Dividing a fraction by a whole number isn't as difficult as it sounds - all you have to do is convert the whole number to a fraction, find its reciprocal, and multiply the result by the first fraction. If you want to know how, just follow these steps.
Steps
Step 1. Write down the problem
The first step in dividing a fraction by a whole number is to simply write the fraction followed by the division sign and the whole number you need to divide it by. Suppose we are working on the following problem: 2/3 ÷ 4.
Step 2. Change the integer to a fraction of
To change an integer to a fraction, all you have to do is put the number above the number 1. The integer becomes the numerator and the denominator of the fraction is 1. Saying 4/1 is really the same as saying 4, since you are just by showing that the number includes four times "1". The problem should become 2/3 ÷ 4/1.
Step 3. Dividing one fraction by another is the same as multiplying that fraction by the reciprocal of the second
Step 4. Write the reciprocal of the whole number
To find the reciprocal of a number, simply swap the numerator with the denominator. Therefore, to find the reciprocal of 1/4, by reversing the numerator and denominator, the number becomes 1/4.
Step 5. Change the division sign to the multiplication sign
The problem should have become 2/3 x 1/4.
Step 6. Multiply the numerators and denominators of the fractions
Therefore, the next step is to multiply the numerators and denominators of the two fractions to get the new numerator and denominator of the final answer.
- To multiply the numerators, just multiply 2 x 1 to get 2.
- To multiply the denominators, just multiply 3 x 4 to get 12.
- 2/3 x 1/4 = 2/12
Step 7. Simplify the fraction
You need to find the greatest common denominator, which means you should find that number that exactly divides the numerator and denominator. Since 2 is the numerator, you should see if 2 is exactly 12 - sure, because 12 is even. Now, divide the numerator and denominator by 2 to get the simplified fraction.
- 2 ÷ 2 = 1
- 12 ÷ 2 = 6
- You can simplify the fraction 2/12 to 1/6. This is the final answer.
Advice
- Here is an easy way to remember how to do all of this. Remember the rhyme: "dividing fractions is easy to do, flip the second number and multiply!"
- Another variation above is to hold the first number, flip the last one and multiply
- If you simplify crosswise before multiplying, you probably won't need to reduce the fraction to its lowest terms because it will already contain the simplified numbers. In our example, multiplying 2/3 × 1/4, we can see that the first numerator (2) and the second denominator (4) have a common factor of 2, which we can cancel out in advance. This changes the problem, which becomes 1/3 × 1/2, giving us 1/6 immediately and saving us the work of reducing the fraction at the end.
- If any fraction is negative, this method can still be applied - just make sure you keep track of the mark in all the steps.
