R4 Finding 33 1/3% and 66 2/3%

33 1/3% equals the fraction 1/3.  Therefore, we can

multiply by 1/3 to find 33 1/3% of a number.  Since

dividing by the reciprocal gives the same results, we

can also divide by 3.

 

300 x 33⅓% = 300 x ⅓ = 300 ÷ 3 = 100

 

45 x 33⅓% = 45 x ⅓ = 45 ÷ 3 = 15

 

 

90 x 33⅓% = 90 x             = 90 ÷       = 

24 x 33⅓% =

 

24 x 1/3=

 

24 ÷ 3 =

48 x 33⅓% =

 

48 x  1/3 =

 

48 ÷       =

6 x 33⅓% =

 

6 x  1/3 =

 

6 ÷       =

12 x 33⅓% =

 

12 x       =

 

12 ÷       =

21 x 33⅓% =

 

21 x       =

 

21 ÷       =

30 x 33⅓% =

 

30 x       =

 

30 ÷       =

36 x 33⅓% =

 

36 x       =

 

36 ÷       =

60 x 33⅓% =

 

60 x       =

 

60 ÷       =

75 x 33⅓% =

 

75 x       =

 

75 ÷       =

If the number is not a multiple of three, the answer

will be a fraction.

 

For example:  11 x 33⅓% = 11 ÷ 3 =  3⅔.

 

 

Since 66⅔% is twice as large as 33⅓%, find one-third

first and then double.

 

For example  90 x 33⅓% = 30 so

                     90 x 66⅔% = 60.

 

This is because 66⅔% equals the fraction ⅔.

To find 45 x 66⅔%, find 45 x ⅓ by dividing by 3.  Then

double.

 

45 x 33 ⅓% = 45 x ⅓ = 45 ÷ 3 = 15.

 

Now double to find 66⅔%.

 

15 doubled is 30.

 

 

 

33⅓% of 60 is 20.

 

So 66⅔% of 60 is        .

To find 45 x 66⅔%, find 45 x ⅓ by dividing by 3.  Then

double.

 

45 x 33 ⅓% = 45 x ⅓ = 45 ÷ 3 = 15.

 

Now double to find 66⅔%.

 

15 doubled is 30.

 

 

 

33⅓% of 90 is 30.

 

So 66⅔% of 90 is        .

To find 45 x 66⅔%, find 45 x ⅓ by dividing by 3.  Then

double.

 

45 x 33 ⅓% = 45 x ⅓ = 45 ÷ 3 = 15.

 

Now double to find 66⅔%.

 

15 doubled is 30.

 

 

 

33⅓% of 24 is 8.

 

So 66⅔% of 24 is        .

To find 45 x 66⅔%, find 45 x ⅓ by dividing by 3.  Then

double.

 

45 x 33 ⅓% = 45 x ⅓ = 45 ÷ 3 = 15.

 

Now double to find 66⅔%.

 

15 doubled is 30.

 

 

 

33⅓% of 45 is 15.

 

So 66⅔% of 45 is        .

To find 45 x 66⅔%, find 45 x ⅓ by dividing by 3.  Then

double.

 

45 x 33 ⅓% = 45 x ⅓ = 45 ÷ 3 = 15.

 

Now double to find 66⅔%.

 

15 doubled is 30.

 

 

 

33⅓% of 27 is 9.

 

So 66⅔% of 27 is        .

33⅓% of  33 is     .

 

66⅔% of 33 is      .

33⅓% of  99 is     .

 

66⅔% of 99 is      .

33⅓% of  123 is     .

 

66⅔% of 123 is      .

33⅓% of  333 is     .

 

66⅔% of 333 is      .

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