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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Introduction to Fractions and Multiplication and Division of Fractions" and contains many exercise problems. Odd problems are accompanied by solutions.

Exercise supplement

Fractions of whole numbers ( [link] )

For Problems 1 and 2, name the suggested fraction.

A circle divided into six equal parts. Two parts are shaded.

2 6 size 12{ { {2} over {6} } } {} or 1 3 size 12{ { {1} over {3} } } {}

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For problems 3-5, specify the numerator and denominator.

4 5 size 12{ { {4} over {5} } } {}

numerator, 4; denominator, 5

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5 12 size 12{ { {5} over {"12"} } } {}

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1 3 size 12{ { {1} over {3} } } {}

numerator, 1; denominator, 3

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For problems 6-10, write each fraction using digits.

Eight elevenths

8 11 size 12{ { {8} over {"11"} } } {}

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Two hundred six-thousandths

200 6, 000 size 12{ { {"200"} over {6,"000"} } } {}

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For problems 11-15, write each fraction using words.

10 17 size 12{ { {"10"} over {"17"} } } {}

ten seventeenths

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21 38 size 12{ { {"21"} over {"38"} } } {}

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606 1431 size 12{ { {"606"} over {"1431"} } } {}

six hundred six, one thousand four hundred thirty-firsts

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0 8 size 12{ { {0} over {8} } } {}

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1 16 size 12{ { {1} over {"16"} } } {}

one sixteenth

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For problems 16-18, state each numerator and denominator and write each fraction using digits.

One minute is one sixtieth of an hour.

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In a box that contains forty-five electronic components, eight are known to be defective. If three components are chosen at random from the box, the probability that all three are defective is fifty-six fourteen thousand one hundred ninetieths.

numerator, 56; denominator, 14,190

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About three fifths of the students in a college algebra class received a “B” in the course.

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For problems 19 and 20, shade the region corresponding to the given fraction.

1 4 size 12{ { {1} over {4} } } {}

A rectangle divided into four parts.

A rectangle divided into four parts. One part is shaded.

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3 7 size 12{ { {3} over {7} } } {}

A rectangle divided into seven parts.

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Proper fraction, improper fraction, and mixed numbers ( [link] )

For problems 21-29, convert each improper fraction to a mixed number.

11 4 size 12{ { {"11"} over {4} } } {}

2 3 4 size 12{2 { {3} over {4} } } {}

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15 2 size 12{ { {"15"} over {2} } } {}

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51 8 size 12{ { {"51"} over {8} } } {}

6 3 8 size 12{6 { {3} over {8} } } {}

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121 15 size 12{ { {"121"} over {"15"} } } {}

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356 3 size 12{ { {"356"} over {3} } } {}

118 2 3 size 12{"118" { {2} over {3} } } {}

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3 2 size 12{ { {3} over {2} } } {}

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5 4 size 12{ { {5} over {4} } } {}

1 1 4 size 12{1 { {1} over {4} } } {}

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20 5 size 12{ { {"20"} over {5} } } {}

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9 3 size 12{ { {9} over {3} } } {}

3

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For problems 30-40, convert each mixed number to an improper fraction.

5 2 3 size 12{5 { {2} over {3} } } {}

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16 1 8 size 12{"16" { {1} over {8} } } {}

129 8 size 12{ { {"129"} over {8} } } {}

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18 1 3 size 12{"18" { {1} over {3} } } {}

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3 1 5 size 12{3 { {1} over {5} } } {}

16 5 size 12{ { {"16"} over {5} } } {}

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2 9 16 size 12{2 { {9} over {"16"} } } {}

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17 20 21 size 12{"17" { {"20"} over {"21"} } } {}

377 21 size 12{ { {"377"} over {"21"} } } {}

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1 7 8 size 12{1 { {7} over {8} } } {}

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1 1 2 size 12{1 { {1} over {2} } } {}

3 2 size 12{ { {3} over {2} } } {}

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2 1 2 size 12{2 { {1} over {2} } } {}

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8 6 7 size 12{8 { {6} over {7} } } {}

62 7 size 12{ { {"62"} over {7} } } {}

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2 9 2 size 12{2 { {9} over {2} } } {}

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Why does 0 1 12 size 12{0 { {1} over {"12"} } } {} not qualify as a mixed number?

because the whole number part is zero

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Why does 8 qualify as a mixed number?

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Equivalent fractions, reducing fractions to lowest terms, and raising fractions to higher term ( [link] )

For problems 43-47, determine if the pairs of fractions are equivalent.

1 2 size 12{ { {1} over {2} } } {} , 15 30 size 12{ { {"15"} over {"30"} } } {}

equivalent

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8 9 size 12{ { {8} over {9} } } {} , 32 36 size 12{ { {"32"} over {"36"} } } {}

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3 14 size 12{ { {3} over {"14"} } } {} , 24 110 size 12{ { {"24"} over {"110"} } } {}

not equivalent

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2 3 8 size 12{2 { {3} over {8} } } {} , 38 16 size 12{ { {"38"} over {"16"} } } {}

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108 77 size 12{ { {"108"} over {"77"} } } {} , 1 5 13 size 12{1 { {5} over {"13"} } } {}

not equivalent

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For problems 48-60, reduce, if possible, each fraction.

