math

A patient's heart beat 422 times over the course of six minutes. About how many times did the value

"About how many indicates you need to estimate how much " estimate 420 to 400 divisible by 6 is 70 beats per minute

what is 30 % of 120?

"of multiplication" 0.30 x 120 =36

decimal in words

0.06 six hundredths 0.6 six tenths 6.0 six

14.5 % of 96 ?

0.145 x 96 =13.92

what is 14.5% of 96?

0.145 x 96=13.92

simplify

0.22+0.5 -(5.5+3.3 /3) first evaluate parenthesis 3.3/3=1.1 +5.5=6.6 re write problem 0.22+0.5-6.6 add subtract from left to right _____ -5.88

example

0.23 = 23% 5.34= 534% 86%=0.86 0.15% =0.0015

HOW DO YOU SOLVE FOR X

0.50/2 =1.50/X 0.50(X)=2(1.50) 0.50X=3 3 THEN DIVIDE 3 /0.50 =6

rational numbers from least to greatest

0.55,17% squareroot 25 64/4 25/50 3 17% 0.17 25 square root =5 64/16=16 25/50=1/2 =0.5

According to a hospital survey,82 % of nurses were highly satisfied at their. Of 145 nurses,how many were highly satisfied ? 0.82 x 145 ?118.9

0.82 x 145 = 118.9

learn how to simplify

1.45 + 1.5 +(6-9/2)+45 first evaluate the terms in parenthesis using proper order of operations. 1.45 +1.5(6-4.5)+45 1.45 +1.5+1.5 +45 finally add from left to right 1.45 +1.5 +1.5 +45=49.45

What is 150% of 20?

1.50 x20 =30

what is 150%of 20

1.50x20 =30

multiplying fractions

1/3 x 2/3 =2/9

how to simplify

1/4+3/6 fractions with denominators can be easily be added or subtracted.Recall that the denominator is the bottom number in the fraction and that the number top is numerator. lowest common denominator is 12 4 , 6 4,9,12,16 6,12,18,24 1/4 3/12 1x3 3x2 3/12 + 6/12 =9/12 reduce in lowest 4x3 6x2 3/4

A patient was given 100 mg of a certain medecine.The patient's dosage was later decreased to 88 mg. What was the percent decrease

100-88 100 12 x 100=12%

Common factor divides exactly into two or more

12 are 1,2,3,4,6,12

mutliplying decimals

12.3 x 2.56 multply as whole count decimals three here 31.488

what is 30 % of 120?

120

Fred buys some CDS FOR 12$ each. He also buys DVDS.The total that fred spent is 60$.So write an equation that shows the connection between the number of CDS and the average cost of a DVD.

12c+2d=60

A patients age is thirteen more than half of 60. How old is the patient?

13+30 =43

Ratios

14 computers in a lab, and the class has 20 students,there is a student to a computer ratio of 20 to 14. 20:14 reduced to 10:7 dividing both sides by 2

15%

15/100 > reduce 3/20 decimal 0.15

14,059.826

1= ten thousands 4=thousands 0=hundreds 5=tens 9=ones 8=tenths 2=hundredths 6=thousandths

Align decimals

2 grams - 0.45 2.00 0.45 1.45 2 whole needs to be displayed as decimal

two weeks 2/3 of the 60 patients were male..last week 3/6 of the patients 80 were male? which week had more males?

2/3 x 60/1 2x60 /3x1=120/3 =40 3/6x 80/1 3x80 /6x1 =240/6=60

dividing fractions

2/3/3/4 = flip N /D of second fraction the multiply 2/3 x 4/3 =8/9

two weeks ago about 2/3 of 60 patients 3/6 of 80 patients during which period were there more males ?

2/3x60=120/3 =40 3/6x80=240/6=40

Prime Factors

2x3 only two factors

CONVERT MIXED NUMBER

3 2/5 2/5 CAN BE DIVIDED 5 INTO 2 GIVES 0.4 ADD WHOLE PART 3.4 THEN TO CHANGE TO PERCENT X 100 340%

At a hospital 3/4 of the 100 beds are occupied. Yesterday 4/5 of the 100 beds were occupied by how much more ?

3/4 x100 = 300/4 then write in lowest terms =75 4/5x100 400/5 then divide it comes out to 80

John and luke play basketball every week. John shoots free throws while Luke shoots three point shots.John can make 5 more shots per minute than luke .On one day ,John made 30 free throws in the same time that it took Luke to make 20 three point shots. How fast are luke and john making shots?

30/x+5 20/x =30x=20(x+5) 30x=20+100 minus 20 from both sides =10x/10 10/100=10.

