To turn a mixed number into an improper fraction you must recognize the following:

\(\displaystyle 4\frac{7}{9}=4+\frac{7}{9}\)

now we need to add 4 and seven ninths, to do that you multiply by a good form of 1 

\(\displaystyle 4+\frac{7}{9}=\frac{9}{9}\cdot4+\frac{7}{9}=\frac{36}{9}+\frac{7}{9}\)

now with the common denominator you can add the fractions to get 

\(\displaystyle \frac{43}{9}\)

To find the improper fraction value, we must effectively add together 71 and ⁵/₇. To do this, we will give 71 a denominator of 7; therefore, we are transforming ⁷¹/₁ to ^x/₇.  The shortest way to do this is to multiply by ⁷/₇ (which really is 1); therefore, 71 = 71 * (⁷/₇) = ⁴⁹⁷/₇.

Now add them: ^{(497 + 5)}/₇ = ⁵⁰²/₇

To find an improper fraction, you need to multiply the whole number that you have by the denominator of the associated fraction.  For our problem, this means that you will multiply \(\displaystyle 14\) by \(\displaystyle 5\), getting \(\displaystyle 70\).  Next, you add this to the numerator of your fraction, giving you \(\displaystyle 70+2\), or \(\displaystyle 72\).  Finally, you place this over your original denominator, giving you: 

\(\displaystyle \frac{72}{5}\)

To find an improper fraction, you need to multiply the whole number that you have by the denominator of the associated fraction.  For our problem, this means that you will multiply \(\displaystyle 27\) by \(\displaystyle 19\), getting \(\displaystyle 513\).  Next, you add this to the numerator of your fraction, giving you \(\displaystyle 513+4\), or \(\displaystyle 517\).  Finally, you place this over your original denominator, giving you: 

\(\displaystyle \frac{517}{19}\)

To determine the numerator of the improper fraction, multiply the denominator with the whole number. Then add this with the numerator. The denominator will remain the same.

\(\displaystyle 2\tfrac{2}{5} = \frac{(5\cdot 2) +2}{5} = \frac{12}{5}\)

Remember that to convert mixed fractions, you can treat it like an addition.  Thus

\(\displaystyle \small 5\frac{7}{11} = 5 + \frac{7}{11}\)

You then find the common denominator of the two which is \(\displaystyle \small 11\):

\(\displaystyle \small 5 + \frac{7}{11} = \frac{55 + 7}{11} = \frac{62}{11}\)

Remember that to convert mixed fractions, you can treat it like an addition.  Thus

\(\displaystyle \small 4 \frac{5}{6} = 4 +\frac{5}{6}\)

You then find the common denominator of the two which is \(\displaystyle \small 6\):

\(\displaystyle \small \frac{24 + 5}{6} = \frac{29}{6}\)

Remember that to convert mixed fractions, you can treat it like an addition.  Thus

\(\displaystyle \small 4 = \frac{2}{3} + 7\frac{1}{3} = 4 + \frac{2}{3} + 7 + \frac{1}{3}\)

Now, using the common denominator of \(\displaystyle \small 3\), you know:

\(\displaystyle \small 4 + \frac{2}{3} + 7 + \frac{1}{3} = \frac{12+2+21+1}{3} = \frac{36}{3} = 12\)

Another way to do this is to notice that \(\displaystyle \small \frac{2}{3} + \frac{1}{3} = 1\).  Then you just add these values to \(\displaystyle \small 4\) and \(\displaystyle \small 7\).

Use your calculator to your advantage.  You know that \(\displaystyle \small \frac{55}{7}\) is \(\displaystyle \small \small 7.85714285714286\).  This means that the mixed fraction equivalent must be of the form:

\(\displaystyle \small 7\frac{x}{7}\)

Now, you find the fractional portion by multiplying \(\displaystyle \small 0.85714285714286\) by \(\displaystyle \small 7\), which when rounded gives you \(\displaystyle \small 6\).  (The quickest way to get \(\displaystyle \small 0.85714285714286\) in your calculator is to subtract \(\displaystyle \small 7\) from \(\displaystyle \small \small 7.85714285714286\).)  Thus, your answer is:

\(\displaystyle \small \small 7\frac{6}{7}\)

Use your calculator to your advantage.  You know that \(\displaystyle \small \frac{71}{6}\) is \(\displaystyle \small 11.83333333333333\).  This means that the mixed fraction equivalent must be of the form:

\(\displaystyle \small \small 11\frac{x}{6}\)

Now, you find the fractional portion by multiplying \(\displaystyle \small \small 0.83333333333333\) by \(\displaystyle \small \small 6\), which when rounded gives you \(\displaystyle \small \small 5\).  (The quickest way to get \(\displaystyle \small \small 0.83333333333333\) in your calculator is to subtract \(\displaystyle \small \small 11\) from \(\displaystyle \small 11.83333333333333\).)  Thus, your answer is:

\(\displaystyle \small 11\frac{5}{6}\)