FRACTIONS

Fraction could be written as P/Q,

where P is numerator

and Q is denominator.

Created by Inna Shapiro ©2007

Problem 1

• John put into his wallet 4/5 of his money, and then the remaining $12. How much money does he have?

Answer

• 1/5 of his money is $12.

• The whole amount is

12*5=60

• John has $60 in his wallet.

Problem 2

• Paul and Bill took equal loans.

• Paul paid 7/8 of his loan, and Bill paid 8/9.

• Who paid more?

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.

Problem 3

• Compare two fractions:

• 48/49 and 49/50

Answer

• 1-48/49=1/49

• 1-49/50=1/50

• 1/49>1/50=>

• 48/49<49/50

Problem 4

• Can you write two fractions, so that each is more than 3/7 and less than 4/7?

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

Problem 5

• How many irreducible fractions can you write with denominator 53?

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.

Problem 6

• How many irreducible fractions can you write with denominator 55?

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.

Problem 7

• Water volume increases by 1/9 when it is frozen.

• How does ice volume decrease when ice is melted?.

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.

Problem 8

• Ann has 2/3 meters of a rope.

• How she can cut ½ meters if she does not have a ruler?

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)

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

Answer

• 0.125=1/8• Each fraction

appears twice except 5/13

• We can exclude 5/13

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

Answer

We can rewrite a table

3/15 4/15 9/15

1/15 2/15 4/15

7/15 1/3 8/15

=>

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

=>