Module 1: Visualizes the Concepts of Percents and its Relationship to Fraction and Decimals Identifying Base, Percentage and Rate in a problem

 

Lesson 1: Visualizes the Concepts of Percent and its Relationship to Fractions and Decimals

Percent comes from the Latin term per centum which means “per hundred” or “hundredths”. Thus, percent is the ratio of a number to 100. The symbol is %.

 

Ø  Percent to Fraction

To change a percent to a fraction, remove the percent symbol (%) and write the number as a numerator, then the denominator is 100.

Example:

Percent	Fraction	Simplest form
23%	23 100	23 100
50%	50 100	1 2

 

Ø  Percent to Decimal

To ways to convert a percent to a decimal

First: Write the percent as a fraction, then divide the numerator by the denominator.

Percent	Fraction	Decimal
23%	23                             100	23 ÷ 100 = 0.23
50%	50 100	50 ÷ 100 = 0.5

 

Second: Remove the percent symbol (%), then move the decimal point two places to the left.

Percent	Decimal
18%	0.18
99.9%	0.999

 

Ø  Decimal to Percent

To write a decimal number to Percent form, we may follow the two methods below.

First: Just multiply the decimal number by 100, then affix the % symbol.

Decimal	×100	Percent
0.45	0.45 × 100	45%
3.9	3.9 × 100	390%

 

Second: A shortcut would be moving the decimal point two places to the right and affixing the % symbol.

Decimal	Percent
0.04	4%
0.95	95%

 

Ø  Fraction to Percent

To change a fraction to percent, change into decimal first by dividing the numerator by the denominator. Then move the decimal point two places to the RIGHT and affix the % symbol.

Fraction	Decimal	Percent
3 2	3 ÷ 2 = 1.5	150%
9 25	9 ÷ 25 = 0.36	36%

Activity 1:

Directions: Express the following in percent form. Write your answers before each number.

_______________1. 0.47

_______________2. 0.03

_______________3. 2.06

_______________4.    14
                            100

_______________5.     55

                             100

 

Activity 2:

Directions: Complete the table.

Percent Form	Decimal Form	Fraction Form
64%
	0.56
		3 4
2.25%
	0.4

Activity 3:

Directions: Match the Fractions, decimals and percentages.

1.      8                    0.5                    30%
        10

2.     3                     0.4                    50%

       10

3.     7                    0.3                    40%

       10

4.     4                    0.8                    70%

       10

5.     5                    0.7                    80%

       10
 

Lesson 2: Identifying the Base, Percentage and Rate in a Problem

 

Percentage (or portion) is the variable in the percentage formula that represents a part of the base. The base is the number represents 100% or the total value of something, or the whole thing, the rate defines what part the percentage is the base.

Teehan’s Triangle

 

Percentage, or part of a whole, is on top, meaning  P = R x B

Example:

1.             1. 16% of 60

We should change the rate first to decimal before we apply the formula.

R = 16% = 0.16            B = 60                P= ?

                            

                            P = R x B
                 P = 0.16 x 60
                  P = 9.6

2.               2.  Let us analyze the problem.

Based on the record of Teacher Jhenie, 80% of the 40 Grade 5 pupils always prepared their homework in Math everyday. How any Grade 5 pupils always prepared their homework in Math everyday?

To solve the problem, find out what is 80% of 40 is?

       R = 80% = 0.8                    B = 60                P = ?

                                   

                       P = R x B
                     P = 0.8 x 40
                      P = 32

Therefore, 32 pupils always prepare their homework in Math everyday.

 

Rate, or the number with % symbol beside it, is at the left because  R = P x 100 . Rate is percentage divided by base multiplied by 100.                                                       B

Example:

1.    1.  49 is  n%  of 70

        B = 70                P = 49            R = n

           

                     R = P x 100
                           B 

      

                     R = 49  x 100

                           70   

    

                     R =  0. 7 x 100

                     

                    R = 70%

                             

2.    2. James bought 24 flowers as a birthday present for his mother. Twelve of the flowers are orchids. What percent of the flower are orchids?

  B = 24                P = 12            R = n

R  = 24 x 100

        12      

R = 0.5 x 100

R = 50%               

Therefore, 50% of the flowers are orchids

 

Base, or the whole or total, is at the right because  B = P . Base is percentage divided by rate.
                                                                                        

Example:

1.    1. 30% of  n   is 12

     B = n             P = 12                R = 30% = 0.3

                    

                        B = P
                              R    

                        B = 12

                               0.3

                        B = 40

             

2.    2. A group of pupils was assigned by their teacher to make an essays of studying a stalagmites. Ten of them wrote an essays about it. Find out 25% of what number is 10.

                       B = n              P = 10                 R = 25% = 0.25

             B =  P

                              R    

                        B =   10

                               0.25

                        B =  40

Therefore, there are 40 pupils who explored the cave.

 

Activity 1:

Directions: Using the given values, find the missing numbers. Write your answer on the blank.

1.            1.  R = ___________        B = 465                P = 150

              2.  R = 16%                       B = 280                P = ______

              3.  R = 40%                       B = _______        P = 26

               4. R = 30%                       B = _______        P = 12

               5. R = 30%                       B = 12000            P = _______

5        

Activity 2:

Directions: Identify the base, rate and percentage.

Given	Base	Rate	Percentage
20% of 4295 is 859
16% of 60 is 9.6
Twenty-six is 40% of 65
49 is 70% of 70
60 is 75% of 80

 

Activity 3:

Directions: find the percentage of each number. Write your answer before each number.

_______________1. 5% of 80

_______________2. 25% of 62

_______________3. 6.2% of 44

_______________4. 65% 0f 650

_______________5. 18% of 120

1.