Division with a mixed number and a whole number Online Quiz

Answer : A

Explanation

Step 1:

First, we write the mixed number $5\frac{1}{3}$ as an improper fraction.

$5\frac{1}{3} = \frac{\left ( 5 \times 3 + 1 \right )}{3} = \frac{16}{3}$; $3 = \frac{3}{1}$

Step 2:

$5\frac{1}{3} \div 3 = \frac{16}{3} \div \frac{3}{1} = \frac{16}{3} \times \frac{1}{3}$

Multiplying numerators and denominators

$\frac{16}{3} \times \frac{1}{3} = \frac{(16 \times 1)}{(3 \times 3)} = \frac{16}{9}$

Step 3:

$\frac{16}{9}$ can be simplified and written as follows

$\frac{16}{9} = 1\frac{7}{9}$

Step 4:

So, $5\frac{1}{3} \div 3 = 1\frac{7}{9}$

Answer : D

Explanation

Step 1:

First, we write the mixed number $9\frac{1}{4}$ as an improper fraction.

$9\frac{1}{4} = \frac{\left ( 9 \times 4 + 1 \right )}{4} = \frac{37}{4}$; $8 = \frac{8}{1}$

Step 2:

$9\frac{1}{4} \div 8 = \frac{37}{4} \div \frac{8}{1} = \frac{37}{4} \times \frac{1}{8}$

Multiplying numerators and denominators

$\frac{37}{4} \times \frac{1}{8} = \frac{(37 \times 1)}{(4 \times 8)} = \frac{37}{32}$

Step 3:

$\frac{37}{32}$ can be simplified and written as follows

$\frac{37}{32} = 1\frac{5}{32}$

Step 4:

So, $9\frac{1}{4} \div 8 = 1\frac{5}{32}$

Answer : B

Explanation

Step 1:

First, we write the mixed number $5\frac{2}{7}$ as an improper fraction.

$5\frac{2}{7} = \frac{\left ( 5 \times 7 + 2 \right )}{7} = \frac{37}{7}$

Step 2:

$5\frac{2}{7} \div 4 = \frac{37}{7} \div \frac{4}{1} = \frac{37}{7} \times \frac{1}{4}$

Multiplying numerators and denominators

$\frac{37}{7} \times \frac{1}{4} = \frac{(37 \times 1)}{(7 \times 4)} = \frac{37}{28}$

Step 3:

$\frac{37}{28}$ can be simplified and written as follows

$\frac{37}{28} = 1\frac{9}{28}$; So, $5\frac{2}{7} \div 4 = 1\frac{9}{28}$

Answer : C

Explanation

Step 1:

First, we write the mixed number $9\frac{1}{8}$ as an improper fraction.

$9\frac{1}{8} = \frac{\left ( 9 \times 8 + 1 \right )}{8} = \frac{73}{8}$; $6 = \frac{6}{1}$

Step 2:

$9\frac{1}{8} \div 6 = \frac{73}{8} \div \frac{6}{1} = \frac{73}{8} \times \frac{1}{6}$

Multiplying numerators and denominators

$\frac{73}{8} \times \frac{1}{6} = \frac{(73 \times 1)}{(8 \times 6)} = \frac{73}{48}$

Step 3:

$\frac{73}{48}$ can be simplified and written as follows

$\frac{73}{48} = 1\frac{25}{48}$

Step 4:

So, $9\frac{1}{8} \div 6 = 1\frac{25}{48}$

Answer : B

Step 1:

First, we write the mixed number $10\frac{1}{6}$ as an improper fraction.

