How do you multiply #4 2/3 div 1 5/8#?

1 Answer
Mar 12, 2016

Answer:

The question is given in fractions so the answer has to be in fractions.

#2color(white)(.)34/39#

Explanation:

#color(brown)("Multiply any number by 1 and you do not change its value")#
#color(brown)("This is a 'trick' to convert a whole number into a fraction."#

We know that #4xx1 =4#

But #3/3# is another way of writing 1

So instead of writing #4xx1 =4# we could write #4xx 3/3 =4#

But #4xx3/3" is the same as "(4xx3)/3 =12/3#

So #12/3 # is 4 converted into thirds!
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Answering your question")#

Given:#color(green)(" "4 2/3 -: 1 5/8)#

Converting 4 into thirds and 1 into eights

#color(green)(" "(12/3 + 2/3) -: (8/8+5/8))#

#color(green)(" "14/3-:13/8)#

Using the shortcut rule of: when dividing turn the divisor (what you are dividing by) upside down and then multiply

#color(green)(" "14/3xx8/13)#

#color(green)(" "(14xx8)/(3xx13))#

#color(green)(" "112/39)#

#color(blue)(" "2 34/39)#
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#color(brown)("Another trick")#

Suppose you have the whole number of say 6. Although not normally done it is perfectly correct to write 6 as #6/1#

So if you have #3 -: 6# you are permitted to write it as

#3/1-: 6/1 = 3/1 xx1/6 = (3xx1)/(1xx6) = 3/6#