Dividing fractions by an integer is not as difficult as it sounds. To do this, all you need to do is convert the whole number to a fraction, find the reciprocal fraction of it, and multiply the result by the first fraction. If you want to know how to do this, just read this article.
Step 1. Write the problem
The first step in dividing a fraction by an integer is simply to write it down followed by the division symbol and the integer you want to divide by. Let's say we are working with the following problem: 2/3 ÷ 4.
Step 2. Turn the whole number into a fraction
To do this, all you need to do is place the number 1 under the whole number. That number will become the numerator and the 1 will become the denominator of the fraction. Saying 4/1 is the same as saying 4, since you're just saying that the number includes "1" 4 times. The problem should look like this: 2/3 ÷ 4/1.
Step 3. Dividing one fraction by another is the same as multiplying the fraction by the reciprocal of the other fraction
Step 4. Write the reciprocal of the whole number
To find the reciprocal of a number, just swap the numerator and the denominator of place. So, to find the reciprocal of 4/1, just swap the numerator with the denominator and the fraction will become 1/4.
Step 5. Change the sign of division to sign of multiplication
The problem should look like this: 2/3 x 1/4.
Step 6. Multiply the numerators and denominators of fractions
So the next step is to multiply the numerators and denominators of the fraction to get 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
To do this, you need to find the least common denominator, which means that you must divide both the numerator and numerator by any number that divides the two equally. Since 2 is the numerator, you should see if 2 divides 12 equally, because 12 is an even number. Then divide the numerator and denominator by 2 to get the simplified answer.
- 2 ÷ 2 = 1.
- 12 ÷ 2 = 6.
- The 2/12 fraction can be simplified to 1/6. This is your final answer.
- Here's a mnemonic, an easy way to remember how to do this. Remember the phrase: "Dividing fractions is as easy as walking, invert the second number and then just multiply!"
- Another variation of the previous tip is MTI/MIT. Keep the first number. Switch to multiplication. Invert the last number. Or I before T.
- If you cancel the numbers before multiplying, you probably won't need to reduce to the lowest common because they will already be that way. In our example, before we multiply 2/3 × 1/4, we can see that the first numerator (2) and second denominator (4) have a common factor of 2, which we can cancel out. This changes the problem to 1/3 × 1/2, giving us 1/6 immediately and saving us the trouble of reducing the fraction in the end.
- If any of your fractions are negative, this method still works; just put the signal correctly as you do the steps.
- Just get the reciprocal of the Monday fraction, the one you are dividing by. Don't change the first one, the one you're going to use to share. In our example, we convert 4/1 to 1/4, but we leave 2/3 as 2/3 (we don't change to 3/2).