Multiplying Fractions and Mixed Numbers | 分数与带分数的乘法

📚 Multiplying Fractions and Mixed Numbers | 分数与带分数的乘法

Multiplying fractions is one of the most useful fraction skills in IGCSE mathematics. It appears in number work, algebra, ratio problems, probability, and measurement. Once you can multiply fractions fluently, you can handle mixed numbers, simplify answers, and solve word problems with confidence.

分数乘法是 IGCSE 数学中最有用的分数技能之一。它出现在数字运算、代数、比例问题、概率和测量中。一旦你能熟练地进行分数乘法，你就能处理带分数、化简结果，并有信心解决应用题。

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1. What Does Fraction Multiplication Mean? | 分数乘法表示什么？

Multiplying fractions often means finding a part of a part. For example, 1/2 × 2/3 means ‘one half of two thirds’. It is not the same as adding fractions, so you do not need a common denominator.

分数乘法通常表示求一个数的一部分的一部分。例如，1/2 × 2/3 表示 “三分之二的一半”。它不同于分数加法，所以不需要通分。

If you shade 2/3 of a rectangle and then take 1/2 of that shaded part, the overlap is 2/6, which simplifies to 1/3.

如果你涂色一个矩形的 2/3，然后取涂色部分的 1/2，重叠部分为 2/6，化简后为 1/3。

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2. The Fraction Multiplication Rule | 分数乘法法则

To multiply two fractions, multiply the numerators together and multiply the denominators together.

两个分数相乘时，将分子相乘，并将分母相乘。

a/b × c/d = (a × c)/(b × d)

Example: 2/5 × 3/7 = (2 × 3)/(5 × 7) = 6/35.

例子：2/5 × 3/7 = (2 × 3)/(5 × 7) = 6/35。

If the result is not in lowest terms, divide both numerator and denominator by their highest common factor.

如果结果不是最简分数，将分子和分母同时除以它们的最大公约数。

Example: 4/6 = 2/3 because 4 and 6 have a common factor of 2.

例子：4/6 = 2/3，因为 4 和 6 有公约数 2。

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3. Multiplying a Fraction by a Whole Number | 分数乘整数

Write the whole number as a fraction over 1, then use the same rule.

把整数写成以 1 为分母的分数，然后使用相同法则。

n × a/b = n/1 × a/b = (n × a)/b

Example: 5 × 2/3 = 5/1 × 2/3 = 10/3 = 3 1/3.

例子：5 × 2/3 = 5/1 × 2/3 = 10/3 = 3 1/3。

This also works when the result is an improper fraction. Convert it to a mixed number if the question asks for one.

当结果为假分数时也可行。如果题目要求，将其化为带分数。

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4. Cross-Cancelling Before Multiplying | 相乘前先约分

You can reduce a numerator and a denominator by a common factor before multiplying. This makes the numbers smaller and the final simplification easier.

你可以在相乘前用一个公因数约去一个分子和一个分母。这会使数字更小，最终化简更简单。

Example: 8/9 × 3/4. The 8 and 4 cancel by 4, and the 3 and 9 cancel by 3.

例子：8/9 × 3/4。8 和 4 约去 4，3 和 9 约去 3。

The result is (2 × 1)/(3 × 1) = 2/3.

结果为 (2 × 1)/(3 × 1) = 2/3。

Always cancel one numerator with one denominator; never cancel two numerators or two denominators.

只能用一个分子与一个分母约分；绝不能约两个分子或两个分母。

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5. Multiplying Mixed Numbers | 带分数乘法

Convert each mixed number to an improper fraction first. Then multiply

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