What is the 9th multiple of 15?

2 Answers
Sep 16, 2016

#9^(th)# multiple is #135#

Explanation:

Multiples of any number can be found by multiplying the number by the series of natural numbers i.e. #{1,2,3,4,5,6,7,8,9,.....}#.

Hence multiples of #15# are #{15xx1,15xx2,15xx3,15xx4,15xx5,15xx6,15xx7,15xx8,15xx9,.....}# or

#{15,30,45,60,75,90,105,120,135,........................}#

and hence #9^(th)# multiple is #135#.

Sep 18, 2016

135

Explanation:

#color(blue)( 9xx15)#

or another way using the fact that multiply by 10 is easier.

15 is the same as #10+5# so we have

#color(blue)( 9(10+5)color(white)("dd")->color(white)("dd")(9xx10)+(9xx5)#

But 5 is #1/2xx10# giving

#color(blue)(color(white)("d")9(10+5)color(white)("d")->color(white)("d")(9xx10)+(9xx1/2xx10)#

#color(white)("dddddddd")color(blue)(color(white)("d")->color(white)("d") (9xx10)+color(white)("dd")1/2(9xx10))#

#color(blue)( color(white)("dddddddddddd.dd") 90color(white)("..dd") + color(white)("ddd")45color(white)("dddd") =135)#