Carpentry & Building Construction © 2004

Math Activities :

Self-Check Math Activity 4

Subtracting Fractions

Carpenters must know how to subtract fractions, especially when measuring and calculating how much material or distance is left. Subtracting fractions is similar to the steps used for adding. First, change mixed numbers (such as 6 1/2 and 3 3/4) to improper fractions (13/2 and 15/4). Next, find the common denominator of the fractions by multiplying each denominator by 1,2,3,4, etc., until you find a common number. Change the fractions to higher terms using the common denominator. Then subtract the numerators of the fractions. Express the answer in lowest terms.

Terms, Symbols, & Abbreviations
common denominator - a number into which other denominators can be divided

Practice Exercise

Subtract 2 1/4 from 5 1/2.
Step 1	Change the mixed numbers to improper fractions.
	2 1/4 = 9/4
	5 1/2 = 11/2
Step 2	Find a common denominator by multiplying each denominator by 1,2,3,4, etc.,
	until you find a common number.
	4 × 1 = 4, and 2 × 2 = 4. The common denominator is 4.
Step 3	Change 11/2 to higher terms so that its denominator is 4.
	11/2 × 2/2 = 22/4
	The fractions are now 22/4 and 9/4.
Step 4	Subtract the numerators.
	22 - 9 = 13
	Therefore 22/4 - 9/4 = 13/4
Step 5	Convert the improper fraction 13/4 to a mixed number by dividing the numerator
	by the denominator.
	13 ÷ 4 = 3 1/4

The fraction 1/4 is already in its lowest terms, so the answer is 3 1/4.

Problem Exercises


1.	What is 18 3/4 minus 7 1/8?
		A)	11 1/8
		B)	11 2/4
		C)	11 5/8
		D)	11 3/32


2.	You need to cut a piece of wallboard that is 17 1/2'' wide from a 23 3/4'' wide scrap piece to repair a wall. Find the width of the material that will be left after you make your cut.
		A)	6 1/4''
		B)	6 1/2''
		C)	6 3/4''
		D)	6 3/8''


3.	A builder has estimated 18 1/2 hours for a job. So far, 5 3/4 hours have been completed. How many hours are left on the job?
		A)	12 1/4
		B)	12 3/4
		C)	13 1/4
		D)	13 3/4


4.	A carpenter cuts 54 1/8'' off a 96'' piece of molding. How much is left?
		A)	42 1/8''
		B)	42 7/8''
		C)	41 7/8''
		D)	41 1/8''


5.	To square up a panel, a carpenter has to trim 3 3/4'' from the 48'' width. Assuming a 1/8'' saw kerf, how wide is the panel after cutting?
		A)	43 1/8''
		B)	43 2/4''
		C)	44 1/4''
		D)	44 1/8''