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Mathematics Magazine for Grades 1-12  

 

Grade 6  
 

 

  

Theory:

Fractions & Decimals


This is the set of all numbers that have fractional or decimal values, positive or negative, that do not equal a whole value.Here are some examples: -3.1, 0.25, , -1.5, ,4.222222…,0.78

Solutions from the Previous Issue:

Washington State Math Olympiad problems

1.        Robin ate some peanuts on Sunday. On Monday she ate 2 more peanuts than on Sunday. On Tuesday, Wednesday, Thursday, Friday, and Saturday she ate 2 more peanuts than the day before. By Saturday night she had eaten 77 peanuts in the whole week. How many peanuts did Robin eat on Wednesday?

Solution:

WORKING BACKWARDS

All the "added" peanuts (2 more every day after Sunday) add up to 42 peanuts (2 + 4 + 6 + 8 + 10 + 12).

Subtracting those 42 added peanuts from 77 gives me 35 peanuts (77 - 42). These 35 peanuts were spread out over 7 days, so the number she ate on Sunday must be a factor of 35.

Since she ate the 35 peanuts over 7 days, she must have eaten 5 (35/7) peanuts each day, plus all the "added" peanuts (42).

So she started on Sunday with 5 peanuts. Since she ate 6 more than this on Wednesday, she ate 6 + 5 = 11 peanuts on Wednesday.

MAKE A TABLE
The following table shows the patterns.
The correct column is the middle column
where Robin begins with 5 peanuts.
The correct answer is 11 peanuts
eaten on Wednesday.

Sun

4

5

6

Mon

6

7

8

Tues

8

9

10

Wed

10

11

12

Thurs

12

13

14

Fri

14

15

16

Sat

16

17

18

TOTAL

70

77

84

<--Starting values

 

 

2.        Calculate: [(-520  518) (-1)1995-(-18) 32] (-3)3

Solution:

[(-520  518) (-1)1995-  (-18) 32] (-3)3  = [(-52 ) (-1)1995-(-2)] (-3)3

= [(-52 ) (-1) + 2] (-3)3 = (52  + 2) (-3)3 = (27) (-3)3 = -1

Proposed Exercises:

Calculate:

1.        (777 –77 –7) ∙ (777 – 77 + 7) =

2.        {24 +[16 –(28 - 75 25) 5] 3} 19 =

3.        484 – {1992 + [(80 - 80 40) ∙ 36 ∙15] 72} 12 =

 
 
 

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