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# Dividing Mixed Numbers – Methods & Examples

## How to Divide Mixed Numbers?

Mixed numbers consist of an integer followed by a fraction. It is initially an improper fraction, which then broken down into a mixed number form. Division of mixed numbers is very similar to the multiplication of the mixed numbers.

*Here are the steps followed when dividing mixed numbers:*

- Begin by converting each mixed fraction to an improper.
- Invert or flip upside down the improper fraction that is the divisor
- Multiply the first fraction by the second fraction. Multiplication of numerators and denominators are done separately.
- Convert the resultant fraction into a mixed number if it is improper.
- Simplify the mixed number to its lowest terms possible.

*Example 1*

Solve the following

1 ^{3}/_{4 }÷ 2 ^{2}/_{5}

__Solution__

- Convert each mixed number into improper fraction.

1 ^{3}/_{4 }= 7/4 and 2 ^{2}/_{5} = 12/5

- Now proceed with the division as:

1 ^{3}/_{4 }÷ 2 ^{2}/_{5} = 7/4 ÷ 12/5

- Determine the reciprocal of the second fraction as 5/12

7/4 ÷ 12/5 = 7/4 x 5/12

- Multiply the numerators together and denominators also together.

7/4 x 5/12= (5 x 7)/(12 x 4)

= 35/48

*Example 2*

Workout:

2 ¾ ÷ 1 ^{2}/_{3}

__Solution__

2 ¾ ÷ 1 2/3

= 11/4 ÷ 5/3

= 11/4 × 3/5

= (11 × 3)/(4 × 5)

= 33/20

= 1 ^{13}/_{20}

*Example 3*

Simplify the following,

2 ^{4}/_{17 }÷ 1 ^{4}/_{17}

__Solution__

2 ^{4}/_{17 }÷ 1 ^{4}/_{17}

= 38/17 ÷ 21/17

= 38/17 × 17/21

= (38 × 17)/(17 × 21)

= 646/357

= 38/21

= 1 ^{17}/_{21}

*Example 4*

Work out: 3 ^{1}/_{3 }÷ 1 ^{5}/_{6}

__Solution__

Step 1:

Convert each mixed number to an improper fraction.

3 ^{1}/_{3} = 10/3 and 1 ^{5}/_{6} = 11/6

Now, 3 ^{1}/_{3 }÷ 1 ^{5}/_{6 }= 10/3 ÷ 11/6

Step 2:

Invert the second fraction and change the operator to multiplication.

10/3 ÷ 11/6 = 10/3 x 6/11

Step 3:

Multiply the numerators at the top and denominators at the bottom.

10/3 x 6/11 = (10 x 6)/(11 x 3)

= 60/33

Step 4:

Simplify the answer.

Both the numerator and denominator have a common factor 3, and therefore simplify the fraction to its lowest terms.

60/33 = 20/11

Now convert the answer back to a mixed number.

20/11= 1 ^{9}/_{11}

Therefore, 3 ^{1}/_{3 }÷ 1 ^{5}/_{6} = 1 ^{9}/_{11}

*Example 5*

Work out: 4 ÷ 2 ^{1}/_{3}

__Solution__

Step 1:

Convert the mixed numbers into improper fractions.

2 ^{1}/_{3 }= 7/3

4 ÷ 2 ^{1}/_{3} = 4/1÷ 7/3

Step 2:

Find the reciprocal of the second fraction and change the operator to multiplication.

4/1÷ 7/3 = 4/1 x 3/7

Step 3:

Multiply the fractions

4 × 3/7 = 12/7

Step 4:

Simplify and convert.

Now convert the fraction back to a mixed number.

12/7 = 1 ^{5}/_{7}

*Example 6*

Two number have a product of 18. If one number is 8 ^{2}/_{5}, Calculate the value of the other number.

__Solution__

The product of the numbers = 18

One of the numbers = 8 ^{2}/_{5 }= {(8 × 5) + 2}/5 = 42/5

To find the value of the other number, divide 18 by the fraction.

= 18 ÷ 42/5 = 18 × 5/42

= 90/42

= 15/7

Therefore, the other number is:

= 2 ^{1}/_{7}

*Example 7*

A 25 m long pole is cut into logs of each 1 ^{2}/_{3 }meters. Calculate the total number of logs cut from the pole.

__Solution__

Total number of logs cut can be calculated by dividing 25 m by 1 ^{2}/_{3 }= 25 ÷ 1 ^{2}/_{3 }

= 25 ÷ 5/3

= 25 × 3/5

= 75/5

Therefore, the number of logs cut = 15