Understanding Relationships between Fractions and Decimals

The dollar represents a whole unit or 1.00

These two Franklin Half Dollars Represent the two 1/2’ s of the whole unit 1/2 + 1/2 = 1 .50 + .50 =1.00

These four Bicentennial Quarters Represent the Four Quarters of a whole Unit Each quarter is equal to .25 of the whole unit .25 + .25 + .25 + .25 = 1.00 1/4 + 1/4 + 1/4 + 1/4 = 1

Thus one quarter equals 1/4 or .25 We can see this by doing 1 divided by 4 equals .25

Two Quarters equal one half 1/4 + 1/4 = 1/2 .25 + .25 = .50

Three Quarters equal 3/4 or .75 1/4 + 1/4 + 1/4 = 3/4 .25 + .25 + .25 =.75

.25 .50 .75 1.00

In the next example we will see that cutting the quarter into two parts the decimal equivalent is also cut in half

= .125 = .125 = _____ .25

If it takes two of these too make one quarter how many will you need to make 1 dollar or one whole Note: the value of money the US mint once minted half cent pieces in the 1800’s

.125 .25 .375 .50 .625 .75 .875 1.00 1/8 2/8 3/8 4/8 5/8 6/8 7/8 1 1/8 1/4 3/8 1/2 5/8 3/4 7/8 1 8

If 8 equal parts make a whole unit we can divide any part of these units to find decimal equivalent Example: 1 divided by 8 = .125 2 divided by 8 = .25 3 divided by 8 = .375 4 divided by 8 = .5 5 divided by 8 = .625 6 divided by 8 = .75 7 divided by 8 =.875 8 divided by 8 = 1

We can find out the fractional equivalent of a decimal by multiplying by the denominator of the fraction. Examples: .125 X 8 =1 or 1/8 .25 X 8 = 2 or 2/8 reduced to ¼ .375 X 8 =3 or 3/8 .5 X 8 =4 or 4/8 reduced to 1/2

What if a fraction does not come out equal? Since we are working with tape measures lets go up to sixteenths of an inch. .1875 X 8 = 1.5 eights which would be ONE Eighth plus one half of one eighth .1875 X 16 = 3 or 3/16

By understanding the basic decimal equivalents it is easy to do computations on your basic calculator for working in construction using a tape marked in inches.

= = = 1/2’s 1/4’s 1/8’s