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Sample set b

Perform the following multiplications.

4 5 5 6 size 12{ { {4} over {5} } cdot { {5} over {6} } } {}

4 2 5 1 5 1 6 3 = 2 1 1 3 = 2 3 size 12{ { { { { {4}}} cSup { size 8{2} } } over { { { {5}}} cSub { size 8{1} } } } cdot { { { { {5}}} cSup { size 8{1} } } over { { { {6}}} cSub { size 8{3} } } } = { {2 cdot 1} over {1 cdot 3} } = { {2} over {3} } } {}

Divide 4 and 6 by 2
Divide 5 and 5 by 5

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8 12 8 10 size 12{ { {8} over {"12"} } cdot { {8} over {"10"} } } {}

8 4 12 3 8 2 10 5 = 4 2 3 5 = 8 15 size 12{ { { { { {8}}} cSup { size 8{4} } } over { { { {1}} { {2}}} cSub { size 8{3} } } } cdot { { { { {8}}} cSup { size 8{2} } } over { { { {1}} { {0}}} cSub { size 8{5} } } } = { {4 cdot 2} over {3 cdot 5} } = { {8} over {"15"} } } {}

Divide 8 and 10 by 2.
Divide 8 and 12 by 4.

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8 5 12 = 8 2 1 5 12 3 = 2 5 1 3 = 10 3 size 12{8 cdot { {5} over {"12"} } = { { { { {8}}} cSup { size 8{2} } } over {1} } cdot { {5} over { { { {1}} { {2}}} cSub { size 8{3} } } } = { {2 cdot 5} over {1 cdot 3} } = { {"10"} over {3} } } {}

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35 18 63 105 size 12{ { {"35"} over {"18"} } cdot { {"63"} over {"105"} } } {}

35 7 1 18 2 63 7 105 21 3 = 1 7 2 3 = 7 6

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13 9 6 39 1 12 size 12{ { {"13"} over {9} } cdot { {6} over {"39"} } cdot { {1} over {"12"} } } {}

13 1 9 6 2 1 39 3 1 1 12 6 = 1 1 1 9 1 6 = 1 54 size 12{ { { { { {1}} { {3}}} cSup { size 8{1} } } over {9} } cdot { { { { {6}}} cSup { size 8{ { { {2}}} cSup { size 6{1} } } } } over { { { {3}} { {9}}} cSub { { { {3}}} cSub { size 6{1} } } } } size 12{ cdot { {1} over {"12"} } = { {1 cdot 1 cdot 1} over {9 cdot 1 cdot 6} } = { {1} over {"54"} } }} {}

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Practice set b

Perform the following multiplications.

2 3 7 8 size 12{ { {2} over {3} } cdot { {7} over {8} } } {}

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

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25 12 10 45 size 12{ { {"25"} over {"12"} } cdot { {"10"} over {"45"} } } {}

25 54 size 12{ { {"25"} over {"54"} } } {}

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40 48 72 90 size 12{ { {"40"} over {"48"} } cdot { {"72"} over {"90"} } } {}

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

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7 2 49 size 12{7 cdot { {2} over {"49"} } } {}

2 7 size 12{ { {2} over {7} } } {}

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

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

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13 7 14 26 size 12{ left ( { {"13"} over {7} } right ) left ( { {"14"} over {"26"} } right )} {}

1

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16 10 22 6 21 44 size 12{ { {"16"} over {"10"} } cdot { {"22"} over {6} } cdot { {"21"} over {"44"} } } {}

14 5 size 12{ { {"14"} over {5} } } {}

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Multiplication of mixed numbers

Multiplying mixed numbers

To perform a multiplication in which there are mixed numbers, it is convenient to first convert each mixed number to an improper fraction, then multiply.

Sample set c

Perform the following multiplications. Convert improper fractions to mixed numbers.

1 1 8 4 2 3 size 12{1 { {1} over {8} } cdot 4 { {2} over {3} } } {}

Convert each mixed number to an improper fraction.

1 1 8 = 8 1 + 1 8 = 9 8 size 12{1 { {1} over {8} } = { {8 cdot 1+1} over {8} } = { {9} over {8} } } {}

4 2 3 = 4 3 + 2 3 = 14 3 size 12{4 { {2} over {3} } = { {4 cdot 3+2} over {3} } = { {"14"} over {3} } } {}

9 3 8 4 14 7 3 1 = 3 7 4 1 = 21 4 = 5 1 4 size 12{ { { { { {9}}} cSup { size 8{3} } } over { { { {8}}} cSub { size 8{4} } } } cdot { { { { {1}} { {4}}} cSup { size 8{7} } } over { {3} cSub { size 8{1} } } } = { {3 cdot 7} over {4 cdot 1} } = { {"21"} over {4} } =5 { {1} over {4} } } {}

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16 8 1 5 size 12{"16" cdot 8 { {1} over {5} } } {}

Convert 8 1 5 size 12{8 { {1} over {5} } } {} to an improper fraction.

