Viewing page 9 of 91

This transcription has been completed. Contact us with corrections.

to have the right-hand figures of all the partial products directly below their corresponding figures in the second factor. 
Example: Multiply 16.53 by 24.07

d. Although there is no very simple way to check a multiplication  it is good practice to anticipate the approximate size of the product before beginning a long multiplication. This is done by "rounding off" the factors to permit easy mental multiplication. Although by no means an accurate check, this will frequently catch mistakes in addition or in the location of the decimal point which would otherwise result in nonsensical answers. 
Example: What is the approximate product of 15.73 multiplied by 187.04?
Solution: Round off 15.73 to 15, and 187.04 to 200. Then the product is roughly 15 by 200=3,000. It is clear then that the product of 15.73 and 187.04 cannot be 150.6 of 6,030.3745, for example.
e. Symbols and units. -The more common symbol for multiplication is X. However, it is quite common simply to write the numbers in parenthesis next to each other: (3.04)(17.78)=3.04X17.78=54.0512, for example.
(1)When the same number is to be multiplied by itself, for example 3.04X3.04, this is usually indicated by a small "2" placed above and to the right of the number: 3.04 X 3.04 = 3.04^2. This is read as "3.04 squared," and 3.04^2 is the "square of 3.04." If the number is to be used as a factor 3 times, then a small "3" is used: 3.04X3.04X3.04=3.04^3. This is is read as "3.04 cubed", and 3.04^3 us the "cube of 3.04."
(2) Unlike addition and subtraction, multiplication of different units can be preformed. The product of the units of the factors. 
(a)Example: Multiply 5 pounds by 7 feet.
Soulution: (5 pounds)(7 feet) = 35 punds-ft= 35 lb-ft = 35 ft-lb
(b)Example: Multiply 9 feet by 17 feet
Solution:(9 feet)(17 feet) = 153 feetXfeet = 153(feet)^2=153 ft^2
(ft^2 is read "square feet")

Please note that the language and terminology used in this collection reflects the context and culture of the time of its creation, and may include culturally sensitive information. As an historical document, its contents may be at odds with contemporary views and terminology. The information within this collection does not reflect the views of the Smithsonian Institution, but is available in its original form to facilitate research. For questions or comments regarding sensitive content, access, and use related to this collection, please contact