Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2016 Grade 6 Number Sense
Problem
Solution
1) The sum of four consecutive integers is 74. What is the largest of these numbers? Let N be the largest number.
Then the sum is
    N - 3 +
    N - 2 +
    N - 1 +
    N =         74
Turn this into an equation and solve for N:
    (N - 3) + (N - 2) + (N - 1) + N = 74
    4N - 6 = 74
    4N = 80
    N = 20
    The consecutive integers are 17, 18, 19 and 20.
2) 4/5 + (1+3+5+7)/(1*3*5*7) = ?
(Express your answer as a fraction in lowest terms)		 1. Perform the division = 16/105
2. Convert the fraction to the other fraction's denominator and add = 4/5 = 84/105 + 16/105 = 100/105 = 20/21
3) The average of five numbers is 42. If 4 is added to the first number, 5 is added to the second number, 6 is added to the third number, and so on, what will the new average be? 1. Add the added numbers together = 4 + 5 + 6 + 7 + 8 = 30
2. Take 5 X the average and add this sum to it and divide by 5 =
    (5 x 42 + 30)/5 = (210 + 30)/5 = 240/5 = 48.

4) Lana is reading a book for a class assignment. Yesterday she read 1/6th of the book. Today she read 78 pages and has finished 3/5 of the book. How many pages are left in the book? 1. Compute the difference between 1/6 and 3/5 =
    3/5 - 1/6 = 18/30 - 5/30 = 13/30
2. Compute the total number of pages in the book using the number she read today =
    (13/30) N = 78
    N = (78 X 30)/13 = 180
3. Subtract 1/6 of this and 78 to get the number of pages left in the book = 180 - 180/6 - 78 = 180 - 30 - 78 = 72
5) Complete the diagram by entering fractions in each of the blank squares such that the sum of the entries in each row, column, and diagonal results in the same value.What is the sum of the missing fractions? (Express as an improper fraction in its lowest terms)
1
8		 11
24		 5
12
15
24		1
3		1
24
6
24		5
24		13
24
 1. Convert the 3 fractions on the diagonal to a common denominator and add =

    3/24 + 8/24 + 13/24 = 1
For each row and column, subtract the 2 numbers from 1 to compute the 3rd value:
2. Top row: 1 - 3/24 - 10/24 = 11/24
3. Right column: 1 - 10/24 - 13/24 = 1/24
4. Middle column: 1 - 11/24 - 8/24 = 5/24
5. Bottom row: 1 - 13/24 - 5/24 = 6/24
6. Left column: 1 - 3/24 - 6/24 = 15/24
7. Add these 5 fractions together and reduce =
    11/24 + 15/24 + 1/24 + 6/24 + 5/24 =
    38/24 = 19/12