Question #d9b10

#1/2# of #8/10# is the same as

#1/2 xx 8/10#.

Multiplying fraction is nice! it's the easier thing to do because we just multiply top times top and bottom times bottom. (For adding or subtracting we need the same denominator -- for multiplying we don't.)

#1/2 xx 8/10 = (1 xx 8)/(2 xx 10) = 8/20#.

Usually we would reduce this answer to lowest terms. We'll remove factors that are common to the top and bottom.

#8/20 = (2 xx 4)/(2 xx 10)#. Removing the #2# that is common we get

#8/20 = (4)/(10)#. But we still have a common factor, so we'll get rid of it.

#4/10 = (2 xx 2)/(2 xx 5) = 2/5#

#2# and #5# do not have any factors in common, so we are finished.

We will use three concepts:

• Given a number #x#, half of #x# is the same as #x xx 1/2#.
  For example, half of #22# is #22xx1/2 = 11#
• The product of two fractions #a/b# and #c/d# is #a/bxxc/d = (ab)/(cd)#
• If the numerator and denominator of a fraction share a factor, we may cancel that factor. #(acancel(c))/(bcancel(c))=a/b#

Using the first concept, we have that half of #8/10# is #8/10xx1/2#.

Using the second, we have

#8/10xx1/2 = (8xx1)/(10xx2) = 8/20#

Using the third, we get our final result:

#8/20 = (2xxcancel(4))/(5xxcancel(4)) = 2/5#