How do I find the quotient of 3/8 and 2?

Question

Genesis Allen · Accepted Answer

Another perspective!!!

Is there a way to do this with fractions? It takes a while to explain what happens, but once understood, the actual process is very quick. For example, you can divide 4 by 2 straight away. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(green)("Point 1")# The reason #4 divide 2# can be done strait off is that they are both of the same unit size. The 'unit size #color(blue)("'when viewed this way'")# is how many of what you are counting it takes to make a whole. So if you have #1/2# then the count is 1 and the unit size is such that it takes 2 of them to make a whole. If you have #2/3# then the count is 2 and the unit size is such that it takes 3 of them to make a whole. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(green)("Point 2")# When counting 'the normal way' such as 1, 2 , 3 and so on, you can write them as: #1/1, 2/1, 3/1 # The bottom number (denominator) is how many of what you are counting it takes to make a whole of something. This is why #4 divide 2# can be done strait off!!! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(green)("Using the idea")# #3/8 divide 2# Write as: #3/8 divide 2/1# #color(blue)("if you make the unit sizes the same you can then divide the counts directly"# Since the two counts are of different unit sizes—one is of unit size 8 and the other is of unit size 1—you cannot divide the count of 2 into the count of 3 directly when dividing. Lets look at how to change #2/1# into the same unit size as #3/8# If we multiply #2/1# by 1 we do not change its value. There are many ways of writing 1. Suppose we chose to write it as #8/8# Then #2/1 times 1 -> 2/1 times 8/8# But #2/1 times 8/8 = 16/8# in order for us to write #3/8 divide 16/8# This is exactly the same as #3 divide 16 -> 3/16#

Julia Adams · Answer

undefined To find the quotient of 3/8 and 2, divide 3 by 8 and then divide the result by 2. The answer is 3/16.