How to Divide Whole Numbers by Mixed Numbers | Dividing Mixed Numbers | MathOGuide

How to Divide Whole Numbers by Mixed Numbers | Dividing Mixed Numbers | MathOGuide

Dividing whole numbers by mixed numbers can seem tricky at first, but it's manageable if you break it down into steps.

Here's how to do it:

Step 1: Convert the Mixed Number to an Improper Fraction:

A mixed number consists of a whole number and a fraction (e.g., (2 whole 1/3).
To convert this to an improper fraction:Multiply the whole number by the denominator of the fraction.
Add the numerator of the fraction to this result.
Place this sum over the original denominator.

For example, to convert (2 whole 1/3) to an improper fraction:
Multiply (2*3 = 6)
Add the numerator: (6 + 1 = 7)
The improper fraction is (7/3).

Step 2: Write the Division as Multiplication by the Reciprocal:

When dividing by a fraction, you can multiply by the reciprocal of that fraction. The reciprocal is simply the fraction flipped upside down (i.e., numerator and denominator are swapped).

For example, if you're dividing 10 by (7/3), rewrite this as:
{10 ÷ (7/3)}
= 10 * (3/7)

Step 3:
Multiply the Whole Number by the Reciprocal

Now multiply the whole number by the reciprocal of the improper fraction:
10 * (3/7)
= {10*3}/{7}
= 30/7

Step 4: Simplify the Fraction:

If possible, simplify the resulting fraction by dividing the numerator and denominator by any common factors.

In this example, 30/7 is already in its simplest form.

Step 5: (Optional) Convert Back to a Mixed Number:

If you want the answer as a mixed number instead of an improper fraction,
divide the numerator by the denominator:
[30 ÷ 7 = 4] remainder (2) So,
(30/7) can be written as
(4 whole 27).

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