To transform a mixed number to an improper fraction, we must multiply the denominator by the large number, and add the numerator.
So for [tex] 14\frac{2}{7} [/tex]: [tex] (14*7)+2=100 [/tex]
But we also put this over the denominator in the mixed number, so we get: [tex] \frac{100}{7} [/tex].
Then we do the same for [tex] 5\frac{2}{3} [/tex]:
[tex] (5*3)+2=\frac{17}{3} [/tex]
Then we must find a common denominator. Let's use 21 (multiply 3 and 7):
[tex] \frac{100}{7} *\frac{3}{3}= \frac{300}{21} [/tex]
[tex] \frac{17}{3}* \frac{7}{7} =\frac{119}{21} [/tex]
Now that we have a common denominator, we can subtract across:
[tex] \frac{300}{21} -\frac{119}{21}= \frac{181}{21} [/tex]
Since [tex] \frac{181}{21} [/tex] cannot be reduced any further, we are going to leave this as our answer.
So the answer is [tex] \frac{181}{21} [/tex].