8 1 5 = 5 8 + 1 5 = 41 5 size 12{8 { {1} over {5} } = { {5 cdot 8+1} over {5} } = { {"41"} over {5} } } {}

16 1 41 5 .

There are no common factors to divide out.

16 1 41 5 = 16 41 1 5 = 656 5 = 131 1 5 size 12{ { {"16"} over {1} } cdot { {"41"} over {5} } = { {"16" cdot "41"} over {1 cdot 5} } = { {"656"} over {5} } ="131" { {1} over {5} } } {}

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9 1 6 12 3 5 size 12{9 { {1} over {6} } cdot "12" { {3} over {5} } } {}

Convert to improper fractions.

9 1 6 = 6 9 + 1 6 = 55 6 size 12{9 { {1} over {6} } = { {6 cdot 9+1} over {6} } = { {"55"} over {6} } } {}

12 3 5 = 5 12 + 3 5 = 63 5 size 12{"12" { {3} over {5} } = { {5 cdot "12"+3} over {5} } = { {"63"} over {5} } } {}

55 11 6 2 63 21 5 1 = 11 21 2 1 = 231 2 = 115 1 2 size 12{ { { { { {5}} { {5}}} cSup { size 8{"11"} } } over { { { {6}}} cSub { size 8{2} } } } cdot { { { { {6}} { {3}}} cSup { size 8{"21"} } } over { { { {5}}} cSub { size 8{1} } } } = { {"11" cdot "21"} over {2 cdot 1} } = { {"231"} over {2} } ="115" { {1} over {2} } } {}

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11 8 4 1 2 3 1 8 = 11 8 9 3 2 1 10 5 3 1 = 11 3 5 8 1 1 = 165 8 = 20 5 8

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Practice set c

Perform the following multiplications. Convert improper fractions to mixed numbers.

2 2 3 2 1 4 size 12{2 { {2} over {3} } cdot 2 { {1} over {4} } } {}

6

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6 2 3 3 3 10 size 12{6 { {2} over {3} } cdot 3 { {3} over {"10"} } } {}

22

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

85 1 2 size 12{"85" { {1} over {2} } } {}

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2 2 5 3 3 4 3 1 3 size 12{2 { {2} over {5} } cdot 3 { {3} over {4} } cdot 3 { {1} over {3} } } {}

30

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Powers and roots of fractions

Sample set d

Find the value of each of the following.

1 6 2 = 1 6 1 6 = 1 1 6 6 = 1 36 size 12{ left ( { {1} over {6} } right ) rSup { size 8{2} } = { {1} over {6} } cdot { {1} over {6} } = { {1 cdot 1} over {6 cdot 6} } = { {1} over {"36"} } } {}

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9 100 size 12{ sqrt { { {9} over {"100"} } } } {} . We’re looking for a number, call it ?, such that when it is squared, 9 100 size 12{ { {9} over {"100"} } } {} is produced.

? 2 = 9 100 size 12{ left (? right ) rSup { size 8{2} } = { {9} over {"100"} } } {}

We know that

3 2 = 9 size 12{3 rSup { size 8{2} } =9} {} and 10 2 = 100 size 12{"10" rSup { size 8{2} } ="100"} {}

We’ll try 3 10 size 12{ { {3} over {"10"} } } {} . Since

3 10 2 = 3 10 3 10 = 3 3 10 10 = 9 100 size 12{ left ( { {3} over {"10"} } right ) rSup { size 8{2} } = { {3} over {"10"} } cdot { {3} over {"10"} } = { {3 cdot 3} over {"10" cdot "10"} } = { {9} over {"100"} } } {}

9 100 = 3 10 size 12{ sqrt { { {9} over {"100"} } ={}} { {3} over {"10"} } } {}

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4 2 5 100 121 size 12{4 { {2} over {5} } cdot sqrt { { {"100"} over {"121"} } } } {}

22 2 5 1 10 2 11 1 = 2 2 1 1 = 4 1 = 4 size 12{ { { { { {2}} { {2}}} cSup { size 8{2} } } over { { { {5}}} cSub { size 8{1} } } } cdot { { { { {1}} { {0}}} cSup { size 8{2} } } over { { { {1}} { {1}}} cSub { size 8{1} } } } = { {2 cdot 2} over {1 cdot 1} } = { {4} over {1} } =4} {}

4 2 5 100 121 = 4 size 12{4 { {2} over {5} } cdot sqrt { { {"100"} over {"121"} } =4} } {}

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Practice set d

Find the value of each of the following.

