📚 Essential Maths Book 7F: Core Topics for Year 7 | 《Essential Maths Book 7F》Year 7 核心主题精讲
Essential Maths Book 7F is a widely used foundation-level textbook for Year 7 students. It builds confidence in whole numbers, decimals, fractions, simple algebra, geometry and statistics. This article summarises the key topics and shows how to master each skill step by step.
《Essential Maths Book 7F》是一本广泛使用的 Year 7 基础数学教材。它帮助学生建立整数、小数、分数、简单代数、几何与统计等方面的信心。本文梳理核心主题，并逐步讲解如何掌握每项技能。
1. Place Value and Ordering Numbers | 数位与数字排序
Place value is the foundation of all number work. Each digit has a value depending on its position. In the number 5,306 the 5 is in the thousands place, the 3 is in the hundreds place, the 0 is in the tens place and the 6 is in the units place. For decimals, the first place after the decimal point is tenths, then hundredths, then thousandths.
数位是所有数字运算的基础。每个数字的值取决于它的位置。在 5,306 中，5 在千位，3 在百位，0 在十位，6 在个位。对于小数，小数点后第一位是十分位，然后是百分位、千分位。
To order numbers, compare the digits from left to right. For example, 0.72 is greater than 0.7 because 2 hundredths is greater than 0 hundredths. Using a place-value grid can help you line up the digits neatly.
排序数字时，要从左到右逐位比较。例如 0.72 大于 0.7，因为 2 个百分之一大于 0 个百分之一。使用数位表可以帮助你把数字整齐排列。
2. Addition and Subtraction of Whole Numbers | 整数加减法
Addition and subtraction are essential arithmetic skills. You should be able to add and subtract whole numbers using mental methods and written column methods. When using column addition, line up the units, tens and hundreds carefully. Carry or exchange when a column total is 10 or more.
加法和减法是基本的算术技能。你需要能够使用心算和竖式方法进行整数的加减。使用竖式加法时，要仔细对齐个位、十位和百位。当某一列的和达到或超过 10 时，就要进位或交换。
is too small. Always check your answer by adding: if a − b = c, then c + b should equal a.
减法要从右向左计算，如果上方的数字太小，就向相邻列借位。最后要用加法验算：如果 a − b = c，那么 c + b 应该等于 a。
3. Multiplication and Division Strategies | 乘除法策略
faster. The grid method and long multiplication help with larger numbers, such as 23 × 14.
乘法是重复相加。你应该熟记 12 × 12 以内的乘法表，因为它们能让心算快得多。网格法和长乘法可以帮助计算较大的数字，例如 23 × 14。
Division is sharing into equal groups. Short division is used for dividing by a single digit, while long division is used for larger divisors. The answer can include a remainder, a decimal or a fraction.
除法是分成相等的组。短除法用于除以一位数，长除法用于除数较大的情况。答案可以包含余数、小数或分数。
dividend ÷ divisor = quotient
被除数 ÷ 除数 = 商
4. Factors, Multiples and Primes | 因数、倍数与质数
A factor is a number that divides exactly into another number. For example, the factors of 12 are 1, 2, 3, 4, 6 and 12. A multiple is the result of multiplying a number by an integer, so the multiples of 5 are 5, 10, 15, 20 and so on.
因数是可以正好整除另一个数的数。例如 12 的因数有 1、2、3、4、6 和 12。倍数是一个数乘以整数得到的结果，所以 5 的倍数是 5、10、15、20 等。
A prime number has exactly two distinct factors: 1 and itself. The first few primes are 2, 3, 5, 7, 11, 13, 17 and 19. Remember that 1 is not prime because it has only one factor.
质数恰好有两个不同的因数：1 和它本身。前几个质数是 2、3、5、7、11、13、17 和 19。请记住 1 不是质数，因为它只有一个因数。
The highest common factor (HCF) is the largest factor shared by two numbers, while the lowest common multiple (LCM) is the smallest multiple they share. These ideas help when simplifying fractions and solving problems.
最大公因数（HCF）是两个数共有的最大因数，最小公倍数（LCM）是它们共有的最小倍数。这些概念有助于化简分数和解决问题。
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