Fractions, Decimals and Percentages: Cambridge Primary Stage 6 Complete Guide — 分数、小数与百分数:剑桥小学六年级数学完全指南

1. 分数、小数与百分数:三种表示同一个数的方式 | Fractions, Decimals and Percentages: Three Ways to Show the Same Number

在剑桥小学数学(Cambridge Primary Mathematics)第 6 阶段的学习中,学生第一次系统地把分数、小数和百分数放在一起学习。这三者看起来是不同的写法,但实际上它们都在描述同一个东西:整体的一部分。例如,一块巧克力被平均分成 4 份,吃掉其中的 1 份,这一份可以写成四分之一(1/4),可以写成 0.25,也可以写成 25%。三种写法表示的是完全相同的数量。

In Cambridge Primary Mathematics Stage 6, pupils systematically learn fractions, decimals and percentages together for the first time. These three look like different notations, but they all describe the same thing: a part of a whole. For example, if a chocolate bar is divided into 4 equal pieces and you eat 1 piece, that piece can be written as one quarter (1/4), as 0.25, or as 25%. All three forms represent exactly the same amount.

为什么要学会在三种形式之间转换?因为日常生活和考试中,不同的场景会使用不同的写法。商店里的折扣通常写成百分数(如”打八折”就是 80% 或 0.8 倍),测量和计算器显示常用小数(如 1.25 米),而分数则广泛用于比例和几何问题(如”三角形的 2/3 被涂色”)。能够熟练转换,就意味着无论题目以哪种形式出现,你都能理解和计算。

Why must pupils learn to convert between the three forms? Because different situations in daily life and in exams use different notations. Discounts in shops are usually written as percentages (a 20% discount means paying 80% or 0.8 times the price), measurements and calculator displays commonly use decimals (such as 1.25 metres), while fractions are widely used in ratio and geometry problems (for example, two thirds of a triangle is shaded). Being able to convert fluently means you can understand and calculate no matter which form a question uses.

这一单元的学习顺序很关键:先掌握小数与分数的位值关系,再学习百分数与小数、分数的互相转换,最后综合运用来解决实际问题和比较大小。本文按照剑桥 Stage 6 大纲的顺序,把每一步转换方法拆开讲解,并配上升级版速查表和典型例题。

The learning sequence of this unit is important: first master the place-value relationship between decimals and fractions, then learn conversions between percentages, decimals and fractions, and finally apply everything to solve real-world problems and compare sizes. This article follows the order of the Cambridge Stage 6 framework, breaking down each conversion method step by step, with a quick reference table and typical worked examples.

2. 分数转小数:把分母变成 10、100 或 1000 | Converting Fractions to Decimals: Changing the Denominator to 10, 100 or 1000

分数转小数最直观的方法是找到与分母等价的、以 10、100 或 1000 为分母的分数。因为小数的位值系统正是基于 10 的幂:十分位、百分位、千分位。例如,3/5 可以分子分母同时乘以 2,变成 6/10,而 6/10 就是 0.6。同理,7/20 乘以 5 变成 35/100,即 0.35。

The most intuitive way to convert a fraction to a decimal is to find an equivalent fraction whose denominator is 10, 100 or 1000. This works because the decimal place-value system is based on powers of 10: tenths, hundredths and thousandths. For example, 3/5 can be multiplied on both top and bottom by 2 to become 6/10, and 6/10 is 0.6. Similarly, 7/20 multiplied by 5 becomes 35/100, which is 0.35.

当分母无法方便地变成 10 的幂时(例如 1/3),Stage 6 学生需要学会用除法来完成转换:分子除以分母。1/3 等于 1 ÷ 3,结果是 0.333…,这是一个无限循环小数。在小学阶段,我们通常把它保留到两位或三位小数,写成 0.33 或 0.333,并在答案旁注明”约等于”(约等号写作 ≈)。

When the denominator cannot easily become a power of 10 (for example 1/3), Stage 6 pupils need to learn to use division: the numerator divided by the denominator. 1/3 equals 1 ÷ 3, which gives 0.333…, a recurring decimal. At primary level we usually round it to two or three decimal places, writing 0.33 or 0.333 with the approximate-equals symbol (≈) next to the answer.

