In this post we will learn how to multiply fractions with mixed number.

First we will understand the concept behind the calculation and then will see the exact steps to multiply the mixed numbers, After that we will move on to solve questions related to the concept.

**Understanding Mixed Number Multiplication**

Suppose you have been asked to multiply following numbers

In the given multiplication, one is mixed number and other is whole number

Let us first understand what does mixed number signifies with the help of pie chart

**Mixed Number Explanation**

We know that mixed number is made of whole number and fraction

In the mixed number:

1 ⟹ full pie

1/7 ⟹ one part of the pie which is divided into 7 parts

**Mixed Number into Fraction**

Convert the mixed number into improper fraction

Representing 8/7 in the form of pie

Now multiply the improper fraction with the whole number

**Multiplication of Fractions**

Writing 16/7 in the form of mixed fraction

Representing mixed number in the form of pie

I hope you have now understood what happens when we multiply mixed number with another number.

Let us now understand exact steps when we multiply mixed number with another mixed number

**Steps to Multiply Mixed Numbers**

Suppose two mixed numbers are given

To multiply mixed number do the following steps:

**Step 01****Convert the mixed number into improper fractio**n

**Step 02****Multiply the numerator**

**Step 03Multiply the denominator**

**Step 04****Simplify the fraction**

Reduce the numerator and denominator to its lowest terms.

Here divide the numerator and denominator by 3

Hence 7/2 is the solution of given multiplication

**Step 05**

Convert the solution into mixed fraction

Hence 3(1/2) is the solution

If you have understood the above steps, you can easily solve the question in one line

Let us look at another example of fraction multiplication

**Example 02**

**Step 01**

Convert the mixed number into improper fraction

**Step 02**

Multiply the numerator and denominator separately

**Step 03**

Simplify the fraction

For fraction 169/6, further simplification is not possible

**Step 04**

Convert the fraction into mixed number

Hence, **28 (1/6) is the solution**

**Example 03**

Multiply the given mixed numbers

**Step 01Convert the mixed number into improper fraction**

**Step 02Multiply the numerators and denominators separately**

**Step 03Simplify the fraction**

Divide numerator and denominator by 3

**Step 04Convert the fraction into mixed number**

Hence 30 (4/5) is the solution

Now you have understood the method, Its time to solve some questions related to multiplication of fractions.

**Mixed Number Multiplication Worksheet**

Below is the collection of mixed number multiplication questions.

All the questions are to the standard of Grade 5 and are provided with detailed solution.

Take out pen and paper and try solving each of the given questions

**Multiplication of Mixed Number**

Two mixed numbers are provided in the question.

Your job is to find the right answer in the form of mixed fraction

(01) Calculate the multiplication of fractions

1\frac{2}{4} \ \times \ 3\frac{5}{6} \\\ \\
Read Solution

Step 01

Convert the mixed number into improper fraction

\Longrightarrow \ \frac{6}{4} \ \times \frac{23}{6}

Step 02

Multiply numerator and denominator separately

\Longrightarrow \ \frac{6\times 23}{4\times 6}\\\ \\ \Longrightarrow \ \frac{138}{24}

Step 03

Simplify the fraction

Divide numerator and denominator by 6

Step 04

Convert the fraction into mixed number

**hence 5(3/4) is the solution**

(02) Find the product of below fractions

3\frac{1}{4} \ \times \ 3\frac{2}{9} \\\ \\
Read Solution

Step 01

Convert the mixed number into improper fraction

\Longrightarrow \ \frac{13}{4} \ \times \frac{29}{9}

Step 02

Multiply numerator and denominator separately

\Longrightarrow \ \frac{13\times 29}{4\times 9}\\\ \\ \Longrightarrow \ \frac{377}{36}

Step 03

Simplify the fraction

The fraction cannot be divided further

Step 04

Convert the fraction into mixed number

**Hence 10(17/36) is the solution**

(03) 2\frac{1}{2} \ \times \ 4\frac{1}{4} \\\ \\
Read Solution

Step 01

Convert the mixed number into improper fraction

\Longrightarrow \ \frac{5}{2} \ \times \frac{17}{4}

Step 02

Multiply numerator and denominator separately

\Longrightarrow \ \frac{5\times 17}{2\times 4}\\\ \\ \Longrightarrow \ \frac{85}{8}

Step 03

Simplify the fraction

The fraction cannot be divided further

Step 04

Convert the fraction into mixed number

**Hence 10(5/8) is the solution**

(04) 7\frac{2}{4} \ \times \ 5\frac{3}{5} \\\ \\ Read Solution

Step 01

Convert the mixed number into improper fraction

\Longrightarrow \ \frac{30}{4} \ \times \frac{28}{5}

Step 02

Multiply numerator and denominator separately

\Longrightarrow \ \frac{30\times 28}{4\times 5}\\\ \\ \Longrightarrow \ \frac{840}{20}

Step 03

Simplify the fraction

Divide the numerator and denominator by 20

**Hence 42 is the solution**

(05) 11\frac{1}{6} \ \times \ 6\frac{3}{4} \\\ \\ Read Solution

Step 01

Convert the mixed number into improper fraction

\Longrightarrow \ \frac{67}{6} \ \times \frac{27}{4}

Step 02

Multiply numerator and denominator separately

\Longrightarrow \ \frac{67\times 27}{6\times 4}\\\ \\ \Longrightarrow \ \frac{1809}{24}

