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The fraction 3 4 size 12{ { {3} over {4} } } {} can be raised to 24 32 size 12{ { {"24"} over {"32"} } } {} by multiplying both the numerator and denominator by 8.

Three fourths equals three times eight, over four time eight, which is equal to twenty-four over thirty-two. Notice that eight over eight is equal to 1.

Most often, we will want to convert a given fraction to an equivalent fraction with a higher specified denominator. For example, we may wish to convert 5 8 size 12{ { {5} over {8} } } {} to an equivalent fraction that has denominator 32, that is,

5 8 = ? 32 size 12{ { {5} over {8} } = { {?} over {"32"} } } {}

This is possible to do because we know the process. We must multiply both the numerator and denominator of 5 8 size 12{ { {5} over {8} } } {} by the same nonzero whole number in order to 8 obtain an equivalent fraction.

We have some information. The denominator 8 was raised to 32 by multiplying it by some nonzero whole number. Division will give us the proper factor. Divide the original denominator into the new denominator.

32 ÷ 8 = 4 size 12{"32 " div " 8 "=" 4"} {}

Now, multiply the numerator 5 by 4.

5 4 = 20 size 12{"5 " cdot "4 "=" 20"} {}

Thus,

5 8 = 5 4 8 4 = 20 32 size 12{ { {5} over {8} } = { {5 cdot 4} over {8 cdot 4} } = { {"20"} over {"32"} } } {}

So,

5 8 = 20 32 size 12{ { {5} over {8} } = { {"20"} over {"32"} } } {}

Sample set d

Determine the missing numerator or denominator.

3 7 = ? 35 size 12{ { {3} over {7} } = { {?} over {"35"} } } {} . Divide the original denominator into the new denominator.

35 ÷ 7 = 5 size 12{"35"¸7=5} {} The quotient is 5. Multiply the original numerator by 5.

3 7 = 3 5 7 5 = 15 35 size 12{ { {3} over {7} } = { {3 cdot 5} over {7 cdot 5} } = { {"15"} over {"35"} } } {} The missing numerator is 15.

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5 6 = 45 ? size 12{ { {5} over {6} } = { {"45"} over {?} } } {} . Divide the original numerator into the new numerator.

45 ÷ 5 = 9 size 12{"45"¸5=9} {} The quotient is 9. Multiply the original denominator by 9.

5 6 = 5 9 6 9 = 45 54 size 12{ { {5} over {6} } = { {5 cdot 9} over {6 cdot 9} } = { {"45"} over {"54"} } } {} The missing denominator is 45.

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Practice set d

Determine the missing numerator or denominator.

4 5 = ? 40 size 12{ { {4} over {5} } = { {?} over {"40"} } } {}

32

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3 7 = ? 28 size 12{ { {3} over {7} } = { {?} over {"28"} } } {}

12

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1 6 = ? 24 size 12{ { {1} over {6} } = { {?} over {"24"} } } {}

4

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3 10 = 45 ? size 12{ { {3} over {"10"} } = { {"45"} over {?} } } {}

150

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8 15 = ? 165 size 12{ { {8} over {"15"} } = { {?} over {"165"} } } {}

88

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Exercises

For the following problems, determine if the pairs of fractions are equivalent.

1 2 , 5 10 size 12{ { {1} over {2} } , { {5} over {"10"} } } {}

equivalent

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

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5 12 , 10 24 size 12{ { {5} over {"12"} } , { {"10"} over {"24"} } } {}

equivalent

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

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3 5 , 12 15 size 12{ { {3} over {5} } , { {"12"} over {"15"} } } {}

not equivalent

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1 6 , 7 42 size 12{ { {1} over {6} } , { {7} over {"42"} } } {}

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16 25 , 49 75 size 12{ { {"16"} over {"25"} } , { {"49"} over {"75"} } } {}

not equivalent

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5 28 , 20 112 size 12{ { {5} over {"28"} } , { {"20"} over {"112"} } } {}

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3 10 , 36 110 size 12{ { {3} over {"10"} } , { {"36"} over {"110"} } } {}

not equivalent

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6 10 , 18 32 size 12{ { {6} over {"10"} } , { {"18"} over {"32"} } } {}

