Grade 6 Mathematics Student Book: Core Skills and Practice | 六年级数学学生用书：核心技能与练习

📚 Grade 6 Mathematics Student Book: Core Skills and Practice | 六年级数学学生用书：核心技能与练习

This student book covers the essential Grade 6 mathematics topics in a clear, step-by-step way. You will build confidence with whole numbers, fractions, decimals, percentages, ratio, algebra, geometry and statistics. Each section pairs key ideas with worked examples so you can learn actively and check your understanding.

本学生用书以清晰、循序渐进的方式涵盖六年级数学的核心主题。你将通过整数、分数、小数、百分比、比、代数、几何和统计等内容建立信心。每一节都配有要点和例题，帮助你主动学习并检查理解。

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1. Number and Place Value | 数与位值

In Grade 6, numbers can run into millions and beyond. Place value tells you the value of each digit according to its position. For example, in 4 728 356, the digit 7 means 700 000 because it is in the hundred-thousands place.

在六年级，数字可以达到百万甚至更大。位值表示每个数字根据位置不同而具有的值。例如，在 4 728 356 中，数字 7 表示 700 000，因为它位于十万位。

You should be able to read, write, order and round whole numbers. Rounding to the nearest 10, 100, 1000 or 1 000 000 is an important skill. For example, 65 432 rounded to the nearest 1000 is 65 000.

你应该能够读写、排序和四舍五入整数。四舍五入到最近的10、100、1000或1 000 000是一项重要技能。例如，65 432 四舍五入到最近的1000是65 000。

Write large numbers in expanded form to show the value of each digit. For example, 6 305 200 = 6 000 000 + 300 000 + 5 000 + 200.

可以用展开式书写大数来显示每个数字的值。例如，6 305 200 = 6 000 000 + 300 000 + 5 000 + 200。

Negative numbers appear on the left of zero on a number line. You can compare negative numbers by remembering that −7 is less than −2 because −7 is further to the left.

负数在数轴上位于零的左侧。比较负数时记住 −7 小于 −2，因为 −7 更靠左。

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2. Operations with Whole Numbers | 整数运算

Addition, subtraction, multiplication and division of whole numbers form the foundation of arithmetic. Always check the reasonableness of an answer by estimating first. For example, 398 + 205 is close to 400 + 200 = 600.

整数的加法、减法、乘法和除法是算术的基础。先进行估算有助于检查答案是否合理。例如，398 + 205 接近 400 + 200 = 600。

Use the order of operations when a calculation mixes several operations. The rule is brackets first, then indices (powers), then multiplication and division from left to right, then addition and subtraction from left to right. For example, 3 + 4 × 5 = 3 + 20 = 23.

当计算包含多种运算时，要使用运算顺序。规则是先算括号，再算指数（幂），然后从左到右算乘法和除法，最后从左到右算加法和减法。例如，3 + 4 × 5 = 3 + 20 = 23。

Long multiplication and long division become manageable when you break the calculation into place-value parts. For 36 × 24, you can calculate 36 × 20 = 720 and 36 × 4 = 144, then add to get 864.

长乘法和长除法可以通过按位值拆分变得简单。对于 36 × 24，可以先算 36 × 20 = 720 和 36 × 4 = 144，再加起来得到 864。

Division can include remainders. For 100 ÷ 7, the quotient is 14 with a remainder of 2 because 14 × 7 = 98 and 100 − 98 = 2.

除法可能有余数。对于 100 ÷ 7，商是 14，余数是 2，因为 14 × 7 = 98，而 100 − 98 = 2。

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3. Fractions: Concepts and Equivalence | 分数概念与等值

A fraction such as 3/4 means 3 parts out of 4 equal parts. The top number is the numerator and the bottom number is the denominator. Equivalent fractions show the same amount using different numbers, such as 3/4 = 6/8 = 9/12.

像 3/4 这样的分数表示 4 等份中的 3 份。上面的数是分子，下面的数是分母。等值分数用不同的数表示相同的量，例如 3/4 = 6/8 = 9/12。

To simplify a fraction, divide the numerator and denominator by their highest common factor. For example, 18/24 can be simplified by dividing both by 6 to get 3/4.

化简分数时，要用分子和分母的最大公因数去除。例如，18/24 的分子和分母都除以 6，得到 3/4。

Improper fractions have a numerator greater than or equal to the denominator. They can be written as mixed numbers, for example 11/4 = 2 3/4.

假分数的分子大于或等于分母。它们可以写成带分数，例如 11/4 = 2 3/4。

To compare fractions, write them with a common denominator. For 2/5 and 3/10, use 10 as the common denominator: 2/5 = 4/10, so 2/5 is greater than 3/10.

比较分数时，先写成同分母分数。对于 2/5 和 3/10，用 10 作公分母：2/5 = 4/10，所以 2/5 大于 3/10。

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4. Adding and Subtracting Fractions | 分数加减

To add or subtract fractions with the same denominator, keep the denominator and add or subtract the numerators. For example, 5/9 + 2/9 = 7/9.

同分母分数相加减，分母不变，分子相加减。例如，5/9 + 2/9 = 7/9。

With unlike denominators, first write equivalent fractions with a common denominator. For 1/4 + 1/6, the common denominator is 12, so 1/4 = 3/12 and 1/6 = 2/12, giving 5/12.

异分母分数相加减时，先化成分母相同的等值分数。对于 1/4 + 1/6，公分母是12，因此 1/4 = 3/12，1/6 = 2/12，结果为 5/12。

When adding mixed numbers, add the whole numbers and fractions separately, then simplify if needed. For example, 2 1/3 + 1 1/6 = 3 3/6 = 3 1/2.

带分数相加时，可以分别把整数部分和分数部分相加，再根据需要化简。例如，2 1/3 +

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