fractions fraction could be written as p/q, where p is numerator and q is denominator. created by...
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![Page 1: FRACTIONS Fraction could be written as P/Q, where P is numerator and Q is denominator. Created by Inna Shapiro ©2007](https://reader034.vdocument.in/reader034/viewer/2022051515/55148889550346b0158b5bbf/html5/thumbnails/1.jpg)
FRACTIONS
Fraction could be written as P/Q,
where P is numerator
and Q is denominator.
Created by Inna Shapiro ©2007
![Page 2: FRACTIONS Fraction could be written as P/Q, where P is numerator and Q is denominator. Created by Inna Shapiro ©2007](https://reader034.vdocument.in/reader034/viewer/2022051515/55148889550346b0158b5bbf/html5/thumbnails/2.jpg)
Problem 1
• John put into his wallet 4/5 of his money, and then the remaining $12. How much money does he have?
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Answer
• 1/5 of his money is $12.
• The whole amount is
12*5=60
• John has $60 in his wallet.
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Problem 2
• Paul and Bill took equal loans.
• Paul paid 7/8 of his loan, and Bill paid 8/9.
• Who paid more?
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Answer
• Paul has to pay 1/8, and Bill has to pay 1/9.
• 1/8>1/9, that means Bill already paid more money then Paul.
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Problem 3
• Compare two fractions:
• 48/49 and 49/50
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Answer
• 1-48/49=1/49
• 1-49/50=1/50
• 1/49>1/50=>
• 48/49<49/50
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Problem 4
• Can you write two fractions, so that each is more than 3/7 and less than 4/7?
![Page 9: FRACTIONS Fraction could be written as P/Q, where P is numerator and Q is denominator. Created by Inna Shapiro ©2007](https://reader034.vdocument.in/reader034/viewer/2022051515/55148889550346b0158b5bbf/html5/thumbnails/9.jpg)
Answer
• 3/7=9/21• 4/7=12/21• Now we can easily find• 9/21<10/21<12/21• 9/21<11/21<12/21• One of the answers is:
10/21, 11/21
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Problem 5
• How many irreducible fractions can you write with denominator 53?
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Answer
• 53 is a prime number.• This means that all fractions with
denominator 53 are irreducible.• 1/53, 2/53,…52/53 makes total of 52 different
fractions.
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Problem 6
• How many irreducible fractions can you write with denominator 55?
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Answer
• 55=5*11• This means that 5/55, 10/55, 11/55,
15/55, 20/55, 22/55, 25/55, 30/55, 33/55, 35/55, 40/55, 44/55, and 50/55 could be reduced
• We can write 54 fractions 1/55, 2/55, … 54/55 and 13 could be
reduced.• So we can write 41 irreducible fractions.
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Problem 7
• Water volume increases by 1/9 when it is frozen.
• How does ice volume decrease when ice is melted?.
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Answer
• Let us suppose that the volume of water is equal to 1. When it is frozen we get the volume of ice 1+1/9=10/9
• From the ice with volume 10/9 we receive water with volume 1.
• This means that ice is decreased by 1/9:10/9=1/10 of it’s volume.
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Problem 8
• Ann has 2/3 meters of a rope.
• How she can cut ½ meters if she does not have a ruler?
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Answer
• Ann can bent a rope twice and measure 1/6m.
• Than she can cut 1/6m from 2/3m and get ½m (2/3-1/6=1/2)
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Problem 9
• Find the rule and exclude one number
1/3 1/8 23/7
23/7 4/11 1/3
0.125 5/13 4/11
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Answer
• 0.125=1/8• Each fraction
appears twice except 5/13
• We can exclude 5/13
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Problem 10
• Rearrange fractions in the table so that al vertical, horizontal and diagonal sums would be equal to 1
1/5 2/5 3/5
1/15 2/15 4/15
7/15 1/3 8/15
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Answer
We can rewrite a table
3/15 4/15 9/15
1/15 2/15 4/15
7/15 1/3 8/15
=>
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Answer (continue )
And than rearrange 1, 2, 3, …9 in the magic square
2/15 7/15 6/15
9/15 5/15 1/15
4/15 3/15 8/15
2/15 7/15 2/5
3/5 1/3 1/15
4/15 1/5 8/15
=>