10 25 size 12{ { {"10"} over {"25"} } } {}

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32 44 size 12{ { {"32"} over {"44"} } } {}

8 11 size 12{ { {8} over {"11"} } } {}

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102 266 size 12{ { {"102"} over {"266"} } } {}

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15 33 size 12{ { {"15"} over {"33"} } } {}

5 11 size 12{ { {5} over {"11"} } } {}

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18 25 size 12{ { {"18"} over {"25"} } } {}

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21 35 size 12{ { {"21"} over {"35"} } } {}

3 5 size 12{ { {3} over {5} } } {}

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9 16 size 12{ { {9} over {"16"} } } {}

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45 85 size 12{ { {"45"} over {"85"} } } {}

9 17 size 12{ { {9} over {"17"} } } {}

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24 42 size 12{ { {"24"} over {"42"} } } {}

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70 136 size 12{ { {"70"} over {"136"} } } {}

35 68 size 12{ { {"35"} over {"68"} } } {}

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182 580 size 12{ { {"182"} over {"580"} } } {}

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325 810 size 12{ { {"325"} over {"810"} } } {}

65 162 size 12{ { {"65"} over {"162"} } } {}

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250 1000 size 12{ { {"250"} over {"1000"} } } {}

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For problems 61-72, determine the missing numerator or denominator.

3 7 = ? 35 size 12{ { {3} over {7} } = { {?} over {"35"} } } {}

15

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4 11 = ? 99 size 12{ { {4} over {"11"} } = { {?} over {"99"} } } {}

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1 12 = ? 72 size 12{ { {1} over {"12"} } = { {?} over {"72"} } } {}

6

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5 8 = 25 ? size 12{ { {5} over {8} } = { {"25"} over {?} } } {}

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11 9 = 33 ? size 12{ { {"11"} over {9} } = { {"33"} over {?} } } {}

27

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4 15 = 24 ? size 12{ { {4} over {"15"} } = { {"24"} over {?} } } {}

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14 15 = ? 45 size 12{ { {"14"} over {"15"} } = { {?} over {"45"} } } {}

42

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12 21 = 96 ? size 12{ { {"12"} over {"21"} } = { {"96"} over {?} } } {}

168

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14 23 = ? 253 size 12{ { {"14"} over {"23"} } = { {?} over {"253"} } } {}

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15 16 = 180 ? size 12{ { {"15"} over {"16"} } = { {"180"} over {?} } } {}

192

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21 22 = 336 ? size 12{ { {"21"} over {"22"} } = { {"336"} over {?} } } {}

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Multiplication and division of fractions ( [link] , [link] )

For problems 73-95, perform each multiplication and division.

4 5 15 16 size 12{ { {4} over {5} } cdot { {"15"} over {"16"} } } {}

3 4 size 12{ { {3} over {4} } } {}

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8 9 3 24 size 12{ { {8} over {9} } cdot { {3} over {"24"} } } {}

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1 10 5 12 size 12{ { {1} over {"10"} } cdot { {5} over {"12"} } } {}

1 24 size 12{ { {1} over {"24"} } } {}

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14 15 7 5 size 12{ { {"14"} over {"15"} } cdot { {7} over {5} } } {}

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5 6 13 22 11 39 size 12{ { {5} over {6} } cdot { {"13"} over {"22"} } cdot { {"11"} over {"39"} } } {}

5 36 size 12{ { {5} over {"36"} } } {}

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2 3 ÷ 15 7 5 6 size 12{ { {2} over {3} } div { {"15"} over {7} } cdot { {5} over {6} } } {}

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3 1 2 ÷ 7 2 size 12{3 { {1} over {2} } div { {7} over {2} } } {}

1

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2 4 9 ÷ 11 45 size 12{2 { {4} over {9} } div { {"11"} over {"45"} } } {}

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8 15 3 16 5 24 size 12{ { {8} over {"15"} } cdot { {3} over {"16"} } cdot { {5} over {"24"} } } {}

1 48 size 12{ { {1} over {"48"} } } {}

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8 15 ÷ 3 3 5 9 16 size 12{ { {8} over {"15"} } div 3 { {3} over {5} } cdot { {9} over {"16"} } } {}

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14 15 ÷ 3 8 9 10 21 size 12{ { {"14"} over {"15"} } div 3 { {8} over {9} } cdot { {"10"} over {"21"} } } {}

4 35 size 12{ { {4} over {"35"} } } {}

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18 5 3 4 size 12{"18" cdot 5 { {3} over {4} } } {}

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3 3 7 2 1 12 size 12{3 { {3} over {7} } cdot 2 { {1} over {"12"} } } {}

50 7 = 7 1 7 size 12{ { {"50"} over {7} } =7 { {1} over {7} } } {}

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4 1 2 ÷ 2 4 7 size 12{4 { {1} over {2} } div 2 { {4} over {7} } } {}