练习建议:先判断分母的质因数是否只含 2 和 5。如果只含 2 和 5(如 4、8、20、25、50),就一定可以化为有限小数;如果含有其他质因数(如 3、7、9),就会得到循环小数。这个判断方法在 Stage 6 的分层作业中经常出现,也是区分”有限小数”与”循环小数”的核心依据。

Practice tip: first check whether the denominator’s prime factors are only 2 and 5. If they are only 2 and 5 (such as 4, 8, 20, 25 or 50), the fraction can always be written as a terminating decimal; if it contains other prime factors (such as 3, 7 or 9), the decimal will recur. This check frequently appears in Stage 6 differentiated worksheets and is the key to distinguishing terminating decimals from recurring decimals.

3. 小数转分数:读出位值并化简到最简形式 | Converting Decimals to Fractions: Reading Place Value and Simplifying

小数转分数是上一节的逆过程,关键在于”读出小数表示的是十分之几、百分之几还是千分之几”。0.7 读作”十分之七”,所以直接写成 7/10;0.42 读作”百分之四十二”,写成 42/100;0.305 读作”千分之三百零五”,写成 305/1000。小数有几位,分母就是 1 后面跟几个 0。

Converting a decimal to a fraction is the reverse of the previous section, and the key is to “read out” whether the decimal represents tenths, hundredths or thousandths. 0.7 is read as “seven tenths”, so it becomes 7/10; 0.42 is read as “forty-two hundredths”, written as 42/100; 0.305 is read as “three hundred and five thousandths”, written as 305/1000. The number of decimal places tells you the denominator: 1 followed by that many zeros.

写出分数之后,还有非常重要的一步:约分到最简形式。例如 42/100 的分子分母都能被 2 整除,约分后是 21/50;0.25 写成 25/100,再约分是 1/4。Stage 6 的评分标准明确要求”答案必须是最简分数”,所以每次转换后都要检查分子分母是否还有公因数。

After writing the fraction, there is a very important extra step: simplify it to its lowest terms. For example, both 42 and 100 in 42/100 are divisible by 2, so it simplifies to 21/50; 0.25 is written as 25/100 and then simplified to 1/4. Stage 6 mark schemes explicitly require answers in simplest form, so always check whether the numerator and denominator still share a common factor after each conversion.

遇到带小数的整数部分时(如 2.6),先处理整数部分,再处理小数部分:2.6 = 2 + 0.6 = 2 又 6/10 = 2 又 3/5,也可以写成假分数 13/5。剑桥教材特别强调”整数部分 + 真分数”的带分数写法,并要求学生能在这两种写法之间自由切换。

When a decimal has a whole-number part (such as 2.6), handle the whole part first, then the fractional part: 2.6 = 2 + 0.6 = 2 and 6/10 = 2 and 3/5, which can also be written as the improper fraction 13/5. The Cambridge textbook emphasises the mixed-number form “whole part plus proper fraction” and requires pupils to switch freely between mixed numbers and improper fractions.

4. 百分数与小数的互转:除以 100 和乘以 100 的规则 | Converting Percentages and Decimals: The Divide-by-100 and Multiply-by-100 Rules

百分数(percent)这个英文单词本身就有线索:”per cent”的意思是”每一百”(per hundred)。所以百分之几就是”每一百份中的几份”。要把百分数转成小数,只需除以 100:45% = 45 ÷ 100 = 0.45;8% = 8 ÷ 100 = 0.08。注意,除以 100 就是把小数点向左移动两位,所以 8% 要先想成 08%,再移动小数点得到 0.08。

The English word “percent” itself contains a clue: “per cent” means “per hundred”. So a percentage is simply “so many parts out of every hundred”. To convert a percentage to a decimal, divide by 100: 45% = 45 ÷ 100 = 0.45; 8% = 8 ÷ 100 = 0.08. Note that dividing by 100 means moving the decimal point two places to the left, so for 8% you first think of it as 08% and then move the point to get 0.08.

反过来,小数转百分数就是乘以 100:0.65 × 100 = 65%,0.04 × 100 = 4%。乘以 100 就是把小数点向右移动两位。当百分数含小数时同样成立:12.5% = 0.125,反过来 0.375 = 37.5%。这一对规则是所有百分数应用题的基础,Stage 6 要求学生达到”看一眼就能口算”的熟练程度。

Going the other way, converting a decimal to a percentage means multiplying by 100: 0.65 × 100 = 65% and 0.04 × 100 = 4%. Multiplying by 100 moves the decimal point two places to the right. The same rule works for percentages containing decimals: 12.5% = 0.125 and, in reverse, 0.375 = 37.5%. This pair of rules underpins every percentage word problem, and Stage 6 expects pupils to become fluent enough to do these conversions mentally at a glance.

