📚 Fractions, Decimals and Percentages: Cambridge Primary Mathematics Workbook 5 | 分数、小数与百分比：剑桥小学数学练习册5核心复习
Cambridge Primary Mathematics Workbook 5 develops number skills through the linked ideas of fractions, decimals and percentages. This revision article explains the key methods, common misconceptions and practice-style questions covered in the workbook.
剑桥小学数学练习册5通过分数、小数和百分比之间的关联来培养数与运算能力。本文讲解这本练习册中的主要方法、常见误区以及练习题型。
1. Understanding unit fractions and non-unit fractions | 认识单位分数与非单位分数
A fraction shows a part of a whole. The bottom number is the denominator and tells how many equal parts the whole is divided into. The top number is the numerator and tells how many of those parts are taken.
分数表示整体的一部分。底部的数是分母，表示整体被平均分成多少份；顶部的数是分子，表示取了多少份。
A unit fraction has numerator 1, such as ½, ⅓ or ¼. A non-unit fraction has a numerator greater than 1, such as ⅔ or ¾.
单位分数的分子是 1，例如 ½、⅓ 或 ¼。非单位分数的分子大于 1，例如 ⅔ 或 ¾。
2. Equivalent fractions and simplifying | 等值分数与约分
Equivalent fractions look different but name the same amount. You can multiply or divide both the numerator and denominator by the same whole number.
等值分数看起来不同，但表示同样的大小。你可以把分子和分母同时乘或除以同一个整数。
To simplify a fraction, divide the numerator and denominator by their highest common factor. For example, 4/8 simplifies to ½ because both 4 and 8 are divided by 4.
化简分数时，用分子和分母的最大公因数同时去除。例如 4/8 化简为 ½，因为 4 和 8 都除以 4。
3. Comparing and ordering fractions | 比较和排序分数
To compare fractions with the same denominator, compare the numerators. For example, 5/8 > 3/8 because 5 parts are more than 3 parts.
分母相同时，比较分子的大小。例如 5/8 > 3/8，因为 5 份比 3 份多。
minator using equivalent fractions. For example, 1/2 = 3/6 and 2/3 = 4/6, so 2/3 > 1/2.
分母不同时，先利用等值分数找到公分母。例如 1/2 = 3/6，2/3 = 4/6，所以 2/3 > 1/2。
4. Adding and subtracting fractions | 分数的加法与减法
r subtract the numerators and keep the denominator the same. For example, 2/7 + 3/7 = 5/7.
同分母分数相加减时，分子相加减，分母不变。例如 2/7 + 3/7 = 5/7。
e the fractions with a common denominator first. For example, 1/4 + 1/2 = 1/4 + 2/4 = 3/4.
分母不同时，先把分数改写为同分母。例如 1/4 + 1/2 = 1/4 + 2/4 = 3/4。
5. Mixed numbers and improper fractions | 带分数与假分数
An improper fraction has a numerator greater than or equal to its denominator, such as 7/4. A mixed number is made of a whole number and a proper fraction, such as 1 ¾.
假分数的分子大于或等于分母，例如 7/4。带分数由一个整数和一个真分数组成，例如 1 ¾。
To change 7/4 into a mixed number, divide 7 by 4. The quotient 1 is the whole number and the remainder 3 becomes the numerator over the denominator 4: 1 ¾.
把 7/4 化成带分数，用 7 除以 4。商 1 是整数部分，余数 3 作为分子，分母仍为 4：1 ¾。
6. Introduction to decimals: tenths and hundredths | 小数的初步认识：十分位与百分位
Decimals are another way to write fractions with denominators 10, 100 or 1000. The first decimal place shows tenths, the second shows hundredths and the third shows thousandths.
小数是分母为 10、100 或 1000 的分数的另一种写法。小数点后第一位表示十分位，第二位表示百分位，第三位表示千分位。
For example, 0.7 means 7/10, and 0.07 means 7/100. A zero immediately after the decimal point changes the place value.
例如，0.7 表示 7/10，而 0.07 表示 7/100。小数点后紧接的零会改变数值的位值。
7. Ordering decimals and place value | 小数的大小比较与位值
To order decimals, align the decimal points and compare digits from left to right. For example, 0.5 is greater than 0.05 because 5 tenths is larger than 5 hundredths.
比较小数时，先把小数点对齐，然后从左到右逐位比较。例如 0.5 大于 0.05，因为 5 个十分之一大于 5 个百分之一。
ecimal does not change its value, but adding a zero immediately after the decimal point does.
位值表可以帮助说明 0.5 = 0.50。在小数末尾加零不改变数值，但在小数点后紧接着加零会改变数值。
8. Connecting fractions and decimals | 分数与小数的互换
inator 10 or 100 are easy to write as decimals. For example, 3/10 = 0.3 and 57/100 = 0.57.
分母为 10 或 100 的分数很容易写成小数。例如 3/10 = 0.3，57/100 = 0.57。
Common equivalents you should remember include ½ = 0.5, ¼ = 0.25, ¾ = 0.75, ⅕ = 0.2 and ⅛ = 0.125.
需要记住的常见等值关系包括 ½ = 0.5、¼ = 0.25、¾ = 0.75、⅕ = 0.2 和 ⅛ = 0.125。
9. Understanding percentages | 认识百分比
Percent means 'out of 100'. The symbol % shows that a quantity is written as a number of hundredths. For example, 25% means 25 out of 100, which is 25/100 or ¼.
百分比表示“每一百份中的份数”。符号 % 表示一个量写成百分之几。例如 25% 表示 100 份中的 25 份，即 25/100 或 ¼。
A whole amount is 100%. Half of a whole is 50%, one quarter is 25% and three quarters is 75%.
整个数量是 100%。整体的一半是 50%，四分之一是 25%，四分之三是 75%。
10. Converting between fractions, decimals and percentages | 分数、小数和百分比的互化
centage, first write it with denominator 100 when possible. For example, 3/5 = 60/100 = 60%.
把分数化成百分数时，如果可以，先把分母变为 100。例如 3/5 = 60/100 = 60%。
| Fraction | 分数 | Decimal | 小数 | Percentage | 百分数 |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/10 | 0.1 | 10% |
| 1/5 | 0.2 | 20% |
11. Applying to word problems | 在应用题中的运用
If a rectangle has 20 equal squares and ¼ are shaded, then 20 × ¼ = 5 squares are shaded.
在应用题中，第一步是确定总数和部分。如果一个长方形平均分成 20 个小方格，其中 ¼ 被涂色，那么涂色方格数是 20 × ¼ = 5 个。
For percentage problems, find 10% first by dividing by 10. For example, 10% of 60 is 6, so 30% of 60 is 18.
解决百分数问题时，可以先除以 10 求出 10%。例如 60 的 10% 是 6，因此 60 的 30% 是 18。
12. Common errors and exam tips | 常见错误与考试技巧
/5. The correct method is to find a common denominator first: 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
常见的错误是把分子和分母分别相加，例如写成 1/2 + 1/3 = 2/5。正确的方法是先通分：1/2 + 1/3 = 3/6 + 2/6 = 5/6。
Another common mistake is treating 0.5 and 0.05 as equal. Always write a place-value chart or add zeros to compare digits in the same place.
另一个常见错误是把 0.5 和 0.05 看成相等。比较时一定要使用位值表或在末位补零，使相同数位对齐。
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