Mixed number division Online Quiz

Answer : B

Explanation

Step 1:

First, we write the mixed number $6\frac{1}{3}$ as an improper fraction.

$6\frac{1}{3} = \frac{\left ( 6 \times 3 + 1 \right )}{3} = \frac{19}{3}$

Step 2:

$9 \div 6\frac{1}{3} = \frac{9}{1} \div \frac{19}{3} = \frac{9}{1} \times \frac{3}{19}$

Multiplying numerators and denominators

$\frac{9}{1} \times \frac{3}{19} = \frac{(9 \times 3)}{(1 \times 19)} = \frac{27}{19}$

Step 3:

$\frac{27}{19}$ can be written as a mixed number as follows

$\frac{27}{19} = 1\frac{8}{19}$

Step 4:

So, $9 \div 6\frac{1}{3} = 1\frac{8}{19}$

Answer : A

Explanation

Step 1:

First, we write the mixed number $8\frac{1}{5}$ as an improper fraction.

$8\frac{1}{5} = \frac{\left ( 8 \times 5 + 1 \right )}{5} = \frac{41}{5}$

Step 2:

$11 \div 8\frac{1}{5} = \frac{11}{1} \div \frac{41}{5} = \frac{11}{1} \times \frac{5}{41}$

Multiplying numerators and denominators

$\frac{11}{1} \times \frac{5}{41}= \frac{(11 \times 5)}{(1 \times 41)} = \frac{55}{41}$

Step 3:

$\frac{55}{41}$ can be written as a mixed number as follows

$\frac{55}{41} = 1\frac{14}{41}$

Step 4:

So, $11 \div 8\frac{1}{5} = 1\frac{14}{41}$

Answer : C

Explanation

Step 1:

First, we write the mixed number $3\frac{1}{3}$ as an improper fraction.

$3\frac{1}{3} = \frac{\left ( 3 \times 3 + 1 \right )}{3} = \frac{10}{3}$

Step 2:

$7 \div 3\frac{1}{3} = \frac{7}{1} \div \frac{10}{3} = \frac{7}{1} \times \frac{3}{10}$

Multiplying numerators and denominators

$\frac{7}{1} \times \frac{3}{10} = \frac{(7 \times 3)}{(1 \times 10)} = \frac{21}{10}$

Step 3:

$\frac{21}{10}$ can be written as a mixed number as follows

$\frac{21}{10} = 2\frac{1}{10}$

Step 4:

So, $7 \div 3\frac{1}{3} = 2\frac{1}{10}$

Answer : D

Explanation

Step 1:

First, we write the mixed number $5\frac{1}{6}$ as an improper fraction.

$5\frac{1}{6} = \frac{\left ( 5 \times 6 + 1 \right )}{6} = \frac{31}{6}$

Step 2:

$\frac{8}{9} \div 5\frac{1}{6} = \frac{8}{9} \div \frac{31}{6} = \frac{8}{9} \times \frac{6}{31}$

Multiplying numerators and denominators

$\frac{8}{9} \times \frac{6}{31} = \frac{(8 \times 6)}{(9 \times 31)} = \frac{48}{279} = \frac{16}{93}$

Step 3:

So, $\frac{8}{9} \div 5\frac{1}{6} = \frac{16}{93}$

Answer : C

Explanation

Step 1:

First, we write the mixed number $6\frac{2}{5}$ as an improper fraction.

$6\frac{2}{5} = \frac{\left ( 6 \times 5 + 2 \right )}{5} = \frac{32}{5}$

Step 2:

$\frac{19}{5} \div 6\frac{2}{5} = \frac{19}{5} \div \frac{32}{5} = \frac{19}{5} \times \frac{5}{32}$

Multiplying numerators and denominators

$\frac{19}{5} \times \frac{5}{32} = \frac{(19 \times 5)}{(5 \times 32)} = \frac{19}{32}$

Step 3:

So, $\frac{19}{5} \div 6\frac{2}{5} = \frac{19}{32}$

Answer : A

Explanation

Step 1:

First, we write the mixed number $3\frac{5}{6}$ as an improper fraction.