一个常见的易错点是 100% 与 1 的关系:100% = 1,所以”增长了 100%”意味着数量翻倍,”打 100% 折扣”等于免费。超过 100% 的百分数(如 150%)转成小数是 1.5,表示比原来的整体还大。剑桥 Stage 6 的挑战题经常用这些边界情况来检验学生是否真正理解百分数的含义。

A common point of confusion is the relationship between 100% and 1: 100% = 1, so “an increase of 100%” means the quantity doubles and “a 100% discount” means the item is free. Percentages greater than 100% (such as 150%) convert to decimals greater than 1, like 1.5, meaning more than the original whole. Cambridge Stage 6 challenge problems often use these boundary cases to test whether pupils truly understand what percentages mean.

5. 分数与百分数的互转:构造以 100 为分母的等价分数 | Converting Fractions to Percentages: Building Equivalent Fractions with Denominator 100

分数转百分数的标准方法,是把分数改写成分母为 100 的等价分数,然后分子直接加上百分号。例如 3/4,分子分母同时乘以 25,得到 75/100,所以 3/4 = 75%。又如 7/10 乘以 10 变成 70/100,即 70%。这种方法不需要计算器,是 Stage 6 书面考试中最受青睐的解法。

The standard method for converting a fraction to a percentage is to rewrite it as an equivalent fraction with denominator 100, then attach the percent sign to the numerator. For example, 3/4: multiply top and bottom by 25 to get 75/100, so 3/4 = 75%. Similarly, 7/10 multiplied by 10 becomes 70/100, which is 70%. This method needs no calculator and is the favourite solution in Stage 6 written exams.

当分母不能直接变成 100 时(如 5/8),可以先用除法把分数转成小数,再乘以 100:5/8 = 5 ÷ 8 = 0.625,0.625 × 100 = 62.5%。反过来,百分数转分数就是先写成分母为 100 的分数再约分:60% = 60/100 = 3/5;75% = 75/100 = 3/4。这两个方向都要熟练,因为题目常常要求”用最简分数表示”。

When the denominator cannot easily become 100 (such as 5/8), first convert the fraction to a decimal by division, then multiply by 100: 5/8 = 5 ÷ 8 = 0.625, and 0.625 × 100 = 62.5%. In the reverse direction, converting a percentage to a fraction means writing it over 100 first and then simplifying: 60% = 60/100 = 3/5 and 75% = 75/100 = 3/4. Both directions need to be fluent, because questions often ask for the answer “in its simplest form”.

记忆一组基准分数会大幅提高速度:1/2 = 50%,1/4 = 25%,3/4 = 75%,1/5 = 20%,2/5 = 40%,3/5 = 60%,4/5 = 80%,1/10 = 10%,1/20 = 5%。这些对应关系在剑桥教材的”心智数学”环节反复训练,掌握后可以秒答大多数百分数题目。

Memorising a set of benchmark fractions greatly increases speed: 1/2 = 50%, 1/4 = 25%, 3/4 = 75%, 1/5 = 20%, 2/5 = 40%, 3/5 = 60%, 4/5 = 80%, 1/10 = 10% and 1/20 = 5%. These correspondences are drilled repeatedly in the “mental maths” section of the Cambridge textbook; once mastered, most percentage questions can be answered in seconds.

6. 等价分数:约分与扩分如何支撑所有转换 | Equivalent Fractions: How Simplifying and Scaling Support Every Conversion

等价分数(equivalent fractions)是整个转换系统的地基。两个分数虽然分子分母不同,但只要它们的比值相同,就是等价的。1/2 和 2/4、3/6、5/10 都是等价分数,因为它们都表示同一个数值 0.5。判断两个分数是否等价,可以交叉相乘:1 × 4 = 2 × 2,两边相等,所以 1/2 和 2/4 等价。

Equivalent fractions are the foundation of the entire conversion system. Two fractions with different numerators and denominators are equivalent as long as their ratios are the same. 1/2, 2/4, 3/6 and 5/10 are all equivalent because they all represent the same value, 0.5. To check whether two fractions are equivalent, cross-multiply: 1 × 4 = 2 × 2; the two products are equal, so 1/2 and 2/4 are equivalent.

