Carpentry & Building Construction © 2004

Math Activities :

Self-Check Math Activity 3

Adding Fractions

Fractions can be added quickly once you have found a common denominator. The common denominator is the number into which the denominators of all the fractions can be divided. For example, to add 3/4 plus 1/2, you need to find a common number for the denominators 4 and 2. You can find the common denominator by multiplying each denominator by 1, 2, 3, 4, etc., until you find a common number.

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

Practice Exercise 1

Add the fractions 1/2 and 3/4.
Step 1	Multiply the denominators 2 and 4 by 1, 2, etc., until you find the common
	denominator.
	2 × 1= 2, 2 × 2 = 4, and 4 × 1 = 4
	Therefore the common denominator is 4.
Step 2	Change 1/2 to higher terms so that its denominator is 4. You can multiply 2 by 2 to make the denominator 4. Whatever you do to the denominator, you must also do to the numerator. This means that you multiply 1/2 × 2/2.
	1 × 2 = 2
	2 × 2 = 4
	Thus, the higher term for 1/2 is 2/4.
Step 3	Add the two fractions.
	2/4 + 3/4 = 5/4
Step 4	Change the improper fraction to a mixed number.
	5/4 = 1 1/4

Hint: Another way to find the common denominator is to multiply the denominators. For example, if you multiply 4 × 2, the result, 8, is a common denominator. Both 2 and 4 can be divided into 8. However, this method will not always yield the lowest common denominator, and you may find yourself working with some large numbers.

Practice Exercise 2

Add the mixed numbers 3 3/8 and 6 1/2.
Step 1	Change both fractions to improper fractions.
	3 3/8 = 27/8
	6 1/2 = 13/2
Step 2	Find the common denominator for 8 and 2.
	1 × 8 and 2 × 4 both equal 8, so the common denominator is 8.
Step 3	Change 13/2 to higher terms so that 8 becomes the denominator.
	13/2 × 4/4 = 52/8
Step 4	Add the fractions.
	27/8 + 52/8 = 79/8
Step 5	Reduce the fraction to lowest terms.
	79/8 = 9 7/8

Problem Exercises


1.	Add the fractions 1/4 and 3/8.
		A)	3/4
		B)	4/8
		C)	5/4
		D)	5/8


2.	Add the fractions 1/2 and 5/16.
		A)	13/16
		B)	6/16
		C)	5/16
		D)	5/32


3.	A carpenter worked 7 1/2 hours on Wednesday, 6 1/4 hours on Thursday, and 4 3/4 hours on Friday to finish a house addition. How many hours did the carpenter work?
		A)	18
		B)	18 1/2
		C)	18 3/4
		D)	18 5/8


4.	A closet will have two interior shelves. Each shelf will be 19 3/4'' long. Allowing 1/8'' for one saw kerf, what length of shelving will need to be ordered?
		A)	19 4/32''
		B)	19 7/8''
		C)	39 4/32''
		D)	39 5/8''


5.	You have two pieces of quarter-round molding left to cut and install. One piece is 60 1/2'' and the other is 11 3/4''. Allowing 1/8'' for one saw kerf, what is the length of the molding you need?
		A)	72 1/4''
		B)	72 2/8''
		C)	72 3/8''
		D)	72 4/4''