$3\frac{5}{6} = \frac{\left ( 3 \times 6 + 5 \right )}{6} = \frac{23}{6}$

Step 2:

$\frac{13}{8} \div 3\frac{5}{6} = \frac{13}{8} \div \frac{23}{6} = \frac{13}{8} \times \frac{6}{23}$

Multiplying numerators and denominators

$\frac{13}{8} \times \frac{6}{23} = \frac{(13 \times 6)}{(8 \times 23)} = \frac{39}{92}$

Step 3:

So, $\frac{13}{8} \div 3\frac{5}{6} = \frac{39}{92}$

Answer : B

Explanation

Step 1:

First, we write the mixed numbers as improper fractions.

$9\frac{1}{3} = \frac{\left ( 9 \times 3 + 1 \right )}{3} = \frac{28}{3}$

$4\frac{1}{4} = \frac{\left ( 4 \times 4 + 1 \right )}{4} = \frac{17}{4}$

Step 2:

$9\frac{1}{3} \div 4\frac{1}{4} = \frac{28}{3} \div \frac{17}{4} = \frac{28}{3} \times \frac{4}{17}$

Multiplying numerators and denominators

$\frac{28}{3} \times \frac{4}{17} = \frac{(28 \times 4)}{(3 \times 17)} = 1\frac{12}{51}$

Step 3:

$1\frac{12}{51}$ can be written as a mixed number as follows

$1\frac{12}{51} = 2\frac{10}{51}$

Step 4:

So, $9\frac{1}{3} \div 4\frac{1}{4} = 2\frac{10}{51}$

Answer : D

Explanation

Step 1:

First, we write the mixed numbers as improper fractions.

$10\frac{3}{4} = \frac{\left ( 10 \times 4 + 3 \right )}{4} = \frac{43}{4}$

$7\frac{1}{4} = \frac{\left ( 7 \times 4 + 1 \right )}{4} = \frac{29}{4}$

Step 2:

$10\frac{3}{4} \div 7\frac{1}{4} = \frac{43}{4} \div \frac{29}{4} = \frac{43}{4} \times \frac{4}{29}$

Multiplying numerators and denominators

$\frac{43}{4} \times \frac{4}{29}= \frac{(43 \times 4)}{(4 \times 29)} = \frac{43}{29}$

Step 3:

$\frac{43}{29}$ can be written as a mixed number as follows

$\frac{43}{29} = 1\frac{14}{29}$

Step 4:

So, $10\frac{3}{4} \div 7\frac{1}{4} = 1\frac{14}{29}$

Answer : A

Explanation

Step 1:

First, we write the mixed numbers as improper fractions.

$8\frac{1}{5} = \frac{\left ( 8 \times 5 + 1 \right )}{3} = \frac{41}{5}$

$9\frac{3}{5} = \frac{\left ( 9 \times 5 + 3 \right )}{5} = \frac{48}{5}$

Step 2:

$8\frac{1}{5} \div 9\frac{3}{5} = \frac{41}{5} \div \frac{48}{5} = \frac{41}{5} \times \frac{5}{48}$

Multiplying numerators and denominators

$\frac{41}{5} \times \frac{5}{48} = \frac{(41 \times 5)}{(5 \times 48)} = \frac{41}{48}$

Step 3:

So, $8\frac{1}{5} \div 9\frac{3}{5} = \frac{41}{48}$

Answer : B

Explanation

Step 1:

First, we write the mixed numbers as improper fractions.

$10\frac{1}{6} = \frac{\left ( 10 \times 6 + 1 \right )}{6} = \frac{61}{6}$

$7\frac{1}{3} = \frac{\left ( 7 \times 3 + 1 \right )}{3} = \frac{22}{3}$

Step 2:

$10\frac{1}{6} \div 7\frac{1}{3} = \frac{61}{6} \div \frac{22}{3} = \frac{61}{6} \times \frac{3}{22}$

Multiplying numerators and denominators

$\frac{61}{6} \times \frac{3}{22} = \frac{(61 \times 3)}{(6 \times 22)} = \frac{61}{44}$

Step 3:

$\frac{61}{44}$ can be written as a mixed number as follows

$\frac{61}{44} = 1\frac{17}{44}$

Step 4:

So, $10\frac{1}{6} \div 7\frac{1}{3} = 1\frac{17}{44}$