扩分(把分子分母同时乘以同一个数)让分数变大但仍保持原值,这是”分母变成 100″这类转换的直接工具;约分(把分子分母同时除以公因数)让分数变小但仍保持原值,这是”最简形式”的要求。例如把 6/8 约分:分子分母同除以 2,得到 3/4。注意约分要”约到底”:如果分子分母还有公因数,就要继续约,直到没有除了 1 以外的公因数为止。

Scaling up (multiplying numerator and denominator by the same number) makes a fraction larger in appearance while keeping its value, and is the direct tool for conversions such as “make the denominator 100”. Simplifying (dividing numerator and denominator by a common factor) makes the fraction smaller in appearance while keeping its value, and is required for “simplest form”. For example, simplify 6/8 by dividing both numbers by 2 to get 3/4. Note that simplifying must continue until the fraction is fully reduced: if the numerator and denominator still share a common factor, keep dividing until the only common factor is 1.

在 Stage 6 的分数加减法中,扩分还有一个关键用途:通分。要计算 1/2 + 1/3,需要先找到公分母 6,把两个分数分别扩分为 3/6 和 2/6,再相加得 5/6。通分和约分是一对互逆操作,学生必须能根据题目的需要灵活选用,这是第 6 阶段分数运算的核心技能。

Scaling up also has a crucial role in Stage 6 fraction addition and subtraction: finding a common denominator. To calculate 1/2 + 1/3, first find the common denominator 6, rewrite the two fractions as 3/6 and 2/6, and then add to get 5/6. Finding a common denominator and simplifying are inverse operations; pupils must be able to choose flexibly according to what the question needs. This is the core skill of fraction arithmetic in Stage 6.

7. 常见转换速查表:分数、小数、百分数对照 | Quick Reference Table: Common Fraction, Decimal and Percentage Equivalents

下面这张对照表覆盖了 Stage 6 考试中出现频率最高的转换值。建议把它抄在笔记本上,每天晨读时默写一遍,两周内就能形成条件反射。

The table below covers the conversions that appear most frequently in Stage 6 exams. Copy it into your notebook and recite it from memory each morning; within two weeks the values will become second nature.

分数 Fraction 小数 Decimal 百分数 Percentage
1/2 0.5 50%
1/4 0.25 25%
3/4 0.75 75%
1/5 0.2 20%
2/5 0.4 40%
3/5 0.6 60%
4/5 0.8 80%
1/10 0.1 10%
3/10 0.3 30%
1/20 0.05 5%
1/8 0.125 12.5%
3/8 0.375 37.5%
5/8 0.625 62.5%
1/3 0.333 (循环) 约 33.3%
2/3 0.667 (循环) 约 66.7%

使用这张表时要注意两点:第一,表中的值必须结合约分规则来记忆,例如记住 3/8 = 0.375 比死记硬背更稳妥,因为 3/8 的分子 3 乘 125 得 375,正好对应千分位;第二,循环小数的百分数形式只能写”约等于”,考试中若题目要求精确值,应保留分数形式。

Two points to note when using this table: first, connect the values to the simplification rules when memorising them; for example, remembering that 3/8 = 0.375 is more reliable through reasoning, because the numerator 3 multiplied by 125 gives 375, which maps directly onto the thousandths place. Second, percentage forms of recurring decimals can only be written as “approximately”; in an exam, if the question asks for an exact value, keep the fraction form.

8. 比较与排序:先统一形式再比较大小 | Comparing and Ordering: Convert to the Same Form First

Stage 6 的典型题型是把一组混合形式(分数、小数、百分数混在一起)的数按大小排序。例如:”把 0.6、3/5、58%、0.57 从小到大排列”。直接比较会非常容易出错,正确策略是先把所有数转换成同一种形式,最常用的是小数形式。

A typical Stage 6 question asks pupils to order a mixed set of numbers: fractions, decimals and percentages all together. For example: “Arrange 0.6, 3/5, 58% and 0.57 in ascending order.” Comparing them directly is very error-prone; the correct strategy is to convert every number into the same form first, and decimal form is the most common choice.

