Division of a Fraction by a Whole Number

Division of a Fraction by a Whole Number

Steps to Divide a Fraction by a Whole Number

1. Convert the Whole Number to an Improper Fraction:

   • To perform the division of a fraction by a whole number, first convert the whole number into an improper fraction by placing it over one. For example, if you have the whole number 5, it would be represented as:
     $5 = \frac{5}{1}$

2. Change the Division to Multiplication:

   • Once the whole number is expressed as an improper fraction, the next step is to change the operation from division to multiplication.

3. Invert the Second Fraction:

   • Following the change of operation, take the second fraction (which is now the improper fraction obtained from the whole number) and invert it (take its reciprocal). If the improper fraction is $\frac{5}{1}$, its reciprocal is:
     $\frac{1}{5}$

4. Find the Product:

   • Now, multiply the first fraction by the inverted second fraction. Therefore, if you are dividing a fraction $\frac{a}{b}$ by the whole number (represented as an improper fraction previously), the operation can be expressed as:
     $\frac{a}{b} \div \frac{5}{1} = \frac{a}{b} \times \frac{1}{5}$
   • In this scenario, the outcome will be:
     $\frac{a \times 1}{b \times 5} = \frac{a}{5b}$

Example

• If you want to divide $\frac{3}{4}$ by 2:
  1. Convert 2 to an improper fraction: $\frac{2}{1}$
  2. Change division to multiplication: $\frac{3}{4} \div \frac{2}{1} \rightarrow \frac{3}{4} \times \frac{1}{2}$
  3. Invert the second fraction: $\frac{1}{2}$
  4. Multiply: $\frac{3 \times 1}{4 \times 2} = \frac{3}{8}$

Conclusion

• The final result of dividing a fraction by a whole number involves converting the whole number into an improper fraction, converting the operation to multiplication, taking the reciprocal of the second fraction, and then performing the multiplication to arrive at the final answer. The overall method can be simply stated as:
  $\frac{a}{b} \div c = \frac{a}{bc}$ where c is the whole number. This procedure ensures clarity and accuracy in performing operations with fractions and whole numbers.