Step 03

Simplify the fraction

Divide the numerator and denominator by 3

Step 04

Convert the fraction into mixed number

**Hence 75 (3/8) is the solution**

(06) 1\frac{5}{8} \ \times \ 2\frac{6}{8} \\\ \\ Read Solution

Step 01

Convert the mixed number into improper fraction

\Longrightarrow \ \frac{13}{8} \ \times \frac{22}{8}

Step 02

Multiply numerator and denominator separately

\Longrightarrow \ \frac{13\times 22}{8\times 8}\\\ \\ \Longrightarrow \ \frac{286}{64}

Step 03

Simplify the fraction

Divide numerator and denominator by 2

Step 04

Convert the fraction into mixed number

Hence **4(15/32) is the solution**

(07) 5\frac{3}{12} \ \times \ 4\frac{1}{9} \\\ \\

Read Solution

Step 01

Convert the mixed number into improper fraction

\Longrightarrow \ \frac{63}{12} \ \times \frac{37}{9}

Step 02

Multiply numerator and denominator separately

\Longrightarrow \ \frac{63\times 37}{12\times 9}\\\ \\ \Longrightarrow \ \frac{2331}{108}

Step 03

Simplify the fraction

Divide numerator and denominator by 9

Step 04

Convert the fraction into mixed number

Hence **21(7/12) is the solution**

(08) 1\frac{1}{2} \ \times \ 1\frac{1}{6} \\\ \\

Read Solution

Step 01

Convert the mixed number into improper fraction

\Longrightarrow \ \frac{3}{2} \ \times \frac{7}{6}

Step 02

Multiply numerator and denominator separately

\Longrightarrow \ \frac{3\times 7}{2\times 6}\\\ \\ \Longrightarrow \ \frac{21}{12}

Step 03

Simplify the fraction

Divide numerator and denominator by 3

Step 04

Write the fraction into the form of mixed number

**1(3/4) is the solution**

**Find the multiplication of Mixed Numbers in Fraction form**

Here two mixed numbers are provided in the question.

Your job is to do the multiplication and find the answer in the form of improper fraction

(01) 2\frac{1}{2} \ \times \ 2\frac{7}{2} \\\ \\ Read Solution

\Longrightarrow \ \frac{5}{2} \ \times \frac{11}{2} \\\ \\ \Longrightarrow \ \frac{5\times 11}{2\times 2}\\\ \\ \Longrightarrow \ \frac{55}{4} \\\ \\

(02) 1\frac{9}{3} \ \times \ 1\frac{8}{2} \\\ \\ Read Solution

\Longrightarrow \ \frac{12}{3} \ \times \frac{10}{2} \\\ \\ \Longrightarrow \ \frac{12\times 10}{3\times 2}\\\ \\ \Longrightarrow \ \frac{120}{6} \\\ \\

Divide numerator and denominator by 6

20 is the solution of this problem

(03) 3\frac{1}{3} \ \times \ 1\frac{4}{10} \\\ \\
Read Solution

\Longrightarrow \ \frac{10}{3} \ \times \frac{14}{10} \\\ \\ \Longrightarrow \ \frac{10\times 14}{3\times 10}\\\ \\ \Longrightarrow \ \frac{30}{140} \\\ \\

Divide numerator and denominator by 10

3/14 is the solution of given problem

(04) 4\frac{2}{3} \ \times \ 5\frac{6}{2} \\\ \\ Read Solution

\Longrightarrow \ \frac{14}{3} \ \times \frac{16}{2} \\\ \\ \Longrightarrow \ \frac{14\times 16}{3\times 2}\\\ \\ \Longrightarrow \ \frac{224}{6} \\\ \\

Dividing numerator and denominator by 2

112/3 is the solution of the above problem

(05) 2\frac{5}{6} \ \times \ 3\frac{5}{10} \\\ \\ Read Solution

\Longrightarrow \ \frac{17}{6} \ \times \frac{35}{10} \\\ \\ \Longrightarrow \ \frac{17\times 35}{6\times 10}\\\ \\ \Longrightarrow \ \frac{595}{60} \\\ \\

Dividing numerator and denominator by 5

119/12 is the solution

(06) 12\frac{1}{2} \ \times \ 11\frac{1}{2} \\\ \\ Read Solution

\Longrightarrow \ \frac{25}{2} \ \times \frac{23}{2} \\\ \\ \Longrightarrow \ \frac{25\times 23}{2\times 2}\\\ \\ \Longrightarrow \ \frac{529}{4} \\\ \\

529/4 cannot be further divided

Hence 529/4 is the solution

(07) 1\frac{5}{8} \ \times \ 2\frac{6}{8} \\\ \\ Read Solution

\Longrightarrow \ \frac{13}{8} \ \times \frac{22}{8} \\\ \\ \Longrightarrow \ \frac{13\times 22}{8\times 8}\\\ \\ \Longrightarrow \ \frac{286}{64} \\\ \\

Divide both numerator and denominator by 2

Hence 143/32 is the solution