# Multiplying Mixed Numbers

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 fraction

Step 02
Multiply the numerator

Step 03
Multiply 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 01
Convert the mixed number into improper fraction

Step 02
Multiply the numerators and denominators separately

Step 03
Simplify the fraction

Divide numerator and denominator by 3

Step 04
Convert 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} \\\ \\

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} \\\ \\

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