1 8 2 size 12{ left ( { {1} over {8} } right ) rSup { size 8{2} } } {}

1 64

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3 10 2 size 12{ left ( { {3} over {"10"} } right ) rSup { size 8{2} } } {}

9 100

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4 9 size 12{ sqrt { { {4} over {9} } } } {}

2 3

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

1 2

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3 8 1 9 size 12{ { {3} over {8} } cdot sqrt { { {1} over {9} } } } {}

1 8

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9 1 3 81 100 size 12{9 { {1} over {3} } cdot sqrt { { {"81"} over {"100"} } } } {}

8 2 5

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2 8 13 169 16 size 12{2 { {8} over {"13"} } cdot sqrt { { {"169"} over {"16"} } } } {}

8 1 2

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Exercises

For the following six problems, use the diagrams to find each of the following parts. Use multiplication to verify your re­sult.

3 4 size 12{ { {3} over {4} } } {} of 1 3 size 12{ { {1} over {3} } } {}

A rectangle divided into twelve parts in a pattern of four rows and three columns.

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

A rectangle divided into twelve parts in a pattern of four rows and three columns. Three of the parts are shaded.

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

A rectangle divided into twelve parts in a pattern of three rows and four columns.

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2 7 size 12{ { {2} over {7} } } {} of 7 8 size 12{ { {7} over {8} } } {}

A rectangle divided into fifty-six parts in a pattern of seven rows and eight columns.

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

A rectangle divided into fifty-six parts in a pattern of seven rows and eight columns. Fourteen of the parts are shaded.

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5 6 size 12{ { {5} over {6} } } {} of 3 4 size 12{ { {3} over {4} } } {}

A rectangle divided into twenty-four parts in a pattern of six rows and four columns.

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1 8 size 12{ { {1} over {8} } } {} of 1 8 size 12{ { {1} over {8} } } {}

A rectangle divided into sixty-four parts in a pattern of eight rows and eight columns.

1 64 size 12{ { {1} over {"64"} } } {}

A rectangle divided into sixty-four parts in a pattern of eight rows and eight columns. One part is shaded.

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7 12 size 12{ { {7} over {"12"} } } {} of 6 7 size 12{ { {6} over {7} } } {}

A rectangle divided into eighty-four parts in a pattern of twelve rows and seven columns.

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For the following problems, find each part without using a diagram.

1 2 size 12{ { {1} over {2} } } {} of 4 5 size 12{ { {4} over {5} } } {}

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

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3 5 size 12{ { {3} over {5} } } {} of 5 12 size 12{ { {5} over {"12"} } } {}

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1 4 size 12{ { {1} over {4} } } {} of 8 9 size 12{ { {8} over {9} } } {}

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

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3 16 size 12{ { {3} over {"16"} } } {} of 12 15 size 12{ { {"12"} over {"15"} } } {}

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2 9  of  6 5 size 12{ { {2} over {9} } "of" { {6} over {5} } } {}

4 15 size 12{ { {4} over {"15"} } } {}

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1 8  of  3 8 size 12{ { {1} over {8} } ital "of" { {3} over {8} } } {}

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2 3  of  9 10 size 12{ { {2} over {3} } ital "of" { {9} over {"10"} } } {}

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

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18 19  of  38 54 size 12{ { {"18"} over {"19"} } ital "of" { {"38"} over {"54"} } } {}

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5 6  of  2 2 5 size 12{ { {5} over {6} } ital "of"2 { {2} over {5} } } {}

2 size 12{2} {}

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3 4  of  3 3 5 size 12{ { {3} over {4} } ital "of"3 { {3} over {5} } } {}

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3 2  of  2 2 9 size 12{ { {3} over {2} } ital "of"2 { {2} over {9} } } {}

10 3  or  3 1 3 size 12{ { {"10"} over {3} } " or "3 { {1} over {3} } } {}

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15 4  of  4 4 5 size 12{ { {"15"} over {4} } ital "of"4 { {4} over {5} } } {}

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5 1 3  of  9 3 4 size 12{5 { {1} over {3} } ital "of"9 { {3} over {4} } } {}

52

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1 13 15  of  8 3 4 size 12{1 { {"13"} over {"15"} } ital "of"8 { {3} over {4} } } {}

