Wood Technology & Processes

Self-Check Math Quizzes : Self-Check Math Quizzes

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

Add the fractions 1/2 and 3/4.

Step 1Multiply 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 2Change 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 3Add the two fractions.
2/4 + 3/4 = 5/4
Step 4Change 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.

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

Practice Exercise

Add the mixed numbers 3 3/8 and 6 1/2.

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

Problem Exercises

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''
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