Question #f7fe4

2 Answers
Aryan V
Sep 24, 2017

#9 13/42#

Explanation:

First, let's rearrange the order to that we can identify the smallest and largest numbers. Here are the symbols that I use and what it means. #># is 'greater than' and #<# is 'less than'.

We know that the negative numbers should be smallest, as they are below 0. Remember the greater the number of the negative the smaller the number, so #-5 1/6 < -2 1/3 # .

We also know that #8/17 < 3/5# because if we convert these fraction into decimals we get #8/17 = 0.42105263157# and #3/5 = 0.6#, and #0.42105263157# is smaller than #0.6# . Therefore #3/5 > 8/19#.

We know #4 1/7# has the greatest value since it is a positive number and it is greater than # 3/5# because. To prove this lets rewrite #4 1/7# as #29/7#.

To get a common denominator for both fractions, we do #29/7 xx 5/5 # and #3/5 xx 7/7#. So we get #29/7 = 135/35 and 3/5 = 21/35 #.

This proves that #4 1/7 > 3/5# because #135/35 > 21/35 #

Now that we know the order. Let's find the difference between the smallest and largest numbers.

Here's the order #-5 1/6, -2 1/3, 8/19, 3/5 and 4 1/7 #

The largest number is #4 1/7# and the smallest is #-5 1/6#.
Let's find their difference #4 1/7 - (-5 1/16)#.
Firstly, we need to convert these mixed numbers into improper fractions so that we can subtract them more easily so # 4 1/7 = color(green)(29/7# and #-5 1/6 = color(green)(-31/6#.

Now let's find the common denominator of these two fractions. Now the LCM of 6 and 7 is 42 so that will be our common denominator.
Let's do the operation to make the denominators of both of these fractions the same.
#29/7 xx 6/6 = color(green)(174/42) and -31/6 xx 7/7 = color(green)(-217/42#

Remember never add or subtract the denominators!

Finally, let's find the difference:
#174/42 -(-217/42) = 174/42 + 217/42 = color(green)(391/42 #

Simplify the fraction so make it a Mixed number. We know that 42 goes into 391 nine times, therefore it will be 9 followed by a fraction. When we multiply 42 by 9 we get 378 and we know that the numerator of the fraction will be 13 because 391 - 378 is 13. Finally, we can write it as a fraction #9 13/42#.

Barney V.
Sep 24, 2017

#color(magenta)(5 23/30#

Explanation:

#:.8/19=0.421052631#

#:.-2 1/3=-2.333333333#

#:.3/5=0.6#

#:.4 1/7=4.142857143#

#:.-5 1/6=-31/6=-5.166666667#

Largest number#=0.6=3/5#

Smallest number#=-5.166666667=-5 1/6=-31/6#

#:.3/5-(-31/6)#

#:.=3/5+31/6#

#:.=(18+155)/30#

#:.=173/30#

#:.color(magenta)(=5 23/30#

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