80% of a number is equal to \(\displaystyle \frac{4}{5}\) multiplied by that number, so 80% of \(\displaystyle \frac{55}{3}\) is 

\(\displaystyle \frac{4}{5} \times \frac{55}{3} = \frac{4}{1} \times \frac{11}{3} = \frac{44}{3}\)

Since \(\displaystyle 44 \div 3 = 14 \textup{ R }2\), 

\(\displaystyle \frac{44}{3} = 14 \frac{2}{3}\).

A number increased by 25% is 125%, or \(\displaystyle \frac{5}{4}\), multiplied by the number. \(\displaystyle \frac{32}{9}\) increased by 25% is therefore 

\(\displaystyle \frac{5}{4} \times \frac{32}{9} = \frac{5}{1} \times \frac{8}{9} = \frac{40} {9}\)

\(\displaystyle 40 \div 9 = 4 \textup{ R }4\), so

\(\displaystyle \frac{40} {9} = 4 \frac{4}{9}\)

Decreasing a number by 12.5% is the same as taking 87.5% of a number, or multiplying it by

\(\displaystyle \frac{87.5}{100} = \frac{87.5 \div 12.5 }{100\div 12.5} = \frac{7}{8}\).

\(\displaystyle \frac{7}{8} \times \frac{88}{21} = \frac{11}{3}\)

\(\displaystyle 11 \div 3 = 3\textup{ R }2\), so

\(\displaystyle \frac{11}{3} = 3\frac{2}{3}\)

To convert from a fraction to a mixed number we must find out how many times the denominator goes into the numerator using division and the remainder becomes the new fraction. 

\(\displaystyle \frac{34}{5} = 6\ r 4 \ so \6\frac{4}{5}\) 

Divide the numerator by the denominator.

\(\displaystyle 91\div4=22 R 3\)

Now, the whole number part will be \(\displaystyle 22\). Write the remainder on top of the denominator to get the fraction.

\(\displaystyle \frac{91}{4}=22\frac{3}{4}\)

The numerator of the improper form of a mixed fraction is the original numerator added to the product of the integer and the original denominator:

\(\displaystyle 5 \times 7 + 4 = 35 + 4 = 39\)

\(\displaystyle \frac{9}{12}\), in lowest terms, is \(\displaystyle \frac{9}{12} = \frac{9 \div 3}{12\div 3} = \frac{3}{4}\), so \(\displaystyle 5\frac{9}{12}\) is rewritten as \(\displaystyle 5\frac{3}{4}\).

The numerator of the improper form of a mixed fraction is the original numerator added to the product of the integer and the original denominator. The new denominator is the same as the old one. Therefore, 

\(\displaystyle 5\frac{3}{4} = \frac{5 \times 4+ 3}{4} = \frac{23}{4}\),

Add the numerator and the denominator: \(\displaystyle 23+4 = 27\).

The correct response is \(\displaystyle 25 < N \le 30\).

\(\displaystyle \frac{16}{20}\) in lowest terms is \(\displaystyle \frac{16 \div 4}{20 \div 4} = \frac{4}{5}\), so first, rewrite \(\displaystyle 8\frac{16}{20}\) as \(\displaystyle 8\frac{4}{5}\).

The numerator of the improper form of a mixed fraction is the original numerator added to the product of the integer and the original denominator:

\(\displaystyle 8 \times 5 + 4 = 40 + 4 = 44\)

The correct response is \(\displaystyle 40 < N \le 50\).

The numerator of the improper form of a mixed fraction is the original numerator added to the product of the integer and the original denominator. The new denominator is the same as the old one. Therefore, 

\(\displaystyle 7\frac{3}{8} = \frac{7 \times 8 + 3}{8} = \frac{56+3}{8}= \frac{59}{8}\)

Add the numerator and the denominator: \(\displaystyle 59+8 = 67\)

To change a mixed fraction into an improper fraction, keep the denominator the same.

To find the numerator, multiply the whole number part of the mixed fraction by the denominator, then add that value to the numerator.

\(\displaystyle 6\frac{4}{7}=\frac{6\times7+4}{7}=\frac{46}{7}\)