Multiplication of a mixed number and a whole number Online Quiz

Answer : B

Explanation

Step 1:

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

$4\frac{3}{8} = \frac{\left ( 4 \times 8 + 3 \right )}{8} = \frac{35}{8}$; $5 = \frac{5}{1}$

Step 2:

$4\frac{3}{8} \times 5 = \frac{35}{8} \times \frac{5}{1}$

Multiplying numerators and denominators

$\frac{35}{8} \times \frac{5}{1} = \frac{(35 \times 5)}{(8 \times 1)} = 1\frac{75}{8}$

Step 3:

$1\frac{75}{8}$ can be written as a mixed number as follows

$1\frac{75}{8} = 21\frac{7}{8}$;

Step 4:

So, $4\frac{3}{8} \times 5 = 21\frac{7}{8}$

Answer : C

Explanation

Step 1:

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

$5\frac{3}{5} = \frac{\left ( 5 \times 5 + 3 \right )}{5} = \frac{28}{5}$; $7 = \frac{7}{1}$

Step 2:

$5\frac{3}{5} \times 7 = \frac{28}{5} \times \frac{7}{1}$

Multiplying numerators and denominators

$\frac{28}{5} \times \frac{7}{1}= \frac{(28 \times 7)}{(5 \times 1)} = 1\frac{96}{5}$

Step 3:

$1\frac{96}{5}$ can be written as a mixed number as follows

$1\frac{96}{5} = 39\frac{1}{5}$

Step 4:

So, $5\frac{3}{5} \times 7 = 39\frac{1}{5}$

Answer : A

Explanation

Step 1:

First, we write the mixed number $4\frac{1}{5}$ as an improper fraction

$4\frac{1}{5} = \frac{\left ( 4 \times 5 + 1 \right )}{5} = \frac{21}{5} = \frac{21}{5}$; $9 = \frac{9}{1}$

Step 2:

$4\frac{1}{5} \times 9 = \frac{21}{5} \times \frac{9}{1}$

Multiplying numerators and denominators

$\frac{21}{5} \times \frac{9}{1} = \frac{(21 \times 9)}{(5 \times 1)} = \frac{189}{5}$

Step 3:

$\frac{189}{5}$ can be written as a mixed number as follows

$\frac{189}{5} = 37\frac{4}{5}$

Step 4:

So, $4\frac{1}{5} \times 9 = 37\frac{4}{5}$

Answer : D

Explanation

Step 1:

First, we write the mixed number $7\frac{1}{3}$ as an improper fraction

$7\frac{1}{3} = \frac{\left ( 7 \times 3 + 1 \right )}{3} = \frac{22}{3}$; $4 = \frac{4}{1}$

Step 2:

$7\frac{1}{3} \times 4 = \frac{22}{3} \times \frac{4}{1}$

Multiplying numerators and denominators

$\frac{22}{3} \times \frac{4}{1} = \frac{(22 \times 4)}{(3 \times 1)} = \frac{88}{3}$

Step 3:

$\frac{88}{3}$ can be written as a mixed number as follows

$\frac{88}{3} = 29\frac{1}{3}$

Step 4:

So, $7\frac{1}{3} \times 4 = 29\frac{1}{3}$

Answer : C

Explanation

Step 1:

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

$5\frac{2}{7} = \frac{\left ( 5 \times 7 + 2 \right )}{7} = \frac{37}{7}$; $8 = \frac{8}{1}$

Step 2:

$5\frac{2}{7} \times 8 = \frac{37}{7} \times \frac{8}{1}$

Multiplying numerators and denominators

$\frac{37}{7} \times \frac{8}{1} = \frac{(37 \times 8)}{(7 \times 1)} = \frac{296}{7}$

Step 3:

$\frac{296}{7}$ can be written as a mixed number as follows

$\frac{296}{7} = 42\frac{2}{7}$

Step 4:

So, $5\frac{2}{7} \times 8 = 42\frac{2}{7}$

Answer : A

Explanation

Step 1:

First, we write the mixed number $4\frac{1}{2}$ as an improper fraction.