解上面这道题:3/5 = 0.6,58% = 0.58,所以四个数分别是 0.6、0.6、0.58、0.57。从小到大排列为 0.57、58%、3/5 和 0.6(0.6 与 3/5 相等,可以并列)。注意最终答案要写回题目给出的原始形式,不能只写转换后的小数,否则会被扣分。

Solving the example: 3/5 = 0.6 and 58% = 0.58, so the four numbers are 0.6, 0.6, 0.58 and 0.57. In ascending order they are 0.57, 58%, 3/5 and 0.6 (0.6 and 3/5 are equal, so they can be listed together). Note that the final answer must be written back in the original forms used in the question; writing only the converted decimals will lose marks.

比较小数大小时,先看整数部分,整数部分大的数就大;整数部分相同再看十分位,十分位相同再看百分位,依此类推。这个”逐位比较”的方法是所有排序题的基础。另外,比较分数时可以先看分母是否相同:分母相同,分子大的分数大;分子相同,分母小的分数大。

When comparing decimals, look at the whole-number part first: the number with the larger whole part is larger. If the whole parts are equal, compare the tenths; if the tenths are equal, compare the hundredths, and so on. This “place-by-place comparison” is the foundation of all ordering questions. When comparing fractions, first check whether the denominators match: with the same denominator, the larger numerator gives the larger fraction; with the same numerator, the smaller denominator gives the larger fraction.

9. 应用题实战:折扣、成绩百分比与数量计算 | Word Problems in Action: Discounts, Test Percentages and Finding Amounts

百分数应用题是 Stage 6 的考试重点,最常见的是”求一个数的百分之几”。方法:先转成小数,再相乘。例如”一件 40 元的玩具打八折”,八折就是 80% = 0.8,40 × 0.8 = 32,所以售价是 32 元。又如”一本书有 200 页,已读 25%”,已读页数 = 200 × 0.25 = 50 页。

Percentage word problems are a major focus of Stage 6 exams, and the most common type is “find a percentage of a quantity”. Method: convert to a decimal first, then multiply. For example, a toy costing 40 yuan with a 20% discount: paying 80% means 0.8, and 40 × 0.8 = 32, so the selling price is 32 yuan. Another example: a book has 200 pages and 25% have been read; the pages read = 200 × 0.25 = 50 pages.

第二类常见题是”已知部分和百分数,求整体”。例如”小明考试得了 36 分,正好是满分的 60%,满分是多少?”设满分为 x,则 0.6x = 36,解得 x = 60。这类题是百分数的逆向应用,Stage 6 学生常用”除以百分数的小数形式”来完成:36 ÷ 0.6 = 60。训练时要把正向和逆向两类题放在一起对比,避免混淆。

The second common type is “given the part and the percentage, find the whole”. For example: Xiaoming scored 36 marks in a test, which is exactly 60% of the full marks; what is the full mark? Let the full mark be x, then 0.6x = 36, so x = 60. This is the reverse application of percentages, and Stage 6 pupils usually solve it by dividing by the decimal form of the percentage: 36 ÷ 0.6 = 60. When practising, compare the forward and reverse types side by side to avoid confusion.

第三类题把分数与小数结合:例如”一根绳子长 2.5 米,用去了它的 3/5,还剩多少米?”用去的部分 = 2.5 × 3/5。先把 3/5 转成 0.6,2.5 × 0.6 = 1.5 米,剩余 = 2.5 – 1.5 = 1 米。也可以先算 2.5 ÷ 5 = 0.5(每份),0.5 × 3 = 1.5(用去),剩下 2 份即 1 米。两种方法都要会,考试时选择更顺手的一种。

The third type combines fractions and decimals. For example: a rope is 2.5 metres long and 3/5 of it has been used; how many metres are left? The used part = 2.5 × 3/5. Convert 3/5 to 0.6 first: 2.5 × 0.6 = 1.5 metres, and the remainder = 2.5 – 1.5 = 1 metre. Alternatively, 2.5 ÷ 5 = 0.5 (one fifth), 0.5 × 3 = 1.5 (used), leaving 2 fifths which is 1 metre. Both methods should be mastered; in the exam, choose the one you are more comfortable with.

