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The ideas in this lesson are taken from Math Mammoth Percent book.


Percent

The concepts and ideas of this lesson are also explained in this video:


Percent (or per cent) means one hundredth.
The symbol for percent is  %.

Therefore, 1% means 1/100 or one hundredth,
and 7% means 7/100 or seven hundredths.

The words “per cent” actually mean “per hundred” in Latin.          

Since percentages are just hundredth parts, we can very easily write them as fractions and as decimals.

 

63%  =  

63

100

  =  0.63
  9%  =  

9

100

  =  0.09

1. Write the shaded part and the unshaded part as fractions, as decimals, and as percentages.

a.

Shaded
  =  _____ = _____%

Unshaded

   =  _____ = _____% 
b.

Shaded

  =  _____ = _____%

Unshaded

   =  _____ = _____%

2. Write as percentages, fractions, and decimals.

a. 28%  =  

28

100

  =  0.28
b. 17%  =      =  _____
c.-f. [available in the book]

 

3. Typically seven out of every 100 babies born in the River Creek hospital have a birth
   defect, most of them minor defects.

    a. What typical percentage of the babies have birth defects?
 

    b. What typical percentage of the babies do not have birth defects?
 

    c. About how many babies with birth defects would you expect to find
    in a group of 500 babies?


Other fractions as percents

What part of the pencils are short?

Two out of five, or 2/5 of them are short.

 

Let’s rewrite 2/5 with a denominator of 100
using the method for equivalent fractions:

20

2

5

=

40

100


20

  Now we can write 40/100 as 40%.
So 40% of the pencils are short.

4. Write what part of the pencils are short, both as a fraction and as a percentage.
    Use equivalent fractions.

 

a.      =   

      

100

  =  ____%

b.      =   

      

100

  =  ____%
[available in the book]

5. Convert the fractions into equivalent fractions with denominator 100, and write
    them as percentages.

a.   

4

10

  =   

      

100

  =  _____%
b.   

11

20

  =   

      

100

  =  _____%
c. [available in the book]

6. Write what part of the rectangle is shaded and what part is unshaded,
    both as fractions and percentages.

a.     

         Shaded:     =  _____%

 

  Unshaded:     =  _____%

b    

         Shaded:     =  _____%

 

  Unshaded:     =  _____%

c.  [available in the book]


Percentages that are more than 100%

The image shows 1 whole and 55/100. As a mixed number,
we write 1 55/100. As a decimal, we write 1.55.

Since 55/100 is 55%, and one whole is 100%, the image shows 155%.

So we can use percentages that are more than 100%. Just remember that 100% is 1, and 1% is 0.01.

 

200%  =  

200

100

  = 2
  308%  =  

308

100

  =  3.08

7. Write as fractions, decimals, and percentages.

a.   

      

100

  =  _____ = _____%

b.   

      

100

  =  _____ = _____%
c. [available in the book]

8. Write as percentages, fractions, and decimals.

a. 105%  =     =   ______
b. 457%  =     =  ______
c.-f.[available in the book]

9. Write the fractions as percentages.

    a. About 4/5 ( _______ %) of the United States population is 14 years old or older.

    b. About 2/25 ( _______ %)  of the world’s population lives in North America.

    c. The continent of Africa covers about 1/5 ( _______ %) of the Earth’s total land mass.

10. Two trees are growing in Sandy’s front yard. The taller one is 5/4 as tall
    as the shorter one.

    a. Write the second sentence using a percent instead of a fraction.

 

    b. If the shorter tree is 160 cm tall, how tall is the taller tree?


Change any fraction to a percentage

To write 1/7 as a percentage, you can either:

  • Divide 1 by 7 using long division or a calculator. You will get
    a decimal number. Express that as a percentage. OR,
  • Find 1/7 of 100%; in other words divide 100 by 7.
    Then your answer is already a percentage.

Dividing 100 by 7, we get 14.28...
Rounded to the nearest whole percent, that is 14%.

How many percent would 2/7 be?
How about 5/7?

 
0 1 4 . 2 8

)

1 0 0 . 0 0 
     7
   3 0
 

 

 - 2 8
          2 0
        - 1 4
   

6 0

   

 - 5 6

   

4

 

11. Write the fractions as percentages. Use long division. Round your
    answers to the nearest percent.

a.      =  ______%

b.      =  ______%
[available in the book]

12. Write the fractions as percentages. Round the answers to
    the nearest percent.

    a. About 1/20 ( _________ %) of the population of India is 65 years old or older.
   (2009 estimate)

    b. About 13/100 ( ________ %) of the population of Australia is 65 years old or older
    (2009 estimate)

    c. [available in the book]

    d. [available in the book]

13. Write as a percentage. Round your answers to the nearest percent.

      a. 8/7   

      b. 1 3/8 

How many percent of
each figure is colored?
 

a.

b. [available
in the book]

 c. [available
in the book]


The ideas in this lesson are taken from Math Mammoth Percent book.


See also these lessons:

Percent of a number using mental math
How to find a percentage of a number using decimals
"What percentage..." / "How many percent...?"

Generate free percent worksheets:

Percent/decimal worksheets
Percent of number (simple)
Percentages/percent word problems


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Practice makes perfect. Practice math at IXL.com



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