How to divide a whole number by a mixed number?

To divide a whole number by a mixed number, follow these steps:

1. Convert to Improper Fractions: Express both the whole number and the mixed number as improper fractions. According to the reference, "Write the whole number and the mixed number as improper fractions with a division sign."

   • A whole number can be written as a fraction by putting it over 1 (e.g., 5 becomes 5/1).
   • To convert a mixed number to an improper fraction, multiply the whole number part by the denominator of the fractional part, add the numerator, and then put the result over the original denominator (e.g., 2 1/2 becomes (2*2 + 1)/2 = 5/2).

2. Invert the Divisor and Multiply: "Write the reciprocal of the divisor and replace the division sign with a multiplication sign." This means you flip the second fraction (the divisor) and change the division to multiplication. The reciprocal of a fraction is obtained by swapping its numerator and denominator (e.g., the reciprocal of 5/2 is 2/5).

3. Simplify (if possible): "Simplify the common factors if they exist." Look for common factors between the numerators and denominators and cancel them out to simplify the multiplication.

4. Multiply: Multiply the numerators together and the denominators together.

5. Simplify the Result (if necessary): If the resulting fraction is improper, convert it back to a mixed number.

Example:

Let's divide 6 by 2 1/4.

1. Convert to Improper Fractions:

   • 6 becomes 6/1
   • 2 1/4 becomes (2*4 + 1)/4 = 9/4
     So the problem becomes: 6/1 ÷ 9/4

2. Invert and Multiply:

   • The reciprocal of 9/4 is 4/9
   • The problem now becomes: 6/1 * 4/9

3. Simplify:

   • 6 and 9 have a common factor of 3. Divide both by 3: 6/3 = 2 and 9/3 = 3
   • The problem becomes: 2/1 * 4/3

4. Multiply:

   • (2 4) / (1 3) = 8/3

5. Simplify:

   • 8/3 converts to the mixed number 2 2/3

Therefore, 6 ÷ 2 1/4 = 2 2/3.