How do you divide #5 5/8 div 2/3#?

3 Answers

Answer:

#8 7/16#

Explanation:

Change the mixed number to an improper fraction

# 5 5/8 = 45/8#

Set up a complex fraction to indicate the division

# ( 45/8)/(2/3)#

eliminate the bottom fraction # 2/3# by multiplying by the inverse.
(Remember that what ever is done to the bottom must always be done to the top. ( fairness)

# {(45/8) xx (3/2)}/{ (2/3) xx (3/2)}#

# 2/3 xx 3/2 = 1# so this leaves

# 45/8 xx 3/2 = 135/16 = 8 7/16#

Jul 9, 2017

Answer:

#= 8 7/16#

Explanation:

For division of fractions, always change mixed numbers to improper fractions:

#5 5/8 div 2/3#

#= 45/8 xx 3/2" "larr# to divide, multiply by the reciprocal

#= 135/16" "larr# multiply straight across, nothing cancels

#= 8 7/16#

The question was given with mixed numbers, answer in the same form.

Jul 9, 2017

Answer:

A slightly different approach.

#8 7/16#

Explanation:

#color(blue)("An example of the method using numbers")#

I choose: #9-:3# but 9 can be written as #6+3# so we may write the same thing as

#9 -:3->(6+3)-:3#

This is the same as: #(6+3)xx1/3#

Multiply everything inside the brackets by #1/3# giving #6/3+3/3=3#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering the question")#

Writ #5 5/8# as #5+5/8# so now we have: #(5+5/8)-:2/3#

This is the same as #(5+5/8)xx3/2#

Note that #-:2/3# give the same answer as #xx3/2#

Multiply everything inside the brackets by #3/2# giving:

#color(green)(15/2+15/16" "=" "[15/2color(red)(xx1)]+15/16)#

Multiply by 1 and you do not change the value. However 1 comes in many forms so you can change the way the fraction looks without changing its inherent value.

#color(green)(" "=" "[15/2color(red)(xx8/8)]+15/16)#

#" = "120/16 " "+15/16" "=" "135/16#

#" "=" "8 7/16#