Estimate the solution to 345,932 + 96,369

300,000 +100,000 aprox 400,000

RAY EARNS 10$ AN HOUR. THIS CAN BE GIVEN WITH EXPRESSION 10X WHERE X IS TO EQUAL NOW LETS SAY RAY MAKES 360

360/10

At a hospital 40 % nurses work in labor and delivery.If 20 nurses work in labor and delivery how many nurses work at the hospital

40 % of the nurses are labor and delivery nurses. Of indicates multiplication and the word is and are indicate equivalence . 20/0.40=50

ONE WAY TO SOLVE FOR X IS TO FIRST CROSS

40/8 =X/24 40/(24)=8(X) 960=8X 960/8=8X/8 X=120

how to express a percentage into a fraction

60% = 60/100 and reduce 3/5 96% =96/100 =24/25

fraction into percent example %

7/10 =70/100 =70% 1/4 =25/100=25%

How to simplify

7/8 - 8/16 Fractions with common denominators are easier to add or subtract look for least common denominator 7x2=14 8x2=16 8x1=8 16x1=16 14/16-8/16 6/16 3/8

Example of inequality

7x>5 divide both side by 7 then its 5/7

convert 4/5 into decimal divide N/D

80/100

According to a hospital survey,82% of nurses were highly satisfied at thier job. Of 145 nurses ,how many were highly satisfied?

82% of 145= 0.82 x 145=118.9

45%/12%=15%/X

CROSS MUTIPLY 0.45(X)=0.12(0.15) 0.45 = 0.0180 0.0180/0.45 X=0.04 =4%

GCF

EXAMPLE 15 1,3,5,15 EXAMPLE 35 1,5,7,35 5 GCF

LCF

EXAMPLE 3 ,6,9,12,15 THE MUTIPLES 5 ,10,15,20

At a hospital,40 % of the nurses work in labor and delivery .If 20 nurses work in labor delivery, how many nurses work at the hospital ?

First think about the number of nurse that work at the hospital. Solving for n gives n=20/40%=20/0.40 =50

Example #2

Graph 10>-2x+4 need to solve for x oppsite of addition is subtraction so subtract 4 from both sides 6>-2x flip symbol -3<x x>-3

continous data

Information (such as time and temperature) that can be expressed by any value with any given range.

primary data

Information that has been collected directly from a survey,investigation,or experiment,such as questionnaire or the recording of daily temperatures.

A farm sells vegetables and dairy products . One third of the sales from dairy products plus half of the sales from vegetables should be greater than the monthly payment (p) for the farm.

Let the d stand for dairy products. Let the v stand for the sales from the vegetables . One third of the sales from the dairy products is the expression d/3. One half of the sales from vegetables is the expression v/2. The sum of these expressions should be greater than the monthly payment for the farm. An inequality for this is d/3 + v/2 >P

numerator / denominator

N: integer on the top of the fraction D: integer of the bottom of the fraction

Unit Rate as Slope

NUMBER OF COPIES SOLD AND TIME IS ON SALE Y=5 X= RISE/RUN SLOPE 5/1 REDUCED =5

In an intensive care unit,the nurse to patient ratio is 1:2 is 7 nurses were on duty how many patients are currently in ICU ?

NUMBER OF NURSES 1 7 NUMBER OF PATIENTS 2 14 CROSS MULIPLY 1/2 =7 X MULTIPLY 7 X2=14

A patient was given 100 mg of a medicine every two hours.How much medication will the patient receive in 5 hours?

Reasoning since 5 hours is 2.5 just multiply 2.5 x the dosage which is 100 mg it will equal =250

A patient was given pain medicine at a dosage of 0.22 grams. The patient's dosage was then increased to 0.80 grams.By how much was the patient's dosage increased?

Remember to line up the decimal when subtracting. 0.80 0.22 0.58

Rounding is reducing the digits in a number while still trying to keep the value smaller

Round 11,47,118 nearest ten 11 rounds to 10 47 to 50 118 to 120

data interpretation

Statistics -is the branch of mathematics deals ,collecting,recording,interpreting,illustrating ,and analyzing large amounts of data.

To write an inequality

The sum of 2 and a number is at most 12. So write 2 +b <_ 12.

Translating Word Problems

To write an expression,you must first put variables with the unknown values in the problem.Then ,translate the words and phrases into expressions that have numbers and symbols. = equals is equal to ,is ,was, were,will be yields,is the same as,amounts to,becomes > is greater than,is more than <less than,fewer than

improper fraction

a fraction whose numerator is larger than the denominator

proper fraction

a fraction with a numerator smaller than the denominator

mixed number

a number made up of a whole number and a fraction examples: 8/3= 6/3+2/3=2+2/3

add and subtract

align all number 4.5+2 =6.5 2.0

nominal data

can not be placed in numerical order

janice will earn 40 $ for the first 5 hours hours of baby sitting, How much will she earn in three more

croos mulitply 40/5 8/x=320 divide 320/5 =64

Direct Porportions

describes a relationship in which quantity increases by a set amount for every increase in the other quantity,or decreases by that same amount for every decrease in the other quantity.

dividing decimals

dividend number being divided 14/7 14 is dividend 7 is divisor

Work unit rate

expresses comparisons in terms of one hour if soda # 1 costs 1.50 for a liter bottle and soda #2 2.75 for a 2 -liter bottle divide second one and answer is 1.375 which is a better deal . If you paint two rooms in 4.5 hours, you can determine how long it will take you to paint 5 rooms by solving for the unit per room and then multiplying by 5.

