1. Home
  2. Contemporary math applications
  3. Exam 1
  4. Fractions
  5. Fractions: equivalent fractions

1.3 Fractions: equivalent fractions  (Page 3/3)

<< Chapter < Page
  Contemporary math applications     Page 3 / 3
Chapter >> Page >

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.

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.

Practice set d

Determine the missing numerator or denominator.

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

32

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

12

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

4

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

150

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

88

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

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

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

equivalent

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

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

not equivalent

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

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

not equivalent

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

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

not equivalent

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

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

equivalent

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

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

not equivalent

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

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

not equivalent

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

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

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

6

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

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

12

2 3 = ? 9

3 4 = ? 16

12

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

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

20

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

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

75

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

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

48

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

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

80

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

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

18

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

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

154

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

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

1,472

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

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

1,850

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

3

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

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

2

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

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

already reduced

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

16

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?

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.

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} } } {}

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.

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

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.

Exercises for review

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

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

0

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

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

6

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

Questions & Answers

summarize halerambos & holbon
David Reply
the Three stages of Auguste Comte
Clementina Reply
what are agents of socialization
Antonio Reply
sociology of education
Nuhu Reply
definition of sociology of education
Nuhu
what is culture
Abdulrahim Reply
shared beliefs, values, and practices
AI-Robot
What are the two type of scientific method
ogunniran Reply
I'm willing to join you
Aceng Reply
what are the scientific method of sociology
Man
what is socialization
ogunniran Reply
the process wherein people come to understand societal norms and expectations, to accept society's beliefs, and to be aware of societal values
AI-Robot
scientific method in doing research
ogunniran
defimition of sickness in afica
Anita
Cosmology
ogunniran
Hmmm
ogunniran
list and explain the terms that found in society
REMMY Reply
list and explain the terms that found in society
Mukhtar
what are the agents of socialization
Antonio
Family Peer group Institution
Abdulwajud
I mean the definition
Antonio
ways of perceived deviance indifferent society
Naomi Reply
reasons of joining groups
SAM
to bring development to the nation at large
Hyellafiya
entails of consultative and consensus building from others
Gadama
World first Sociologist?
Abu
What is evolutionary model
Muhammad Reply
Evolution models refer to mathematical and computational representations of the processes involved in biological evolution. These models aim to simulate and understand how species change over time through mechanisms such as natural selection, genetic drift, and mutation. Evolutionary models can be u
faruk
what are the modern trends in religious behaviours
Selekeye Reply
what are social norms
Daniel Reply
shared standards of acceptable behavior by the group or appropriate behavior in a particular institution or those behaviors that are acceptable in a society
Lucius
that is how i understood it
Lucius
examples of societal norms
Diamond
Discuss the characteristics of the research located within positivist and the interpretivist paradigm
Tariro Reply
what is Industrialisation
Selekeye Reply
industrialization
Angelo
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Contemporary math applications' conversation and receive update notifications?

Ask