Divide Mixed Fractions with whole numbers

Whole numbers: Whole numbers are natural numbers including zero.

Mixed fraction: A “Mixed Fraction” is a combination of a whole number and a proper fraction.

How to divide fractions by mixed Fraction

A number is divided by 1 is the number itself, so convert the whole number into a fraction write the whole number in the fractional form, by placing ‘1’ in the denominator.

Let us see the steps to divide a given mixed fraction with a whole number given below.

Step 1: Convert the given mixed fraction and whole number as into improper fraction.

Step2: Change division sign to multiply sign and multiply by the reciprocal of the divisor.

Step 4: Simplify/reduce the answer if needed/possible.

Let us understand with an example.

Example1: Solve: 4 1/2 ÷ 2

Convert mixed fraction into improper fraction.

4 1/2 = [(2 x 4) + 1]/2

= (8 + 1)/2

= 9/2

Here, 2 is a whole number that can be written as 2/1,

Now the question is multiply 9/2 ÷ 2/1

We can divide it as a regular fraction.

reciprocal of the divisor 2 is 1/2

= (9/2 x 1/2)

= (9 x 1)/(2 x 2)

= 9/4

Simplify/reduce if needed/possible.

Therefore, 4 1/2 ÷ 2 = 9/4

Example2: Solve 1 7/3 ÷ 9

Convert mixed fraction into improper fraction.

1 7/3 = [(3 x 1) + 7]/3

= (3 + 7)/3

= 10/3

Here, 9 is a whole number that can be written as 9/1,

Now our problem is 10/3 ÷ 9/1

reciprocal of the divisor 9/1 is 1/9.

Multiply by 1/9

= (10/3 x 1/9)

= (10 x 1)/(3 x 9)

∴ (10 x 1)/(3 x 9) = 10/27

= (10)/(27)

Simplify/reduce if needed/possible.

Therefore, 1 7/3 ÷ 9/1 = 10/27

Example3: Divide 3 3/5 ÷ 6

Convert mixed fraction into improper fraction.

3 3/5 = [(5 x 3) + 3]/5

= (15 + 3)/5

= 18/5

Here, 6 is a whole number that can be written as 6/1,

Now problem is 18/5 ÷ 6/1

= 18/5 ÷ 6/1

reciprocal of the divisor 6/1 is 1/6.

Multiply by the reciprocal of the divisor.

= 18/5 x 1/6

= (18 x 1)/(5 x 6)

= 18 ÷ 30

Simplify/reduce if needed/possible.

= 18 ÷ 30 = 3/5

Therefore, 3 3/5 ÷ 6 = 3/5

Example4: Divide 5 3/4 ÷ 5

Convert mixed fraction into improper fraction.

5 3/4 = [(4 x 5) + 3]/4

= (20 + 3)/4

= 23/4

Here, 5 is a whole number that can be written as 5/1,

Now problem is 23/4 ÷ 5/1

= 23/4 ÷ 5/1

reciprocal of the divisor 5/1 is 1/5.

Multiply by the reciprocal of the divisor.

= 23/4 x 1/5

= (23 x 1)/(4 x 5)

= 23 ÷ 20

Simplify/reduce if needed/possible.

= 23 ÷ 20 = 23/20

Therefore, 5 3/4 ÷ 5 = 23/20