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8 9  of  3 4  of  2 3 size 12{ { {8} over {9} } ital "of" { {3} over {4} } ital "of" { {2} over {3} } } {}

4 9 size 12{ { {4} over {9} } } {}

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1 6 of 12 13 of 26 36 size 12{ { {1} over {6} } " of " { {"12"} over {"13"} } " of " { {"26"} over {"36"} } } {}

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1 2 of 1 3 of 1 4 size 12{ { {1} over {2} } " of " { {1} over {3} } " of " { {1} over {4} } } {}

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

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1 3 7 of 5 1 5 of 8 1 3 size 12{1 { {3} over {7} } " of 5" { {1} over {5} } " of 8" { {1} over {3} } } {}

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2 4 5 of 5 5 6 of 7 5 7 size 12{2 { {4} over {5} } " of 5" { {5} over {6} } " of 7" { {5} over {7} } } {}

126

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For the following problems, find the products. Be sure to reduce.

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

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

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

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3 4 3 8 size 12{ { {3} over {4} } cdot { {3} over {8} } } {}

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2 5 5 6 size 12{ { {2} over {5} } cdot { {5} over {6} } } {}

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

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

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5 6 14 15 size 12{ { {5} over {6} } cdot { {"14"} over {"15"} } } {}

7 9 size 12{ { {7} over {9} } } {}

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4 7 7 4 size 12{ { {4} over {7} } cdot { {7} over {4} } } {}

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3 11 11 3 size 12{ { {3} over {"11"} } cdot { {"11"} over {3} } } {}

1

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9 16 20 27 size 12{ { {9} over {"16"} } cdot { {"20"} over {"27"} } } {}

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35 36 48 55 size 12{ { {"35"} over {"36"} } cdot { {"48"} over {"55"} } } {}

28 33 size 12{ { {"28"} over {"33"} } } {}

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21 25 15 14 size 12{ { {"21"} over {"25"} } cdot { {"15"} over {"14"} } } {}

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76 99 66 38 size 12{ { {"76"} over {"99"} } cdot { {"66"} over {"38"} } } {}

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

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3 7 14 18 6 2 size 12{ { {3} over {7} } cdot { {"14"} over {"18"} } cdot { {6} over {2} } } {}

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4 15 10 3 27 2 size 12{ { {4} over {"15"} } cdot { {"10"} over {3} } cdot { {"27"} over {2} } } {}

12

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14 15 21 28 45 7 size 12{ { {"14"} over {"15"} } cdot { {"21"} over {"28"} } cdot { {"45"} over {7} } } {}

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8 3 15 4 16 21 size 12{ { {8} over {3} } cdot { {"15"} over {4} } cdot { {"16"} over {"21"} } } {}

7 13 21 or 160 21 size 12{7 { {"13"} over {"21"} } " or " { {"160"} over {"21"} } } {}

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18 14 21 35 36 7 size 12{ { {"18"} over {"14"} } cdot { {"21"} over {"35"} } cdot { {"36"} over {7} } } {}

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3 5 20 size 12{ { {3} over {5} } cdot "20"} {}

12

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8 9 18 size 12{ { {8} over {9} } cdot "18"} {}

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6 11 33 size 12{ { {6} over {"11"} } cdot "33"} {}

18

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18 19 38 size 12{ { {"18"} over {"19"} } cdot "38"} {}

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5 6 10 size 12{ { {5} over {6} } cdot "10"} {}

25 3 or 8 1 3 size 12{ { {"25"} over {3} } " or 8" { {1} over {3} } } {}

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1 9 3 size 12{ { {1} over {9} } cdot 3} {}

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5 3 8 size 12{5 cdot { {3} over {8} } } {}

15 8 =1 7 8 size 12{ { {"15"} over {8} } "=1" { {7} over {8} } } {}

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16 1 4 size 12{"16" cdot { {1} over {4} } } {}

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

6

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3 8 24 2 3 size 12{ { {3} over {8} } cdot "24" cdot { {2} over {3} } } {}

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5 18 10 2 5 size 12{ { {5} over {"18"} } cdot "10" cdot { {2} over {5} } } {}

10 9 =1 1 9 size 12{ { {"10"} over {9} } "=1" { {1} over {9} } } {}

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16 15 50 3 10 size 12{ { {"16"} over {"15"} } cdot "50" cdot { {3} over {"10"} } } {}

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5 1 3 27 32 size 12{5 { {1} over {3} } cdot { {"27"} over {"32"} } } {}

9 2 =4 1 2 size 12{ { {9} over {2} } "=4" { {1} over {2} } } {}

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2 6 7 5 3 5 size 12{2 { {6} over {7} } cdot 5 { {3} over {5} } } {}