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5 8 , 15 24 size 12{ { {5} over {8} } , { {"15"} over {"24"} } } {}

equivalent

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10 16 , 15 24 size 12{ { {"10"} over {"16"} } , { {"15"} over {"24"} } } {}

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4 5 , 3 4 size 12{ { {4} over {5} } , { {3} over {4} } } {}

not equivalent

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5 7 , 15 21 size 12{ { {5} over {7} } , { {"15"} over {"21"} } } {}

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

not equivalent

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For the following problems, determine the missing numerator or denominator.

1 3 = ? 12 size 12{ { {1} over {3} } = { {?} over {"12"} } } {}

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1 5 = ? 30 size 12{ { {1} over {5} } = { {?} over {"30"} } } {}

6

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2 3 = ? 9 size 12{ { {2} over {3} } = { {?} over {9} } } {}

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1 5 = ? 30 size 12{ { {1} over {5} } = { {?} over {"30"} } } {}

12

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5 6 = ? 18 size 12{ { {5} over {6} } = { {?} over {"18"} } } {}

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4 5 = ? 25 size 12{ { {4} over {5} } = { {?} over {"25"} } } {}

20

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1 2 = 4 ? size 12{ { {1} over {2} } = { {4} over {?} } } {}

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9 25 = 27 ? size 12{ { {9} over {"25"} } = { {"27"} over {?} } } {}

75

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3 2 = 18 ? size 12{ { {3} over {2} } = { {"18"} over {?} } } {}

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5 3 = 80 ? size 12{ { {5} over {3} } = { {"80"} over {?} } } {}

48

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1 8 = 3 ? size 12{ { {1} over {8} } = { {3} over {?} } } {}

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4 5 = ? 100 size 12{ { {4} over {5} } = { {?} over {"100"} } } {}

80

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1 2 = 25 ? size 12{ { {1} over {2} } = { {"25"} over {?} } } {}

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3 16 = ? 96 size 12{ { {3} over {"16"} } = { {?} over {"96"} } } {}

18

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15 16 = 225 ? size 12{ { {"15"} over {"16"} } = { {"225"} over {?} } } {}

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11 12 = ? 168 size 12{ { {"11"} over {"12"} } = { {?} over {"168"} } } {}

154

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9 13 = ? 286 size 12{ { {9} over {"13"} } = { {?} over {"286"} } } {}

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32 33 = ? 1518 size 12{ { {"32"} over {"33"} } = { {?} over {"1518"} } } {}

1,472

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19 20 = 1045 ? size 12{ { {"19"} over {"20"} } = { {"1045"} over {?} } } {}

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37 50 = 1369 ? size 12{ { {"37"} over {"50"} } = { {"1369"} over {?} } } {}

1,850

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For the following problems, reduce, if possible, each of the fractions to lowest terms.

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

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

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

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

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6 14 size 12{ { {6} over {"14"} } } {}

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

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

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4 14 size 12{ { {4} over {"14"} } } {}

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

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1 6 size 12{ { {1} over {6} } } {}

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4 6 size 12{ { {4} over {6} } } {}

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

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18 14 size 12{ { {"18"} over {"14"} } } {}

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20 8 size 12{ { {"20"} over {8} } } {}

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

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4 6 size 12{ { {4} over {6} } } {}

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

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

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6 14 size 12{ { {6} over {"14"} } } {}

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14 6 size 12{ { {"14"} over {6} } } {}

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

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

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16 70 size 12{ { {"16"} over {"70"} } } {}

8 35 size 12{ { {8} over {"35"} } } {}

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40 60 size 12{ { {"40"} over {"60"} } } {}

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

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

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32 28 size 12{ { {"32"} over {"28"} } } {}

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36 10 size 12{ { {"36"} over {"10"} } } {}

18 5 size 12{ { {"18"} over {5} } } {}

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36 60 size 12{ { {"36"} over {"60"} } } {}

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

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

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18 27 size 12{ { {"18"} over {"27"} } } {}

