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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

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
7hours 36 min - 4hours 50 min
Tanis Reply

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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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