Dividing a mixed number by a whole number can seem a bit tricky at first, but once you understand the steps, it becomes straightforward! Let’s break it down step by step.
Step 1: Convert the Mixed Number to an Improper Fraction
A mixed number consists of a whole number and a fraction. To make calculations easier, convert the mixed number to an improper fraction. For example, if you have the mixed number 2 1/3:
- Multiply the whole number by the denominator: 2 x 3 = 6.
- Add the numerator to this result: 6 + 1 = 7.
- Put this sum over the original denominator: 7/3.
So, 2 1/3 becomes 7/3.
Step 2: Write the Whole Number as a Fraction
Next, we need to express the whole number as a fraction. For example, if you are dividing by 4, you can write 4 as 4/1.
Step 3: Multiply by the Reciprocal
Now, instead of dividing, we will multiply by the reciprocal of the whole number. The reciprocal of a fraction is simply flipping the numerator and denominator. In our case, the reciprocal of 4/1 is 1/4.
So, our problem of dividing 7/3 by 4/1 becomes:
(7/3) ÷ (4/1) = (7/3) x (1/4)Step 4: Carry Out the Multiplication
Now we multiply the fractions:
(7 x 1) / (3 x 4) = 7 / 12So, 2 1/3 divided by 4 equals 7/12.
Step 5: Convert Back to a Mixed Number (if necessary)
If you prefer your answer in mixed number form and the result is an improper fraction, you can convert it back:
- Divide the numerator by the denominator: 7 ÷ 12 = 0 remainder 7, which is already a proper fraction.
Thus, your final result is 7/12.
In summary, to divide a mixed number by a whole number, you:
- Convert the mixed number to an improper fraction.
- Write the whole number as a fraction.
- Multiply by the reciprocal of the whole number.
- Simplify the result if possible.
And that’s it! With practice, this process will become easy and intuitive!