Jane ate at a local restaurant.She ordered a 4.99 appetizer,a 12.50 entree,and a 1.25 soda.If she wanted to tip

first add 4.99+12.50+1.25=18.74 x 0.20=3.75 total cost 22.49

A patient complaining of fatigue and weight gain was diagnosed with hypothyroidism and was prescribed 125 mg of medication . Three months later, her symptoms

first dosage 125 the second 100 first divide the change which is 25 and divide ny original =1/5 then calculator says 0.2 make it into percent which is move two to the right

The McDonald are taking a family road trip,driving 300 miles to their cabin. It took them 2 hours to drive the first 120 miles.They will drive at the same speed all the way to their cabin.Find the speed at which the McDonald are driving and how much longer it will take them to get to the cabin.

first look at total miles 300 divide 120/2=60 then how much longer 300-120=180 180/60=3

ADDITION

if signs are same add / when different keep sign of bigger number but subtract

adding subtracting fractions

if two fractions have a common denominator they can be added or subtracted 1/2 +1/4 =2/4 +1/4=3/4

Qualitive data

information scientists first collect, describes anything physical (color, odor, shape) can not be measured in numbers

discrete data

information that can be expressed only by a specific value, such as whole or half numbers. For example, since people can be counted only in whole numbers,a population would be counted in discreet data.

secondary data

information that has been collected,sorted,and processed by the researcher

line graph

is a graph that connects points to show how data increases or decreases over time. Time line is a horizontal axis.

Inverse proportions

is a relationship in which an increase in one quantity is accompanied by a decrease in the other,or vice versa. Example

It takes Andy 10 minutes to read 6 pages of his book. He has already read 150 pages in his book that is 210 pages long. Find how long it takes Andy to read 1 page and also find how long it will take him to finish his book if he continues to read at the same speed.

it takes 1 minute and 40 seconds 10/6 1 2/3 it will take and another 100 minutes ad 40 seconds to finish book 210-150=60 x 1 2/3 x 60=40

A patient's was given blood pressure dosage of 2 grams .The patient's dosage was then decreased to 0.45 what was the decreased?

line up before subtracting 2.00 0.45 1.55

Quantitative data

measurements (such as length ,mass,and speed) that provide information about quantities in numbers

to convert from a decimal to a percent

move the decimal two points to the right

to convert from percent to decimal

move two spaces to the left

of

multiplication

3/2 + (4(0.5)-0.75)+2

multiply 4x0.5 then add it to 0.75=1.25 3/2 +1.25+2 change all fraction to decimals 1.5+1.25+2=4.75

A patient was given 40 mg of a certain medicine. Later,the patient's dosage was increased to 45 mg. What is the percent increase

new amount-original amount original amount x 100 5/40 x100 =12.5%

ordinal data

numerical order

percent

per hundred

multiplcation

signs same postive 4x8=32 -4 x -8=32 opposite signs 4x-8=-32 -4x8=-32

Graphing and Solving Inequalities

solving inequalities can be done with the same rules. However,when multiplying or dividing by a negative number,The direction of the inequality sign must be flipped or reversed.

In a performance review, an employee received a score of 70 for efficiency and 90 for meeting project deadlines.later it increased to 65 and meeting to 96

subtract 70-65 =5/70 =7.1% subtract 90-96 =6/90=6.7%

Data

the collective name for pieces of information (singular is datum )

constant of proportionality

the constant value of the ratio of two proportional quantities x and y

At a hospital, for every 20 females there are 15 male patients.The same ratio happens to exsist at another hospital. If there are 100 female patients at the second hospital,how many male patients are there?

three numbers most of the time mean cross multiply so 20/x and 100 x 15 1500 then divide each side by 20 1500 divided by 20 =75

BAR GRAPH

uses bar to compare data as if each bar were a ruler

pictograph

uses pictures or symbols to show data. The pictograph will have a key to identify what each symbol means.

How to simplify

when dividing a fraction with fraction,one must first rewrite the problem as multiplication. change the reciprocal / Multiply and reduce 2/5 / 4/7 change 2/5 x 7/4 =14/20 reduce 7/10

In a hospital emergency room,there are 4 nurses for every 12 patients.What is the ratio of nurses to patients?if the nurse-to patient ratio remains if it were 24 patients?

write is as 4/12, 4:12 ,4 to 12 reduce it for 1:3 there must be 8 for 24 it remain the same it will also be three since it is 8 16 (24) three ><

Slope

x 1 x 2 stands for m upward postive downward negative

ABSOLUTE VALUE

|3| |-3|