Working with fractions can be challenging, especially when dealing with different denominators. However, learning how to divide fractions with different denominators is an essential skill that can come in handy in various real-life scenarios. In this article, we will provide a step-by-step guide on how to divide fractions with different denominators, along with some common questions and answers to help clarify any doubts. Step-by-Step Guide: 1. Find a common denominator: The first step to divide fractions with different denominators is to find a common denominator. To do this, identify the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide evenly into. Once you have the LCM, you can use it as the common denominator for both fractions. 2. Create equivalent fractions: To maintain the same value of the original fractions, you need to create equivalent fractions with the newfound common denominator. Multiply the numerator and denominator of each fraction by the same value so that the denominators become equal. 3. Simplify the fractions: After finding a common denominator and creating equivalent fractions, you should simplify both fractions if possible. Simplify by dividing the numerator and denominator of each fraction by their greatest common divisor (GCD) to get the simplest form. 4. Divide the fractions: Now that you have both fractions with the same denominator, you can directly divide the numerators. Simply divide the numerator of the first fraction by the numerator of the second fraction. Examples: Let's illustrate the steps above with a couple of examples: Example 1: 5/6 ÷ 2/3 Step 1: The LCM of 6 and 3 is 6, so the common denominator is 6. Step 2: Create equivalent fractions: (5/6) x (2/2) ÷ (2/3) x (3/3) = 10/12 ÷ 6/9 Step 3: Simplify the fractions: 10/12 can be simplified to 5/6, and 6/9 can be simplified to 2/3. Step 4: Divide the fractions: (5/6) ÷ (2/3) = (5/6) x (3/2) = 15/12 = 1 1/4 Example 2: 3/8 ÷ 4/5 Step 1: The LCM of 8 and 5 is 40, so the common denominator is 40. Step 2: Create equivalent fractions: (3/8) x (5/5) ÷ (4/5) x (8/8) = 15/40 ÷ 32/40 Step 3: Simplify the fractions: Both fractions are already in simplified form. Step 4: Divide the fractions: (15/40) ÷ (32/40) = (15/40) x (40/32) = 600/1280 = 15/32 Common Questions and Answers:

Can I skip the step of finding a common denominator?

No, finding a common denominator is crucial in dividing fractions with different denominators.

Do I have to simplify the fractions before dividing?

It is recommended to simplify the fractions after finding a common denominator to obtain the simplest form of the result.

How do I know if I should add or subtract when dividing fractions?

When dividing fractions, you always multiply the first fraction by the reciprocal (inverse) of the second fraction. There is no addition or subtraction involved. Dividing fractions with different denominators may seem complicated at first glance, but by following the step-by-step guide provided in this article, you can tackle this mathematical operation with confidence. Remember to always find a common denominator, create equivalent fractions, simplify when possible, and then divide the fractions. Keep practicing, and soon dividing fractions will become second nature.
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