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

Step 2:

$10\frac{1}{6} \div 9 = \frac{61}{6} \div \frac{9}{1} = \frac{61}{6} \times \frac{1}{9}$

Multiplying numerators and denominators

$\frac{61}{6} \times \frac{1}{9} = \frac{(61 \times 1)}{(6 \times 9)} = \frac{61}{54}$

Step 3:

$\frac{61}{54}$ can be simplified and written as follows

$\frac{61}{54} = 1\frac{7}{54}$

Step 4:

So, $10\frac{1}{6} \div 9 = 1\frac{7}{54}$

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:

$6\frac{2}{5} \div 4 = \frac{32}{5} \div \frac{4}{1} = \frac{32}{5} \times \frac{1}{4}$

Multiplying numerators and denominators

$\frac{32}{5} \times \frac{1}{4} = \frac{(32 \times 1)}{(5 \times 4)} = \frac{32}{20}$

Step 3:

$\frac{32}{20}$ can be simplified and written as follows

$\frac{32}{20} = 1\frac{12}{20} = 1\frac{3}{5}$

Step 4:

So, $6\frac{2}{5} \div 4 = 1\frac{3}{5}$

Answer : A

Explanation

Step 1:

First, we write the mixed number $9\frac{1}{3}$ as an improper fraction.

$9\frac{1}{3} = \frac{\left ( 9 \times 3 + 1 \right )}{3} = \frac{28}{3}$; $5 = \frac{5}{1}$

Step 2:

$9\frac{1}{3} \div 5 = \frac{28}{3} \div \frac{5}{1} = \frac{28}{3} \times \frac{1}{5}$

Multiplying numerators and denominators

$\frac{28}{3} \times \frac{1}{5} = \frac{(28 \times 1)}{(3 \times 5)} = \frac{28}{15}$

Step 3:

$\frac{28}{15}$ can be simplified and written as follows

$\frac{28}{15} = 1\frac{13}{15}$

Step 4:

So, $9\frac{1}{3} \div 5 = 1\frac{13}{15}$

Answer : D

Explanation

Step 1:

First, we write the mixed number $7\frac{1}{4}$ as an improper fraction.

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

Step 2:

$7\frac{1}{4} \div 6 = \frac{29}{4} \div \frac{6}{1} = \frac{29}{4} \times \frac{1}{6}$

Multiplying numerators and denominators

$\frac{29}{4} \times \frac{1}{6} = \frac{(29 \times 1)}{(4 \times 6)} = \frac{29}{24}$

Step 3:

$\frac{29}{24}$ can be simplified and written as follows

$\frac{29}{24} = 1\frac{5}{24}$; So, $7\frac{1}{4} \div 6 = 1\frac{5}{24}$

Answer : C

Explanation

Step 1:

First, we write the mixed number $6\frac{2}{7}$ as an improper fraction.

$6\frac{2}{7} = \frac{\left ( 6 \times 7 + 2 \right )}{7} = \frac{44}{7}$; $5 = \frac{5}{1}$

Step 2:

$6\frac{2}{7} \div 5 = \frac{44}{7} \div \frac{5}{1} = \frac{44}{7} \times \frac{1}{5}$

Multiplying numerators and denominators

$\frac{44}{7} \times \frac{1}{5} = \frac{(44 \times 1)}{(7 \times 5)} = \frac{44}{35}$

Step 3:

$\frac{44}{35}$ can be simplified and written as follows

$\frac{44}{35} = 1\frac{9}{35}$

Step 4:

So, $6\frac{2}{7} \div 5 = 1\frac{9}{35}$

Answer : A

Explanation

Step 1:

First, we write the mixed number $11\frac{1}{8}$ as an improper fraction.

$11\frac{1}{8} = \frac{\left ( 11 \times 8 + 1 \right )}{8} = \frac{89}{8}$; $8 = \frac{8}{1}$

Step 2:

$11\frac{1}{8} \div 8 = \frac{89}{8} \div \frac{8}{1} = \frac{89}{8} \times \frac{1}{8}$

Multiplying numerators and denominators

$\frac{89}{8} \times \frac{1}{8} = \frac{(89 \times 1)}{(8 \times 8)} = \frac{89}{64}$

Step 3:

$\frac{89}{64}$ can be simplified and written as follows

$\frac{89}{64} = 1\frac{25}{64}$

Step 4:

So, $11\frac{1}{8} \div 8 = 1\frac{25}{64}$