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### Solved Examples

Question 1: Divide 32 into two parts such that the five times the smaller part is equal to three times the bigger part. Assuming the smaller part as x, from an equation. Find both the parts.

Solution:
Let the smaller part be x

Then the greater part  = 32 - x
(Sum of two parts is 32)

Step 1:

The problem states:
Five times the smaller part = Three times the bigger part

=> 5x = 3(32 - x)

Step 2:

Solve for x,

=> 5x = 3(32 - x)

=> 5x = 3 * 32 - 3x

=> 5x = 96 - 3x

=> 5x + 3x = 96

=> 8x = 96

Divide each side by 8

=> $\frac{8x}{8} = \frac{96}{8}$

=> x = 12

Step 3:

The larger part = 32 - 12

= 20

Hence two parts are 12 and 20. answer

Question 2: Perform the indicated operation (5.2 * 103 )(6.2 * 10- 5 ). Express the answer in decimal form.
Solution:
Given (5.2 * 103)(6.2 * 10- 5 )

= (5.2 * 6.2)(103 * 10- 5 )

= 32.24 * 103 + (- 5)

= 32.24 * 103 - 5

= 32.24 * 10- 2
Move the decimal 2 to the left

= .3224

or 0.3224

=> (5.2 * 103)(6.2 * 10- 5 ) =  0.3224. answer

Question 3: Find the LCM of 21 and 35
Solution:
Prime factors of 21 = 3 * 7

Prime factors of 35 = 5 * 7

The LCM of 21 and 35 is 3 * 5 * 7 = 105

or LCM(21, 35) = 105. answer