Answer to Question #205888 in Algebra for Sadisha janith

Question

1. Mr.Steve has 120 pastel sticks and 30 pieces of paper to give to his students.

a) Calculate the largest number of students he can have in his class so that each student gets equal number of pastel sticks and equal number of paper.

b) Briefly explain the technique you used to solve (a).

2. Maya is making a game board that is 16 inches by 24 inches. She wants to use square tiles. Calculate metrics of the largest tile she can use?

Answer 1

(1)Solution:

(a) No of pastel sticks = 120

No of pieces of papers = 30

1.To find the largest no students o that each student gets equal number of pastel sticks and equal number of paper we need to find out the GCF of 120 and 30.

Now to find the GCF we need

To find the prime factor of the 120 and 30

120 = 2 x 2 x 2 x 3 x 5

30 = 2 x 3 x 5

2.Multiply those factors both numbers have in common

There is one 2, one 3 and one 5 is common

So GCF(120,30) = 2 x 3 x 5 = 30

Answer: So Mr Steve can have 30 students in the class so that each student can get equal number of pastel sticks and piece of paper.

(b) When we need to equally distribute two or more set of items into the largest group we have to find the GCF(the Greatest Common Factor).

To find the Greatest Common Factor we need to follow the two steps.

1.Find the prime factor of the numbers

2.Multiply those factors which all numbers have in common.

-------------------------------------------------

(2)

The task is to divide the game board into equal square cells of maximum size. It is clear that the side of such a cell should be a whole divisor of both 16 and 24 inches. A suitable number is the largest integer divisor of these numbers, that is, 8. Thus, the game board contains only 6 square cells measuring 8x8 inches. 2 rows on the side of 16 inches and 3 columns on the side of 24 inches.

Answer: Maya can use the largest tile of dimension 8x8 inches.