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18 24 size 12{ { {"18"} over {"24"} } } {}

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

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32 40 size 12{ { {"32"} over {"40"} } } {}

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11 22 size 12{ { {"11"} over {"22"} } } {}

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

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27 81 size 12{ { {"27"} over {"81"} } } {}

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17 51 size 12{ { {"17"} over {"51"} } } {}

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

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16 42 size 12{ { {"16"} over {"42"} } } {}

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39 13 size 12{ { {"39"} over {"13"} } } {}

3

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44 11 size 12{ { {"44"} over {"11"} } } {}

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66 33 size 12{ { {"66"} over {"33"} } } {}

2

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

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

already reduced

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15 40 size 12{ { {"15"} over {"40"} } } {}

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36 100 size 12{ { {"36"} over {"100"} } } {}

9 25 size 12{ { {9} over {"25"} } } {}

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45 32 size 12{ { {"45"} over {"32"} } } {}

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30 75 size 12{ { {"30"} over {"75"} } } {}

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

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121 132 size 12{ { {"121"} over {"132"} } } {}

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72 64 size 12{ { {"72"} over {"64"} } } {}

9 8 size 12{ { {9} over {8} } } {}

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30 105 size 12{ { {"30"} over {"105"} } } {}

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46 60 size 12{ { {"46"} over {"60"} } } {}

23 30 size 12{ { {"23"} over {"30"} } } {}

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75 45 size 12{ { {"75"} over {"45"} } } {}

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40 18 size 12{ { {"40"} over {"18"} } } {}

20 9 size 12{ { {"20"} over {9} } } {}

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108 76 size 12{ { {"108"} over {"76"} } } {}

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7 21 size 12{ { {7} over {"21"} } } {}

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

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6 51 size 12{ { {6} over {"51"} } } {}

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

17 4 size 12{ { {"17"} over {4} } } {}

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8 100 size 12{ { {8} over {"100"} } } {}

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51 54 size 12{ { {"51"} over {"54"} } } {}

17 18 size 12{ { {"17"} over {"18"} } } {}

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A ream of paper contains 500 sheets. What frac­tion of a ream of paper is 200 sheets? Be sure to reduce.

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There are 24 hours in a day. What fraction of a day is 14 hours?

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

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A full box contains 80 calculators. How many calculators are in 1 4 size 12{ { {1} over {4} } } {} of a box?

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There are 48 plants per flat. How many plants are there in 1 3 size 12{ { {1} over {3} } } {} of a flat?

16

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A person making $18,000 per year must pay $3,960 in income tax. What fraction of this per­son's yearly salary goes to the IRS?

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For the following problems, find the mistake.

3 24 = 3 3 8 = 0 8 = 0 size 12{ { {3} over {"24"} } = { { { {3}}} over { { {3}} cdot 8} } = { {0} over {8} } =0} {}

Should be 1 8 size 12{ { {1} over {8} } } {} ; the cancellation is division, so the numerator should be 1.

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8 10 = 2 + 6 2 + 8 = 6 8 = 3 4 size 12{ { {8} over {"10"} } = { { { {2}}+6} over { { {2}}+8} } = { {6} over {8} } = { {3} over {4} } } {}

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

Cancel factors only, not addends; 7 15 size 12{ { {7} over {"15"} } } {} is already reduced.

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6 7 = 5 + 1 5 + 2 = 1 2 size 12{ { {6} over {7} } = { { { {5}}+1} over { { {5}}+2} } = { {1} over {2} } } {}

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9 9 = 0 0 = 0 size 12{ { { { {9}}} over { { {9}}} } = { {0} over {0} } =0} {}

Same as [link] ; answer is 1 1 size 12{ { {1} over {1} } } {} or 1.

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Exercises for review

( [link] ) Round 816 to the nearest thousand.

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( [link] ) Perform the division: 0 ÷ 6 size 12{0 div 6} {} .

0

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( [link] ) Find all the factors of 24.

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( [link] ) Find the greatest common factor of 12 and 18.

6

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( [link] ) Convert 15 8 size 12{ { {"15"} over {8} } } {} to a mixed number.

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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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