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6 1 4 2 4 15 size 12{6 { {1} over {4} } cdot 2 { {4} over {"15"} } } {}

85 6 =14 1 6 size 12{ { {"85"} over {6} } "=14" { {1} over {6} } } {}

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9 1 3 9 16 1 1 3 size 12{9 { {1} over {3} } cdot { {9} over {"16"} } cdot 1 { {1} over {3} } } {}

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3 5 9 1 13 14 10 1 2 size 12{3 { {5} over {9} } cdot 1 { {"13"} over {"14"} } cdot "10" { {1} over {2} } } {}

72

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20 1 4 8 2 3 16 4 5 size 12{"20" { {1} over {4} } cdot 8 { {2} over {3} } cdot "16" { {4} over {5} } } {}

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2 3 2 size 12{ left ( { {2} over {3} } right ) rSup { size 8{2} } } {}

4 9 size 12{ { {4} over {9} } } {}

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3 8 2 size 12{ left ( { {3} over {8} } right ) rSup { size 8{2} } } {}

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2 11 2 size 12{ left ( { {2} over {"11"} } right ) rSup { size 8{2} } } {}

4 121 size 12{ { {4} over {"121"} } } {}

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8 9 2 size 12{ left ( { {8} over {9} } right ) rSup { size 8{2} } } {}

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1 2 2 size 12{ left ( { {1} over {2} } right ) rSup { size 8{2} } } {}

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

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3 5 2 20 3 size 12{ left ( { {3} over {5} } right ) rSup { size 8{2} } cdot { {"20"} over {3} } } {}

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1 4 2 16 15 size 12{ left ( { {1} over {4} } right ) rSup { size 8{2} } cdot { {"16"} over {"15"} } } {}

1 15 size 12{ { {1} over {"15"} } } {}

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1 2 2 8 9 size 12{ left ( { {1} over {2} } right ) rSup { size 8{2} } cdot { {8} over {9} } } {}

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1 2 2 2 5 2 size 12{ left ( { {1} over {2} } right ) rSup { size 8{2} } cdot left ( { {2} over {5} } right ) rSup { size 8{2} } } {}

1 25 size 12{ { {1} over {"25"} } } {}

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3 7 2 1 9 2 size 12{ left ( { {3} over {7} } right ) rSup { size 8{2} } cdot left ( { {1} over {9} } right ) rSup { size 8{2} } } {}

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For the following problems, find each value. Reduce answers to lowest terms or convert to mixed numbers.

4 9 size 12{ sqrt { { {4} over {9} } } } {}

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

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16 25 size 12{ sqrt { { {"16"} over {"25"} } } } {}

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81 121 size 12{ sqrt { { {"81"} over {"121"} } } } {}

9 11 size 12{ { {9} over {"11"} } } {}

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36 49 size 12{ sqrt { { {"36"} over {"49"} } } } {}

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144 25 size 12{ sqrt { { {"144"} over {"25"} } } } {}

12 5 = 2 2 5 size 12{ { {"12"} over {5} } =2 { {2} over {5} } } {}

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2 3 9 16 size 12{ { {2} over {3} } cdot sqrt { { {9} over {"16"} } } } {}

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3 5 25 81 size 12{ { {3} over {5} } cdot sqrt { { {"25"} over {"81"} } } } {}

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

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8 5 2 25 64 size 12{ left ( { {8} over {5} } right ) rSup { size 8{2} } cdot sqrt { { {"25"} over {"64"} } } } {}

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1 3 4 2 4 49 size 12{ left (1 { {3} over {4} } right ) rSup { size 8{2} } cdot sqrt { { {4} over {"49"} } } } {}

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

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2 2 3 2 36 49 64 81 size 12{ left (2 { {2} over {3} } right ) rSup { size 8{2} } cdot sqrt { { {"36"} over {"49"} } } cdot sqrt { { {"64"} over {"81"} } } } {}

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Exercises for review

( [link] ) How many thousands in 342,810?

2

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( [link] ) Find the sum of 22, 42, and 101.

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( [link] ) Is 634,281 divisible by 3?

yes

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( [link] ) Is the whole number 51 prime or composite?

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( [link] ) Reduce 36 150 size 12{ { {"36"} over {"150"} } } {} to lowest terms.

6 25 size 12{ { {6} over {"25"} } } {}

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Questions & Answers

what is biology
Hajah Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
what is biology
Victoria Reply
HOW CAN MAN ORGAN FUNCTION
Alfred Reply
the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza 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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