT is VD.

Calculate the VD/VT when the VD 100 ml and the VT is 500 ml

100 ml : 500ml = reduce = 1:5

Convert to decimal --- 1/5 = .20

VD/VT = .20

VD in ml / VT in ml / VD:VT / reduced / VD/VT in decimal
200 / 300 / 200:300 / 2:3 or 1:1.5 / .66
150 / 650 / 150:650 / 1:4.3 / .23
125 / 500 / 125:500 / 1:4 / .25
  1. [pp. 21-22] Be able to calculate conversion from liter/minute to liter/second.
  2. Respiratory therapists frequently have to measure the speed a patient is breathing. The units are liter/minute or liter/second.
  3. To convert from liter/minute [LPM] to liter/second, we need only divide the liter/minute by 60 [60 seconds in a minute]
  4. To convert from liters/second to liters/minute, we would multiply the liters/second by 60.
  5. An easy method to remember this is that when we go from seconds to minutes we are getting larger time frames so we would have to multiply by 60.

You do these:

300 Liter/minute / 5 liters/second
25 liters/second / 1500 Liter/minute
555 Liters/minutes / 9.25 liters/second
  1. [pp. 64-69] Be able to work with and convert between different units in the international system (SI).

In 1960, the scientific community decided to use the same system of units and to use the metric system. Actually the USA adopted the metric system in 1890s but like Burma, we have held onto old-fashioned apothecary measurements such as gallons and pints for way, way too long.

  1. Know the units of measurement of mass, volume, length temperature and time.
  • For mass we will use grams as the basic unit of measurement.
  • For length we use the meter, and for time the second.
  • We use liters for volume as the basic unit of measurement.
  1. Know the derived prefixes for the above SI units of measurement.

100 grams = hectogram

100 meters = hectometer

1000 grams = kilogram [kg]

1000 meters – kilometer

1/10 meter = 1 decimeter

1/10 gram = 1 decigram

1/100 meter = 1 centimeter

1/100 gram = 1 centigram

1/1000 meter = millimeter [ml]

1/1000 gram = milligram [mg]

You do the following

1/10th / 1/100th / 1/1000th
mass / decigram / centigram / miligram
volume / deciliter / centiliter / mililiter
Length / decimeter / centimeter / milimeter
10 / 100 / 1000
mass / dekagram / hectogram / kilogram
volume / dekaliter / hectoliter / kiloliter
Length / dekameter / hectometer / kilometer

A hint:

To convert from milligrams to grams, you would divide by 1000 because you are going from many tiny units to a larger unit.

To convert from liters to ml, you would multiple by 1000 because you are going from a large unit to many smaller units.

You do these:

  1. A person whose body weight [mass] is 65 kg would also weigh --- grams.
  1. A person whose trachea is 23 centimeters long, would also have a trachea that is --- meters long.
  1. A person whose VT is .8 Liters, would also have a VT that is – milliliters.
  1. [pp. 70-73] Conversion of metric system to English [apothecary.]
  • 1 meter = 39.37 inches and 3.28 feet
  • 1 kilograms = 2.2 pounds
  • 1 ounce = 28 grams

You do these

If you have: / You would have:
3 meters / 118.11 inches
3 milimeters / .003 meters = .11811inches
150 ounces / 4200 grams
15 meters / 49.2feet
1.5 meters / 4.92 feet
254 kilograms / 558.8pounds
35,000 grams = 35kg / 35 kg = 77pounds

Your patient weights 25 kilograms, how many pounds does he weigh?

25 kg x 2.2 = 55 pounds

Your patient weights 120 pounds, how many kilograms does he weigh?

120/ 2.2 = 54.4 kg

  1. Be able to answer word problems based on the math skills in Part I