解答应用题时,建议养成三个习惯:第一,把题目中的关键信息先转换成同一种形式再动笔;第二,写出完整的计算步骤,不要跳步,因为 Stage 6 评分会给过程分;第三,答完把答案代回题目检查合理性,例如”折扣后的价格不可能高于原价”。

When solving word problems, develop three habits: first, convert the key information in the question into one common form before calculating; second, write out the full calculation steps without skipping, because Stage 6 marking awards method marks; third, check the reasonableness of your answer by substituting it back, for example a discounted price can never be higher than the original price.

10. Stage 6 常见易错点与检查清单 | Common Mistakes and a Checking List for Stage 6

根据剑桥教学团队多年批改经验,学生在分数、小数、百分数这一单元最常犯五类错误。第一类:小数转分数忘记约分,把 0.75 写成 75/100 就结束,正确应为 3/4。第二类:移动小数点方向搞反,百分数转小数应向左移(除以 100),小数转百分数应向右移(乘以 100)。

Based on years of marking experience from Cambridge teaching teams, pupils make five common types of mistakes in this unit. Type one: forgetting to simplify when converting a decimal to a fraction, stopping at 75/100 for 0.75 instead of the correct 3/4. Type two: moving the decimal point in the wrong direction; converting a percentage to a decimal moves it left (divide by 100), while converting a decimal to a percentage moves it right (multiply by 100).

第三类:混淆”百分比折扣”与”折扣后价格”。题目说”降价 20%”,售价是原价的 80%,而不是 20%。第四类:排序题最终答案写成了转换后的形式而不是题目原始形式。第五类:对 1 与 100% 的关系不敏感,导致”增加 100%”理解为”增加 1 倍以上”之类的错误。

Type three: confusing “percentage discount” with “price after discount”. If a question says “reduce the price by 20%”, the selling price is 80% of the original, not 20%. Type four: writing the final answer of an ordering question in the converted form instead of the original forms given in the question. Type five: being insensitive to the relationship between 1 and 100%, leading to errors such as misunderstanding “an increase of 100%” as “more than doubling”.

答题前使用这张两分钟检查清单:一、所有分数是否已经约到最简?二、百分号是否写在了正确的位置?三、小数点移动的位数和方向是否正确?四、答案是否使用了题目要求的表示形式?五、是否代回原题验证了合理性?每道大题做完后用 30 秒过一遍清单,可以显著减少低级失误。

Before submitting, run this two-minute checking list: one, are all fractions fully simplified? Two, is the percent sign in the correct place? Three, are the number of places and the direction of the decimal-point movement correct? Four, is the answer in the form the question asks for? Five, has the answer been substituted back to check its reasonableness? Spending 30 seconds on this list after each big question significantly reduces careless mistakes.

Summary | 总结

本文系统梳理了剑桥小学数学 Stage 6″分数、小数与百分数”单元的全部核心内容:三种形式的本质含义、六类互转方法(分数与小数、百分数与小数、分数与百分数)、等价分数与约分扩分的支撑作用、高频转换速查表、混合形式排序策略以及三类典型应用题。掌握这一单元的关键,是理解三种形式都表示”整体的一部分”,并熟练运用”分母为 10 的幂”和”除以 100 / 乘以 100″这两条主线。

This article has systematically covered all the core content of the Cambridge Primary Mathematics Stage 6 unit on fractions, decimals and percentages: the meaning of the three forms, six conversion methods (fractions and decimals, percentages and decimals, fractions and percentages), the supporting role of equivalent fractions with simplifying and scaling, a high-frequency conversion table, strategies for ordering mixed forms, and three typical types of word problems. The key to mastering this unit is understanding that all three forms represent “a part of a whole”, and fluently applying the two main threads: denominators as powers of 10, and the divide-by-100 / multiply-by-100 rules.

建议的学习路线:第一步,把速查表中的 14 组基准值全部默写过关;第二步,每天完成 10 道转换练习,覆盖六个方向;第三步,每周做 2 道综合应用题并把解题步骤写完整;第四步,用检查清单复盘每一道错题,找出自己的易错类型并针对性训练。坚持四周,这一单元的得分率会有明显提升。

The suggested learning route: first, memorise all 14 benchmark values in the quick reference table until you can write them from memory; second, complete 10 conversion drills every day covering all six directions; third, solve 2 comprehensive word problems each week and write out the full steps; fourth, review every wrong answer with the checking list, identify your personal error types and train on them specifically. Stick with this for four weeks and your score rate in this unit will improve noticeably.

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