4 MATHEMATICS 



= lg. If there are mixed numbers, reduce them to fractions, 

 and then divide as just shown; thus, li^S^-^-J-- 1 ^, or -^XfS 



-4*-*. 



DECIMAL FRACTIONS 



In decimals, whole numbers are divided into tenths, hun- 

 dredths, etc.; thus, iV is written .1 ; .08 is read rSff, the value of 

 the number being indicated by the position of the decimal 

 point; that is, one figure after the decimal point is read as 

 so many tenths; two figures as so many hundredths; etc. 

 Moving the decimal point to the right multiplies the number 

 by 10 for every place the point is moved; moving it to the 

 left divides the number by 10 for every place the point is 

 moved. Thus, in 125.78 (read 125 and J&), if the decimal 

 point is moved one place to the right, the result is 1,257.8, 

 which is 10 times the first number; or, if the point is moved to 

 the left one place, the result is 12.578, which is rV the first num- 

 ber, moving the point being equivalent to dividing 125.78 by 10. 



Annexing a cipher to the right of a decimal does not change 

 its value; but each cipher inserted between the decimal point 

 and the decimal divides the decimal by 10; thus, in 125.078, 

 the decimal part is rV of .78. 101.257 



Addition of Decimals. Place the numbers so 12.965 



that the decimal points are in a vertical line, and 43.005 



add in the ordinary way, placing the decimal 920.600 



point of the sum under the other points. _ s __ 



Subtraction of Decimals. Place the number to 

 be subtracted with its decimal point under that 

 of the other number, and subtract in the ordinary 

 way. 434.968 



Multiplication of Decimals. Multiply in the ordinary way, 

 and point off from the right of the result as many figures as there 

 are figures to the right of the decimal points in 21.72 



both numbers multiplied; thus, in the example 34 j 



here given, there are three figures to the right ~2172 



of the points and that many are pointed off in sfiRS 



the result. If either number contains no deci- 6516 



mal, point off as many places as are in the num- 

 ber that does. 740.652 