$4\frac{1}{2} = \frac{\left ( 4 \times 2 + 1 \right )}{2} = \frac{9}{2}$; $9 = \frac{9}{1}$

Step 2:

$4\frac{1}{2} \times 9 = \frac{9}{2} \times \frac{9}{1}$

$\frac{9}{2} \times \frac{9}{1} = \frac{(9 \times 9)}{(2 \times 1)} = \frac{81}{2}$

Step 3:

$\frac{81}{2}$ can be written as a mixed number as follows

$\frac{81}{2} = 40\frac{1}{2}$; So, $4\frac{1}{2} \times 9 = 40\frac{1}{2}$

Answer : B

Explanation

Step 1:

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

$3\frac{1}{3} = \frac{\left ( 3 \times 3 + 1 \right )}{3} = \frac{10}{3}$; $8 = \frac{8}{1}$

Step 2:

$3\frac{1}{3} \times 8 = \frac{10}{3} \times \frac{8}{1}$

Multiplying numerators and denominators

$\frac{10}{3} \times \frac{8}{1} = \frac{(10 \times 8)}{(3 \times 1)} = \frac{80}{3}$

Step 3:

$\frac{80}{3}$ can be written as a mixed number as follows

$\frac{80}{3} = 26\frac{2}{3}$

Step 4:

So, $3\frac{1}{3} \times 8 = 26\frac{2}{3}$

Answer : D

Explanation

Step 1:

First, we write the mixed number $5\frac{1}{4}$ as an improper fraction

$5\frac{1}{4} = \frac{\left ( 5 \times 4 + 1 \right )}{4} = \frac{21}{4}$; $5 = \frac{5}{1}$

Step 2:

$5\frac{1}{4} \times 5 = \frac{21}{4} \times \frac{5}{1}$

Multiplying numerators and denominators

$\frac{21}{4} \times \frac{5}{1} = \frac{(21 \times 5)}{(4 \times 1)} = \frac{105}{4}$

Step 3:

$\frac{105}{4}$ can be written as a mixed number as follows

$\frac{105}{4} = 26\frac{1}{4}$

Step 4:

So, $5\frac{1}{4} \times 5 = 26\frac{1}{4}$

Answer : A

Explanation

Step 1:

First, we write the mixed number $7\frac{2}{3}$ as an improper fraction.

$7\frac{2}{3} = \frac{\left ( 7 \times 3 + 2 \right )}{3} = \frac{23}{3}$; $5 = \frac{5}{1}$

Step 2:

$7\frac{2}{3} \times 5 = 23//3 \times \frac{5}{1}$

Multiplying numerators and denominators

$\frac{23}{3} \times \frac{5}{1} = \frac{(23 \times 5)}{(3 \times 1)} = \frac{115}{3}$

Step 3:

$\frac{115}{3}$ can be written as a mixed number as follows

$\frac{115}{3} = 38\frac{1}{3}$

Step 4:

So, $7\frac{2}{3} \times 5 = 38\frac{1}{3}$

Answer : C

Explanation

Step 1:

First, we write the mixed number $5\frac{3}{8}$ as an improper fraction

$5\frac{3}{8} = \frac{\left ( 5 \times 8 + 3 \right )}{8} = \frac{43}{8}$; $4 = \frac{4}{1}$

Step 2:

$5\frac{3}{8} \times 4 = \frac{43}{8} \times \frac{4}{1}$

Multiplying numerators and denominators

$\frac{43}{8} \times \frac{4}{1} = \frac{(43 \times 4)}{(8 \times 1)} = \frac{172}{8}$

Step 3:

$\frac{172}{8}$ can be written as a mixed number as follows

$\frac{172}{8} = 21\frac{4}{8} = 21\frac{1}{2}$

Step 4:

So, $5\frac{3}{8} \times 4 = 21\frac{1}{2}$