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6 1 2 ÷ 3 1 4 size 12{6 { {1} over {2} } div 3 { {1} over {4} } } {}

2

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3 5 16 ÷ 2 7 18 size 12{3 { {5} over {"16"} } div 2 { {7} over {"18"} } } {}

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7 ÷ 2 1 3 size 12{7 div 2 { {1} over {3} } } {}

3

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17 ÷ 4 1 4 size 12{"17" div 4 { {1} over {4} } } {}

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5 8 ÷ 1 1 4 size 12{ { {5} over {8} } div 1 { {1} over {4} } } {}

1 2 size 12{ { {1} over {2} } } {}

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2 2 3 3 3 4 size 12{2 { {2} over {3} } cdot 3 { {3} over {4} } } {}

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20 18 4 size 12{"20" cdot { {"18"} over {4} } } {}

90

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0 ÷ 4 1 8 size 12{0 div 4 { {1} over {8} } } {}

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1 ÷ 6 1 4 25 4 size 12{1 div 6 { {1} over {4} } cdot { {"25"} over {4} } } {}

1

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Applications involving fractions ( [link] )

Find 8 9 size 12{ { {8} over {9} } } {} of 27 2 size 12{ { {"27"} over {2} } } {} .

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What part of 3 8 size 12{ { {3} over {8} } } {} is 21 16 size 12{ { {"21"} over {"16"} } } {} ?

7 2 size 12{ { {7} over {2} } } {} or 3 1 2 size 12{3 { {1} over {2} } } {}

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What part of 3 1 5 size 12{3 { {1} over {5} } } {} is 1 7 25 size 12{1 { {7} over {"25"} } } {} ?

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Find 6 2 3 size 12{6 { {2} over {3} } } {} of 9 15 size 12{ { {9} over {"15"} } } {} .

4

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7 20 size 12{ { {7} over {"20"} } } {} of what number is 14 35 size 12{ { {"14"} over {"35"} } } {} ?

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What part of 4 1 16 size 12{4 { {1} over {"16"} } } {} is 3 3 4 size 12{3 { {3} over {4} } } {} ?

12 13 size 12{ { {"12"} over {"13"} } } {}

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Find 8 3 10 size 12{8 { {3} over {"10"} } } {} of 16 2 3 size 12{"16" { {2} over {3} } } {} .

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3 20 size 12{ { {3} over {"20"} } } {} of what number is 18 30 size 12{ { {"18"} over {"30"} } } {} ?

4

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Find 1 3 size 12{ { {1} over {3} } } {} of 0.

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Find 11 12 size 12{ { {"11"} over {"12"} } } {} of 1.

11 12 size 12{ { {"11"} over {"12"} } } {}

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Questions & Answers

how does Neisseria cause meningitis
Nyibol Reply
what is microbiologist
Muhammad Reply
what is errata
Muhammad
is the branch of biology that deals with the study of microorganisms.
Ntefuni Reply
What is microbiology
Mercy Reply
studies of microbes
Louisiaste
when we takee the specimen which lumbar,spin,
Ziyad Reply
How bacteria create energy to survive?
Muhamad Reply
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Muhamad
they make spores
Louisiaste
what is sporadic nd endemic, epidemic
Aminu Reply
the significance of food webs for disease transmission
Abreham
food webs brings about an infection as an individual depends on number of diseased foods or carriers dully.
Mark
explain assimilatory nitrate reduction
Esinniobiwa Reply
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
Elkana
Examples of thermophilic organisms
Shu Reply
Give Examples of thermophilic organisms
Shu
advantages of normal Flora to the host
Micheal Reply
Prevent foreign microbes to the host
Abubakar
they provide healthier benefits to their hosts
ayesha
They are friends to host only when Host immune system is strong and become enemies when the host immune system is weakened . very bad relationship!
Mark
what is cell
faisal Reply
cell is the smallest unit of life
Fauziya
cell is the smallest unit of life
Akanni
ok
Innocent
cell is the structural and functional unit of life
Hasan
is the fundamental units of Life
Musa
what are emergency diseases
Micheal Reply
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life
Lubega
Heyy Lubega hussein where are u from?
_Adnan
en français
Adama
which site have a normal flora
ESTHER Reply
Many sites of the body have it Skin Nasal cavity Oral cavity Gastro intestinal tract
Safaa
skin
Asiina
skin,Oral,Nasal,GIt
Sadik
How can Commensal can Bacteria change into pathogen?
Sadik
How can Commensal Bacteria change into pathogen?
Sadik
all
Tesfaye
by fussion
Asiina
what are the advantages of normal Flora to the host
Micheal
what are the ways of control and prevention of nosocomial infection in the hospital
Micheal
what is inflammation
Shelly Reply
part of a tissue or an organ being wounded or bruised.
Wilfred
what term is used to name and classify microorganisms?
Micheal Reply
Binomial nomenclature
adeolu
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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