Question #9ddf0

4 Answers
Oct 1, 2016

#128#

Explanation:

We have: #42 (2) / (3) div (1) / (3)#

#= (42 (2) / (3)) / ((1) / (3))#

#= ((42 cdot 3 + 2) / (3)) / ((1) / (3))#

#= ((128) / (3)) / ((1) / (3))#

#= (128) / (3) cdot (3) / (1)#

#= (128) / (3) cdot 3#

#= 128#

Oct 1, 2016

It is #128#

Explanation:

#42 2/3-:1/3#

#=42 2/3xx3#

#=42xx3+2/3xx3#

#=126+2#

#=128#

I used the following properties of division and multiplication:

  • division by a fraction is the same as multiplication by the fraction's reciprocal

#a-:b/c=axxc/b #

  • distributive property:

#axx(b+c)=ab+ac #

Oct 1, 2016

#128#

Explanation:

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dividing with fractions: #rarr# In a nutshell

Step 1 . change all mixed numbers to improper fractions

Step 2 .# div rarr xx # and flip the next fraction

Step 3 : cancel any numerator with any denominator through #xx#

Step 4 : #("top x top")/("bottom x bottom")#

Step 5 : simplify if necessary.

Step 6 : Keep improper fractions or change to mixed numbers depending on what you have been told to do.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#42 2/3 div 1/3#

#=128/3 div 1/3 " "larr# step 1

#=128/3 xx3/1" "larr# step 2

#=128/cancel3 xxcancel3/1" "larr# step 3 and step 4

#= 128" "larr# step 5. no further simplifying necessary

Oct 4, 2016

#42 2/3 -: 1/3=128#

Explanation:

#color(blue)("For a moment consider just the "42 2/3)#

write this as #42+2/3#

This is the same as:

#" "[42color(magenta)(xx1)]+2/3#

But we can write 1 as #3/3# giving:

#" "[42color(magenta)(xx3/3)]+2/3#

#" "[126/3]" "+2/3 = 128/3#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Putting it all together")#

#42 2/3 -: 1/3" "=" "128/3-:1/3#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Shortcut method")#
Turn the #1/3# upside down and multiply

#128/3xx3/1 " "=" "3/3xx128/1 " "=" "1xx128" "=" "128#

Or by cancelation (which is the same thing really):

#128/(cancel(3))xx(cancel(3))/1 = 128/1=128#