Subtracting Fractions with Denominators of 10 and 100 | 分母为 10 和 100 的分数减法

📚 Subtracting Fractions with Denominators of 10 and 100 | 分母为 10 和 100 的分数减法

In this lesson, you will learn how to subtract fractions with denominators of 10 and 100. This skill builds a bridge between fractions and decimals and prepares you for harder fraction work in IGCSE mathematics.

本课你将学习如何计算分母为 10 和 100 的分数减法。这项技能在分数与小数之间架起桥梁，为 IGCSE 数学中更难的分数内容做好准备。

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1. What Are Tenths and Hundredths? | 什么是十分之一和百分之一？

A tenth is one part of a whole divided into 10 equal parts. A hundredth is one part of a whole divided into 100 equal parts.

十分之一是把一个整体平均分成 10 份后取其中的 1 份；百分之一是把一个整体平均分成 100 份后取其中的 1 份。

On a place value chart, tenths sit immediately to the right of the decimal point, and hundredths sit second.

在数位表中，十分位位于小数点右边第一位，百分位位于小数点右边第二位。

Examples: 1/10 = 0.1, 1/100 = 0.01, 3/10 = 0.3, 7/100 = 0.07.

例如：1/10 = 0.1，1/100 = 0.01，3/10 = 0.3，7/100 = 0.07。

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2. Equivalent Fractions: Tenths to Hundredths | 等值分数：从十分之一到百分之一

ince 1 whole = 100 hundredths and 1 whole = 10 tenths, one tenth is exactly 10 hundredths.

要计算分母不同的分数减法，首先要化成分母相同的分数。因为 1 个整体 = 100 个百分之一，也 = 10 个十分之一，所以 1 个十分之一正好等于 10 个百分之一。

1/10 = 10/100

This equivalence lets us rewrite any tenth as hundredths by multiplying both the numerator and the denominator by 10.

利用这个等值关系，我们可以把任何十分之一化成分母为 100 的分数：分子和分母同时乘以 10。

3/10 = (3 × 10)/(10 × 10) = 30/100

Fraction	Decimal	Hundredths
1/10	0.1	10/100
2/10	0.2	20/100
3/10	0.3	30/100
4/10	0.4	40/100

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3. Why We Convert Before Subtracting | 为什么减法前要先转换？

You cannot subtract two fractions unless they refer to the same size parts. Subtracting 7/100 from 3/10 directly would be like comparing 3 large slices with 7 tiny slices.

如果两个分数表示的单位大小不同，就不能直接相减。直接计算 3/10 - 7/100，就像用 3 个大块减去 7 个小块，单位不一致。

Always convert tenths to hundredths so every part is one hundredth of the whole.

因此，先把十分之一化成百分之一，使每一份都表示 1/100，然后才能相减。

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4. Worked Example: Subtract 7/100 from 3/10 | 例题：计算 3/10 - 7/100

Example: Calculate 3/10 - 7/100.

例题：计算 3/10 - 7/100。

Step 1: Rewrite 3/10 as 30/100.

步骤 1：把 3/10 改写为 30/100。

3/10 = 30/100

Step 2: Subtract the hundredths: 30/100 - 7/100 = 23/100.

步骤 2：计算百分之一分数减法：30/100 - 7/100 = 23/100。

30/100 - 7/100 = 23/100

Step 3: Write the decimal answer if needed: 0.30 - 0.07 = 0.23.

步骤 3：如果需要小数答案：0.30 - 0.07 = 0.23。

So, 3/10 - 7/100 = 23/100 = 0.23.

所以，3/10 - 7/100 = 23/100 = 0.23。

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5. Worked Example: Subtract 45/100 from 6/10 | 例题：计算 6/10 - 45/100

Example: Calculate 6/10 - 45/100.

例题：计算 6/10 - 45/100。

Rewrite 6/10 as 60/100, then 60/100 - 45/100 = 15/100.

把 6/10 改写为 60/100，然后 60/100 - 45/100 = 15/100。

You can simplify 15/100 to 3/20 by dividing both the numerator and the denominator by 5.

可以把 15/100 化简为 3/20：分子和分母同时除以 5。

15/100 = (15 ÷ 5)/(100 ÷ 5) = 3/20

The decimal form is 0.60 - 0.45 = 0.15.

小数形式为 0.60 - 0.45 = 0.15。

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6. Addition as a Check | 用加法验算

the subtracted part. If 30/100 - 7/100 = 23/100, then 23/100 + 7/100 should equal 30/100.

做完减法后，可以用加法验算。如果 30/100 - 7/100 = 23/100，那么 23/100 + 7/100 应等于 30/100。

This reverse check is useful in exams to catch careless mistakes.

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