COMMON FRACTION/DECIMAL/PERCENT EQUIVALENT RELATIONSHIPS

 

You should be trilingual when it comes to fractions, decimals, and percents.  For example, you probably know without doing any computation that if you get half of the answers right on a test your grade will be 50%.  Graph problems especially require a sense of numbers and fractional parts.  Remember, often you won't have to calculate answers because they have already been calculated.  You just need to be able to spot the correct answer.

 

These are the common fraction / decimal /percent equivalent relationships you should know.  The ones that are very, very important have an *.

 

1

1.0

100%*

1/100

0/01

1%*

1/2

0.5

50%*

1/4

  0.25

25%*

3/4

0.75

75%*

1/3

0.333...

33 1/3%*

2/3

0.666...

66 2/3%

1/8

0.125

12 1/2% or 12.5%*

3/8

0.375

37 1/2% or 37.5%

5/8

0.625

62 1/2% or 62.5%

7/8

0.875

87 1/2% or 87.5%

1/5

0.2

20%*

2/5

0.4

40%

3/5

0.6

60%

4/5

0.8

80%

1/10

0.1

 

10%*

3/10

0.3

30%

7/10

0.7

70%

9/10

0.9

90%

1/9

0.111 ...

11 1/9%

2/9

0.222 ...

22 2/9%

1/11

0.0909 ...

9 1/11%

2/11

0.1818 ...

18 2/11%

1/6

0.1666 ...

16 2/3%

1/7

approx. 0.14

14 1/7%

1/12

0.08333 ...

8 1/3%

1/20

0.05

5%

Comments About Common Fraction / Decimal /Percents

 

Memorizing the chart of common fraction/decimal/percent relationships is equivalent to memorizing about 20 long distance phone numbers, so let's look for some patterns. 

 

If I have 1/4 (that is, a quarter) of a dollar I have $0.25, and of course if I have three quarters I have $0.75.

 

A third is easy because of all the threes:  1/3=33 1/3%

Now 1/3 doubled is 2/3 , 0.333 ...  doubled is 0.666 … ,

and 33 1/3% doubled is 66  2/3 %

 

Eighths are very handy to know.  One eighth is half of a fourth and half of 25% is 12  1/2%.  Now add 1/4 and 1/8 (that's really

 2/8+1/8) to get 3/8.  That is, 12 1/2% and 25% gives you 37 1/2%.  Now add 12 1/2% to 50% to get 62 1/2%.  Finally, 7/8 is just 1/8 less than 100% (which is 8/8) so 100% ­– 12 1/2% = 87 1/2%.

 

Fifths are easy:  Know that 1/5 is 20%.  Double that and you have  2/5 = 40%.  Note the pattern:  20%, 40%, 60% 80% and  of course

5/5=1= 100%.

 

Tenths are the easiest of all:  1/10, 2/10, 3/10  ... equals 0.1, 0.2, 0.3, etc.  Of course, 1/10 of a dollar is a dime or $0.10 so again, just think of money.

 

 

More Comments About Common Fraction / Decimal /Percents

 

The rest of the items in the chart aren't as crucial but they can be handy.  Notice that the ninths and elevenths are related:  1/9  is about 11% and 1/11 is about 9%.  If you know that 1/9 is 11%, then twice as much, or 2/9 is 22%, 3/9 is 33% (OK, OK, it's really 33 1/3% since 3/9=1/3, but you get the picture)!

 

Silly fact:  one-six is one-six.  What does that mean?  Just that 1/6 is close to 16%.  (OK, we know it's a tad closer to 17%, but that's not as easy to remember and 16% is close enough!) 

 

Silly fact:  7 x 2 = 14.  Why do we care?  Because 1/7 is roughly 14%, and 2/7 = 28% etc.

 

Notice the 8s and 12s are kind of related too.  Remember that 1/8 was around 12%?  Well, 1/12 is about 8%. 

 

Lastly, 1/20 is handy to know.  If 1/20 is 5%, (think of the 20 nickels in a dollar) then 7/20 is 35%, etc.

 

Examples:

Find percent equivalents for the following fractions:

 

2/3

4/5

8/8

3/7

3/12

5/8

 

Answers:

 

2/3=66 2/3%

4/5=80%

8/8=100%

3/7=approximately 42% (14x3)

3/12=25% (Note that 3/12=1/4)

5/8=62 1/2%