Content

• To step
• Tips
• Warnings

Dividing fractions by a whole number is not as difficult as it seems. To divide a fraction by a whole number, all you have to do is make a fraction of the whole number, find the reverse of the fraction, and then multiply the result by the first fraction. If you want to know how, follow these steps:

To step

1. Write down the sum. The first step in dividing a fraction by a whole number is writing the fraction, followed by the division sign and the whole number to divide it by. Let's say we have to solve for the following sum: 2/3 ÷ 4.
2. Make a fraction of the whole number. To turn the whole number into a fraction, just put the number 1 below it. The whole number becomes the numerator, and the 1 becomes the denominator of the fraction. 4/1 is the same as 4, because you just show that you mean 4 times the number "1". So now the sum becomes 2/3 ÷ 4/1.
3. Dividing one fraction by another fraction is the same as multiplying that fraction by the reciprocal of the other fraction.
4. Write the reverse of the whole number. To find the reverse of a number, simply flip the numerator and denominator. So the reverse of 4/1 is 1/4.
5. Change the division sign to a multiplication sign. The sum now becomes 2/3 x 1/4.
6. Multiply the numerators and denominators of the fraction. The next step is to multiply the numerators and denominators of the fraction to get the new numerator and denominator of the final answer.
   • To multiply the numerators, do 2 x 1 to get 2.
   • To multiply the denominators, do 3 x 4 to get 12.
   • 2/3 x 1/4 = 2/12
7. Simplify the fraction. To simplify the fraction, you need to find the greatest common divisor (gcd). The gcd is the largest number so that two numbers, in this case the numerator and the denominator, are divisible. Since the numerator is 2, you have to see if 12 is divisible by 2 - and it is, because 12 is an even number. Divide both the numerator and denominator by 2 to get the new numerator and denominator, then you've simplified the fraction.
   • 2 ÷ 2 = 1
   • 12 ÷ 2 = 6
   • You can simplify the fraction 2/12 to 1/6. This is your final answer.

Tips

• Here's a mnemonic to make it easy to remember: "Divide by a fraction = multiply by the reverse!"
• You can also cross off numbers before multiplying, so you don't have to look for the gcd at the end. In our example, before we multiply 2/3 × 1/4, we can see that the first numerator (2) and the second denominator (4) match the factor of 2. If we now cross off against each other, we get 1/3 × 1/2, and now the result is 1/6 immediately.
• The method will still work if one of the fractions is negative, but keep an eye on the minus sign as you complete the steps. Keep in mind that in a fraction, the minus belongs to the numerator.
• Cross out the numbers for multiplication, instead of simplifying at the end.

Warnings

• Only turn the second fraction at step 3. Do not change the first fraction. In our example, we're changing 4/1 to 1/4, but we're leaving 2/3 intact (we're not changing it to 3/2).