Podcast
Questions and Answers
کدام مرحله برای تبدیل یک کسر به یک کسر معادل با یک مخرج مشترک اشتباه است؟
کدام مرحله برای تبدیل یک کسر به یک کسر معادل با یک مخرج مشترک اشتباه است؟
- تقسیم کننده و مخرج را در همان عدد تقسیم کنید
- ضرب کننده و مخرج را در همان عدد ضرب کنید
- تقسیم کننده را تقسیم کنید توسط مخرج جدید
- ضرب کننده را تقسیم کنید توسط مخرج جدید (correct)
با توجه به متن، چگونه \(rac{2}{5}\) را به یک کسر معادل با مخرج \(rac{10}{3}\) تبدیل میکنیم؟
با توجه به متن، چگونه \(rac{2}{5}\) را به یک کسر معادل با مخرج \(rac{10}{3}\) تبدیل میکنیم؟
- \\(rac{2}{5} * rac{3}{10} = rac{6}{50}\\) (correct)
- \\(rac{2}{5} * rac{10}{3} = rac{20}{15}\\)
- \\(rac{2}{5} * rac{3}{10} = rac{6}{15}\\)
- \\(rac{2}{5} * rac{10}{3} = rac{20}{50}\\)
با توجه به توضیحات، نتیجه تقسیم \(rac{3}{4}\) بر \(rac{6}{7}\) چیست؟
با توجه به توضیحات، نتیجه تقسیم \(rac{3}{4}\) بر \(rac{6}{7}\) چیست؟
- \\(rac{7}{8}\\)
- \\(rac{21}{24}\\) (correct)
- \\(rac{1}{2}\\)
- \\(rac{9}{12}\\)
چگونه میتوان \(rac{5}{6}\) را به یک کسر ساده تقلیل داد؟
چگونه میتوان \(rac{5}{6}\) را به یک کسر ساده تقلیل داد؟
در اثر جمعزمان از اثار زیر، چه نتیجهای به دست خواهید آورد؟
در اثر جمعزمان از اثار زیر، چه نتیجهای به دست خواهید آورد؟
برای تقسیم کردن کدامیک از موارد زیر باید ابتدا مطمئن شویم که هر دو اشتراکی در مخرج دارند؟
برای تقسیم کردن کدامیک از موارد زیر باید ابتدا مطمئن شویم که هر دو اشتراکی در مخرج دارند؟
چگونه میتوانید گراندههای اولیه مخرجهای کسورهای با مخرجهای متفاوت را تعیین کنید؟
چگونه میتوانید گراندههای اولیه مخرجهای کسورهای با مخرجهای متفاوت را تعیین کنید؟
چگونه میتوان تعیین کرد که آیا دو کسر با مخرجهای مختلف، دارای یک مخرج مشترک هستند یا خیر؟
چگونه میتوان تعیین کرد که آیا دو کسر با مخرجهای مختلف، دارای یک مخرج مشترک هستند یا خیر؟
چگونه میتوانید جمع سودمند فوقانیهای گرانده شده را تعیین کنید؟
چگونه میتوانید جمع سودمند فوقانیهای گرانده شده را تعیین کنید؟
چگونه میتوانید مخارج تقسیم شدهها را با هم بچسبانید؟
چگونه میتوانید مخارج تقسیم شدهها را با هم بچسبانید؟
Study Notes
Fraction Division: Dividing Fractions with Unlike Denominators
When it comes to solving mathematical problems involving fractions, one of the most common operations is division. However, this operation can become tricky when dealing with fractions that have different denominators, known as unlike fractions. In such cases, you cannot simply divide two numbers because they don't share a common factor. Instead, you need to find a common denominator before performing the division. Let's dive deeper into how to solve fraction divisions with unlike denominators.
Finding Common Denominators
Before dividing fractions, you must first ensure that they share a common denominator. A common denominator is a number that appears in both the numerator and the denominator of each fraction. To find the common denominator of unlike fractions, follow these steps:
- List all the denominators, including their prime factors.
- Identify the greatest common divisor (GCD) of all the denominators. This is your common denominator. It may also be called the lowest common multiple (LCM).
For example, if we want to find the common denominator of (\frac{1}{3}), (\frac{1}{4}), and (\frac{1}{5}), we would list their denominators: (3), (4), and (5), respectively. Then, we identify their GCD or LCM, which in this case is (12): ((3 * 2)(4 * 1)(1 * 5) = 12). Therefore, the common denominator for these three fractions is (12).
Converting Fractions to Equivalent Fractions with a Common Denominator
Once you have found the common denominator, the next step is to convert each fraction into equivalent fractions with the new denominator. An equivalent fraction is a fraction that has the same value as the original fraction, but with different numerators and denominators. To convert a fraction to an equivalent fraction with a given denominator, follow these steps:
- Divide the denominator by the new denominator.
- Multiply the numerator and the denominator by the same number (the result from step 1).
For example, let's convert (\frac{1}{3}) to an equivalent fraction with a denominator of (12). We divide (12) by (3), which gives us (4). Then, we multiply the numerator (1) and the denominator (3) by (4): ((1 * 4) + (3 * 4) = 4 + 12 = 16). Therefore, the equivalent fraction of (\frac{1}{3}) with a denominator of (12) is (\frac{16}{12}).
Performing the Division
Now that we have equivalent fractions with the same denominator, we can perform the division. To divide two fractions, we simply divide their numerators. For example, to divide (\frac{4}{12}) by (\frac{8}{12}), we can rewrite it as (\frac{4}{12} \div \frac{8}{12}). Then, we divide their numerators: (4) divided by (8), which gives us (\frac{1}{2}). Therefore, (\frac{4}{12} \div \frac{8}{12} = \frac{1}{2}).
Simplifying the Result
Finally, to simplify the result, we can reduce the fraction to its simplest form. If the numerator and the denominator have a common factor, we can divide both by that factor to simplify the fraction. For example, if we have (\frac{3}{5}), we can divide both the numerator and the denominator by (3): (\frac{1}{1} = \frac{1}{5}). Therefore, (\frac{3}{5} = \frac{1}{5}).
In conclusion, dividing fractions with unlike denominators involves finding a common denominator, converting each fraction into equivalent fractions with the common denominator, performing the division, and simplifying the result, if necessary. By following these steps, you can accurately solve fraction division problems with unlike denominators.
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Description
Explore the process of dividing fractions with different denominators, also known as unlike fractions. Learn how to find common denominators, convert fractions to equivalent forms, perform the division, and simplify the results. Mastering these steps will help you tackle fraction division problems effortlessly.