Mixed number multiplication Online Quiz

Answer : A

Explanation

Step 1:

First, we write the mixed number $2\frac{3}{5}$ as an improper fraction

$2\frac{3}{5} = \frac{\left ( 2 \times 5 + 3 \right )}{5} = \frac{13}{5}$

Step 2:

$2\frac{3}{5} \times \frac{3}{4} = \frac{13}{5} \times \frac{3}{4} = \frac{(13 \times 3)}{(5 \times 4)} = \frac{39}{20}$

Step 3:

$\frac{39}{20}$ can be written as a mixed number as follows

$\frac{39}{20} = 1\frac{19}{20}$; So, $2\frac{3}{5} \times \frac{3}{4} = 1\frac{19}{20}$

Answer : C

Explanation

Step 1:

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

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

Step 2:

$3\frac{1}{5} \times \frac{3}{4} = \frac{16}{5} \times \frac{3}{4}$

Cross cancelling 16 and 4 we get

$\frac{16}{5} \times \frac{3}{4} = \frac{4}{5} \times \frac{3}{1} = \frac{(4 \times 3)}{(5 \times 1)} = \frac{12}{5}$

Step 3:

$\frac{12}{5}$ can be written as a mixed number as follows

$\frac{12}{5} = 2\frac{2}{5}$; So, $3\frac{1}{5} \times \frac{3}{4} = 2\frac{2}{5}$

Answer : B

Explanation

Step 1:

First, we write the mixed number $4\frac{2}{3}$ as an improper fraction

$4\frac{2}{3} = \frac{\left ( 4 \times 3 + 2 \right )}{3} = \frac{14}{3}$

Step 2:

$4\frac{2}{3} \times \frac{3}{5} = \frac{14}{3} \times \frac{3}{5}$

Cross cancelling 3 and 3 we get

$\frac{14}{3} \times \frac{3}{5} = \frac{14}{1} \times \frac{1}{5} = \frac{(14 \times 1)}{(1 \times 5)} = \frac{14}{5}$

Step 3:

$\frac{14}{5}$ can be written as a mixed number as follows

$\frac{14}{5} = 2\frac{4}{5}$; So, $4\frac{2}{3} \times \frac{3}{4} = 2\frac{4}{5}$

Answer : D

Explanation

Step 1:

First, we write the mixed number $3\frac{3}{4}$ as an improper fraction

$3\frac{3}{4} = \frac{\left ( 3 \times 4 + 3 \right )}{4} = \frac{15}{4}$

Step 2:

$3\frac{3}{4} \times \frac{3}{4} = \frac{15}{4} \times \frac{3}{4} = \frac{(15 \times 3)}{(4 \times 4)} = \frac{45}{16}$

Step 3:

$\frac{45}{16}$ can be written as a mixed number as follows

$\frac{45}{16} = 2\frac{13}{16}$; So, $3\frac{3}{4} \times \frac{3}{4} = 2\frac{13}{16}$

Answer : A

Explanation

Step 1:

First, we write the mixed number $6\frac{2}{3}$ as an improper fraction

$6\frac{2}{3} = \frac{\left ( 6 \times 3 + 2 \right )}{3} = \frac{20}{3}$

Step 2:

$6\frac{2}{3} \times \frac{3}{7} = \frac{20}{3} \times \frac{3}{7}$

Cross cancelling 3 and 3 we get

$\frac{20}{3} \times \frac{3}{7} = \frac{20}{1} \times \frac{1}{7} = \frac{(20 \times 1)}{(1 \times 7)} = \frac{20}{7}$

Step 3:

$\frac{20}{7}$ can be written as a mixed number as follows

$\frac{20}{7} = 2\frac{6}{7}$; So, $6\frac{2}{3} \times \frac{3}{7} = 2\frac{6}{7}$

Answer : C

Explanation

Step 1:

First, we write the mixed number $6\frac{3}{8}$ as an improper fraction

$6\frac{3}{8} = \frac{\left ( 6 \times 8 + 3 \right )}{8} = \frac{51}{8}$

Step 2:

$6\frac{3}{8} \times \frac{4}{5} = \frac{51}{8} \times \frac{4}{5}$

Cross cancelling 8 and 4 we get

$\frac{51}{8} \times \frac{4}{5} = \frac{51}{2} \times \frac{1}{5} = \frac{(51 \times 1)}{(2 \times 5)} = \frac{51}{10}$

Step 3:

$\frac{51}{10}$ can be written as a mixed number as follows

$\frac{51}{10} = 5\frac{1}{10}$; So, $6\frac{3}{8} \times \frac{4}{5} = 5\frac{1}{10}$

Answer : B

Explanation

Step 1:

First, we write the mixed number $8\frac{1}{4}$ as an improper fraction

$8\frac{1}{4} = \frac{\left ( 8 \times 4 + 1 \right )}{4} = \frac{33}{4}$

Step 2:

$8\frac{1}{4} \times \frac{2}{5} = \frac{33}{4} \times \frac{2}{5}$

Cross cancelling 4 and 2 we get

$\frac{33}{4} \times \frac{2}{5} = \frac{33}{2} \times \frac{1}{5} = \frac{(33 \times 1)}{(2 \times 5)} = \frac{33}{10}$

Step 3:

$\frac{33}{10}$ can be written as a mixed number as follows

$\frac{33}{10} = 3\frac{3}{10}$; So, $8\frac{1}{4} \times \frac{2}{5} = 3\frac{3}{10}$

Answer : D

Explanation

Step 1:

First, we write the mixed number $9\frac{4}{5}$ as an improper fraction.

$9\frac{4}{5} = \frac{\left ( 9 \times 5 + 4 \right )}{5} = \frac{49}{5}$

Step 2:

$9\frac{4}{5} \times \frac{5}{6} = \frac{49}{5} \times \frac{5}{6}$

$\frac{49}{5} \times \frac{5}{6} = \frac{49}{1} \times \frac{1}{6} = \frac{(49 \times 1)}{(1 \times 6)} = \frac{49}{6}$

Step 3:

$\frac{49}{6}$ can be written as a mixed number as follows

$\frac{49}{6} = 8\frac{1}{6}$; So, $9\frac{4}{5} \times \frac{5}{6} = 8\frac{1}{6}$

Answer : A

Explanation

Step 1:

First, we write the mixed number $4\frac{2}{3}$ as an improper fraction

$4\frac{2}{3} = \frac{\left ( 4 \times 3 + 2 \right )}{3} = \frac{14}{3}$

Step 2:

$4\frac{2}{3} \times \frac{3}{4} = \frac{14}{3} \times \frac{3}{4}$

Cross cancelling 3 and 3 and simplifying we get

$\frac{14}{3} \times \frac{3}{4} = \frac{7}{1} \times \frac{1}{2} = \frac{(7 \times 1)}{(1 \times 2)} = \frac{7}{2}$

Step 3:

$\frac{7}{2}$ can be written as a mixed number as follows

$\frac{7}{2} = 3\frac{1}{2}$; So, $4\frac{2}{3} \times \frac{3}{4} = 3\frac{1}{2}$

Answer : C

Explanation

Step 1:

First, we write the mixed number $8\frac{3}{4}$ as an improper fraction

$8\frac{3}{4} = \frac{\left ( 8 \times 4 + 3 \right )}{4} = \frac{35}{4}$

Step 2:

$8\frac{3}{4} \times \frac{2}{5} = \frac{35}{4} \times \frac{2}{5}$

Cross cancelling 35 and 5 and simplifying we get

$\frac{35}{4} \times \frac{2}{5} = \frac{7}{2} \times \frac{1}{1} = \frac{(7 \times 1)}{(2 \times 1)} = \frac{7}{2}$

Step 3:

$\frac{7}{2}$ can be written as a mixed number as follows

$\frac{7}{2} = 3\frac{1}{2}$; So, $8\frac{3}{4} \times \frac{2}{5} = 3\frac{1}{2}$