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Questions and Answers
當要除以混合數時，應該先把混合數轉換為什麼形式？
不恰當分數
如何簡化分數除法中的結果？
找到分子和分母的共同因子，然後從分數的兩部分中除掉這些因子。
計算 (3/5) ÷ (4/5) 的結果。
3/4
將混合數 2 1/3 轉換為不恰當分數。
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簡化 12/36 的結果。
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計算 (1/2) ÷ 3 的結果。
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點樣將分數同整數做除法？
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除法分數同分數點樣計算？
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解決涉及分數除法的文字問題有什麼要點？
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點樣將分數同整數做除法時，整數應該點做？
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為咗解決分數除法問題，簡化分數有咩用途？
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除法分數同分數計算時，點解要用第二個分數嘅倒數？
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Study Notes
Fraction Division
Fraction division is a mathematical operation that involves dividing one fraction by another. It can be applied to various situations and contexts, including financial calculations and measurement problems.
With fraction division, we consider two types of divisions:
-
Division of fractions with whole numbers: Here, we divide a fraction by a whole number, resulting in a new fraction. This operation follows the rules of multiplication and can be calculated using the
x/nnotation, where n represents the whole number.Example: 2/3 ÷ 1/2 = 2/3 × 2/1 = 4/3
-
Division of fractions with fractions: In this case, we divide two fractions together, obtaining a result that is equivalent to multiplying the first fraction by the reciprocal of the second fraction. Reciprocal refers to flipping the numerator and denominator of the second fraction.
Example: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3
When solving word problems involving fraction division, it's essential to identify the relationship between the fractions and the whole number. In addition, simplifying fractions can help make the division process easier by reducing larger numbers into smaller, more manageable parts.
Division of Fractions with Whole Numbers
To divide fractions by whole numbers, follow these steps:
- Keep the fraction as it is.
-
Flip the whole number to make it a fraction. If we have
x, we flip it to become1/x. -
Change the sign into multiplication. Replace the division symbol
÷with the multiplication sign×.
Example: To calculate 2/3 ÷ 6, we keep the fraction 2/3 the same, flip 6 to 1/6, and change the division sign to multiplication: 2/3 × 1/6 = 1/3.
Division of Fractions with Mixed Numbers
When dividing mixed numbers, we consider them as improper fractions before performing the division operation. Follow these steps:
- Keep the fraction as it is.
- Convert the mixed number to an improper fraction. Add the denominator of the whole number part to the numerator and multiply both parts by the original denominator of the mixed number. The result is now an improper fraction.
- Flip the second fraction and change the sign into multiplication between the fractions.
Example: To calculate (5/7) ÷ (2/7), we keep 5/7 the same, convert 2/7 to an improper fraction by adding its denominator to the numerator, which gives us 9/7, and then flip it to 7/9. The division operation becomes 5/7 × 7/9 = 5/9.
Simplifying Fractions in Division
To simplify fractions during division, use the following steps:
- Find the common factors of both the numerator and denominator.
- Divide the common factors from both parts of the fraction.
- Redeuce the resulting fraction if possible.
Example: To simplify 14/28 in the division operation, we find the common factor of 2 between both parts and divide it: 14/28 → 7/14. This fraction is already reduced to the lowest terms, so no further simplification is needed.
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Description
這個測驗涵蓋分數除法的操作，包括分數和整數、分數和分數、分數和混合數的除法。另外，測驗亦包括如何簡化分數以便進行除法運算。通過練習，你可以掌握如何有效地操作不同類型的分數除法問題。
