Dividing fractions by a whole number isn't as hard as it looks. To divide a fraction by a whole number, all you have to do is to convert the whole number into a fraction, find the reciprocal of that fraction, and multiply the result by the first fraction. If you want to know how to do it, just follow these steps:
Steps
- Write the problem. The first step to dividing a fraction by a whole number is to simply write out the fraction followed by the division sign and the whole number you need to divide it by. Let's say we're working with the following problem: 2/3 ÷ 4.[1]
- Change the whole number into a fraction. To change a whole number into a fraction, all you have to do is place the number over the number 1. The whole number becomes the numerator and 1 becomes the denominator of the fraction. Saying 4/1 is really the same as saying 4, since you're just showing that the number includes "1" 4 times. The problem should read 2/3 ÷ 4/1.
- Dividing a fraction by another fraction is the same as multiplying that fraction by the reciprocal of the other fraction.
- Write the reciprocal of the whole number. To find the reciprocal of a number, simply switch the numerator and the denominator of the number. Therefore, to find the reciprocal of 4/1, simply switch the numerator and denominator so that the number becomes 1/4.
- Change the division sign into a multiplication sign. The problem should read 2/3 x 1/4.
- Multiply the numerators and denominators of the fractions. Therefore, 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, 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
- Simplify the fraction. To simply the fraction, you need to find the lowest common denominator, which means that you should divide both the numerator and denominator by any number that divides evenly into both numbers. Since 2 is the numerator, you should see if 2 divides evenly into 12 -- it does because 12 is even. Then, divide both the numerator and denominator by 2 to get the new numerator and denominator to get a simplified answer.
- 2 ÷ 2 = 1
- 12 ÷ 2 = 6
- The fraction 2/12 can be simplified to 1/6. This is your final answer.
Tips
- Here's a mnemonic, an easy way to remember how to do all of this. Remember the following: "Dividing fractions is easy as pie, flip the second number and multiply!"
- Another Variation of the above is KCF/KFC. Keep the first number. Change to multiplication. Flip the last number. Or F before C.
- If you cross-cancel before you multiply, you probably won't need to reduce to lowest terms because its already on its lowest term as you can see. In our example, before we multiply 2/3 × 1/4, we might notice that the first numerator (2) and the second denominator (4) have a common factor of 2, which we can cancel in advance. This changes the problem to 1/3 × 1/2, giving us 1/6 immediately and saving us the work of reducing the fraction at the end.
- If any of your fractions is negative, this method still applies; just make sure you keep track of the sign as you go through the steps.
- Do cross simplify before multiplying instead of simplifying at the end.
Warnings
- Only take the reciprocal of the second fraction, the one you're dividing by. Don't change the first one, the one you're dividing into. In our example, we converted the 4/1 to 1/4, but we left the 2/3 as 2/3 (we didn't change it to 3/2).
Related Articles
Sources and Citations
What links here
- Read more ...
