Carpentry & Building Construction © 2004

Math Activities :

Self-Check Math Activity 5

Multiplying Fractions

Carpenters multiply fractions for tasks such as laying out distances for framing or marking studs. Multiplying fractions begins with changing mixed numbers to improper fractions. The improper fractions are reduced to lowest terms and then multiplied. The answer is changed from an improper fraction back to a mixed number. Check the number for lowest terms.

Terms, Symbols, & Abbreviations
mixed number - whole number and fraction
improper fraction - numerator equals the denominator, or numerator is greater than denominator

Practice Exercise 1

Convert the mixed number 4 3/8 to an improper fraction.
Step 1	Multiply the whole number (4) by the denominator (8).
	4 × 8 = 32
Step 2	Add 32 to the numerator (3).
	32 + 3 = 35
Step 3	Place the numerator (35) over the denominator (8).
Thus 4 3/8 = 35/8.

Practice Exercise 2

Multiply the mixed number 4 3/8 by 3.
Step 1	Convert 4 3/8 to an improper fraction.
	4 3/8 = 35/8
Step 2	Change the whole number 3 to a fraction (3/1).
Step 3	Multiply the numerators.
	35 × 3 = 105
Step 4	Multiply the denominators.
	8 × 1 = 8
Step 5	The new fraction is 105/8. Convert this improper fraction to a mixed number.
	105 ÷ 8 = 13 1/8

Problem Exercise


1.	Convert 3 5/16 to an improper fraction.
		A)	15/16
		B)	35/16
		C)	48/16
		D)	53/16


2.	Multiply the mixed number 3 3/4 by 1 1/8.
		A)	4 7/32
		B)	4 3/32
		C)	3 3/32
		D)	3 5/8


3.	Multiply the mixed number 2 5/8 by 3/4.
		A)	1 15/32
		B)	1 31/32
		C)	2 15/32
		D)	2 31/32


4.	Multiply the mixed number 7 1/2 by 4.
		A)	28 1/2
		B)	28/2
		C)	30
		D)	30 1/2


5.	Multiply the mixed number 1 3/4 by 10 1/2.
		A)	18 3/8
		B)	18 3/4
		C)	10 3/8
		D)	10 3/4