Interest (I) is an amount of money earned for using another’s money over a period of time.

Formula:          Interest (I) = Principal (P) × Rate of Interest (R) × Time (T)

I = P × R × T

Problem:

Jaypee opens a savings account in National Commercial Bank where the money earns 1.5% interest per year. If he has ₱ 7,500.00 in his account, how much interest will the money earn in one year?

Step 1: What is asked

How much interest will the money in one year.

Step 2: What is the given.

P = ₱ 7,500.00 R

= 1.5% T

= 1 year

I = ?

Step 3: What is the formula.

I = P × R × T

Step 4: Solve

I = P × R × T

= ₱ 7,500 × 1.5% × 1

= ₱ 7,500 × 0.015 × 1

= ₱ 112.50

• Substitute the given.

• Change 1.5% to decimal. Then, multiply

Step 5: Answer what is asked.

The amount of interest the money will earn in one year is ₱ 112.50

Ratio is the spoken language of arithmetic. It is a way of comparing two or more quantities having the same units. The quantities may be separate entities or they may be different parts of a whole. We can right the ratio of ” a”  and ” b ” in three ways:

Word form – a is to b
Colon form –   a:b
Fraction form –  a/b

Problem:
                   Multiply:  2/6 × 3/4

Step 1: Multiply both numerator and denominator

Example: 
                           2/6 × 3/4  = 2×3/ 6×4

Step 2:  Get the common factor of both numerators and denominators

Example:
                          2×3 / 2×3×4

Step 3:  Group them according to their common factor.

Example:
                          2/3 × 3/3 × 1/4

Step 4:  Simplify the numerator and denominator with common factor. Then multiply

Example:
                            1 × 1 × 1/4

Step 5:   Answer
Example: 
                       1/4

Step 6:  Whole computation
Multiply :  2/6 × 3/4

           2/6 × 3/4  =  2×3/6×4
                            = 2 × 3 / 2× 3 × 4
                            = 2/2 × 3/3 × 1/4
                            = 1 × 1 × 1/4
                            = 1/4

In solving the statistics and probability use the formula ” Z= x- μ/σ “. The ” x “ is the value , the ” μ ” is the mean, while the ” σ ” is the standard deviation.

Sample Problem:
              A survey found out that the battery life of a gadget last for 3 years and the standard deviation is 1 year. What is the probability the battery life of gadget will last between 3 and 4 years.


Step 1:  Read and understand the problem.
Step 2:  Identify the variable
               The variable presented by a capital letter ” X “ .

Example:
                      X = Battery life

Step 3: List the given information/ data from the problem.
Example:
                  μ = mean = 3 years
                  x = value  = 3 and 4 years
                 σ = standard deviation  =  1 year
(Noted):
             The mean can be a probability, percentage and chances.

Step 4: Express in symbols what is being asked in the problem.

Example:
                 P( 3 < X < 4 )
(Noted):
              Use the capital letter ” X” because it is normal distribution.

Step 5: Draw the curve
Example:(Noted) :
               In normal distribution the center of the curve is the given mean not zero ( 0 ).

Step 6: Convert the normal distribution into standard normal distribution by computing the ” Z – scores ” use the given formula.

Example:
        Z= x- μ/σ.                       Z= x- μ/σ
          = 3 – 3 ÷ 1                       = 4 – 3 ÷ 1
          = 0 ÷1                              = 1 ÷ 1
          = 0                                   = 1
(Noted) :
           Use two solutions because the problem ask for two possible probability but if not just use one solution.

Step 7: Expressed what is being asked in standard normal symbol.

Example:
            P( 0 < Z < 1 )
( Noted ):
                 Transfer ” X ” into ” Z ” and use the corresponding Z – scores.

Step 8: Draw the standardized normal curved.
Example:

( Noted ) :
           Use zero ( 0 )in the center because it is already standardized.

Step 9: Find the are require needed by finding it in the table of standard normal distribution.

Table
Example:
     P( 0 < Z < 1 )
     = .50000 – .84134
    = .34134 or 34.13%  – convert it to       percentage.

( Noted ) :
           Subtract the smaller number than the bigger number.

Step 10:  Answer the questions.

Example:
      The probability that battery life of gadget will last between 3 and 4 years is 34.13%