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.
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. EXPERT TIP Joseph Meyer Joseph Meyer Math Teacher Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University. Joseph Meyer Joseph Meyer Math Teacher To simplify fractions, you can divide both the numerator and denominator by a common factor. This creates a new, easier-to-use fraction with smaller components, but it represents the same value. For instance, if you divide both the numerator and denominator of 6/12 by 2, you get 3/6, which is equal to 1/2.
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