Grade 7 Maths Practice Workbook | 七年级数学练习册

📚 Grade 7 Maths Practice Workbook | 七年级数学练习册

Welcome to the Grade 7 Maths Practice Workbook. This bilingual guide is designed to help students build a strong foundation in core mathematical skills, including number operations, algebra, geometry, and data handling. Each section includes key ideas, worked examples, and practice prompts that match typical international Grade 7 curricula.

欢迎使用七年级数学练习册。本双语指南旨在帮助学生巩固核心数学技能，包括数的运算、代数、几何和数据处理。每节都包含关键概念、例题和练习提示，与典型国际七年级课程相匹配。

1. Integers and Rational Numbers | 整数与有理数

In Grade 7, students extend whole numbers to include negative integers and rational numbers. A rational number is any number that can be written as a fraction a/b, where a and b are integers and b ≠ 0. The number line is a useful model for comparing and ordering these numbers. The sign rules for addition and subtraction are fundamental: adding a negative number is the same as subtracting its positive counterpart, and subtracting a negative number is equivalent to adding. For example, −3 + 5 = 2 and −4 − 6 = −10.

在七年级，学生将整数扩展到负整数和有理数。有理数是可以写成 a/b 形式的任何数，其中 a 和 b 是整数且 b ≠ 0。数轴是比较和排序这些数的有用模型。加减法的符号规则是基础：加上一个负数等同于减去它的正数；减去一个负数等同于加上一个正数。例如，−3 + 5 = 2，−4 − 6 = −10。

For multiplication and division, the sign rules are: positive × positive = positive, negative × negative = positive, positive × negative = negative. The same holds for division. Remember that dividing by zero is undefined.

对于乘法和除法，符号规则为：正 × 正 = 正，负 × 负 = 正，正 × 负 = 负。除法同理。请记住，除以零是未定义的。

2. Fractions, Decimals and Percentages | 分数、小数与百分数

Being able to move fluently between fractions, decimals and percentages is a core Grade 7 skill. To convert a fraction to a decimal, divide the numerator by the denominator: 3/4 = 0.75. To convert to a percentage, multiply the decimal by 100: 0.75 × 100 = 75%. For adding and subtracting fractions with unlike denominators, first find a common denominator. For example, 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2.

能够在分数、小数和百分数之间熟练转换是七年级的核心技能。将分数转换为小数，用分子除以分母：3/4 = 0.75。转换为百分数，将小数乘以100：0.75 × 100 = 75%。对于分母不同的分数加减法，首先要找到公分母。例如，1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2。

Common equivalents you should memorise include: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20%, and 1/10 = 0.1 = 10%. Percent increase and decrease questions often appear in real-world contexts such as discounts and interest.

你应该记住的常见等价关系包括：1/2 = 0.5 = 50%，1/4 = 0.25 = 25%，3/4 = 0.75 = 75%，1/5 = 0.2 = 20%，以及 1/10 = 0.1 = 10%。百分数增加和减少问题经常出现在折扣和利息等实际情境中。

3. Algebraic Expressions | 代数式

Algebra uses letters called variables to represent unknown or changing quantities. A term is a single number, variable, or product such as 3x or 7. Like terms have the same variable part and can be combined: 3x + 5 − x + 2 simplifies to 2x + 7. The distributive property lets you expand expressions: a(b + c) = ab + ac. For example, 2(x + 3) = 2x + 6.

代数使用称为变量的字母来表示未知或变化的量。一个项是单个数字、变量或乘积，如 3x 或 7。同类项具有相同的变量部分，可以合并：3x + 5 − x + 2 化简为 2x + 7。分配律可用来展开表达式：a(b + c) = ab + ac。例如，2(x + 3) = 2x + 6。

To evaluate an expression, replace each variable with its given value and follow the order of operations (brackets, indices, division and multiplication, addition and subtraction). If a = 4 and b = 2, then 2a + 3b = 2×4 + 3×2 = 8 + 6 = 14.

要求代数式的值，将每个变量替换为给定的值，并遵循运算顺序（括号、指数、乘除、加减）。如果 a = 4，b = 2，那么 2a + 3b = 2×4 + 3×2 = 8 + 6 = 14。

3a + 2a = 5a and a(b + c) = ab + ac

4. Solving Linear Equations | 解一元一次方程

An equation is a statement that two expressions are equal. The goal is to find the value of the unknown that makes the statement true. Use inverse operations to isolate the variable while keeping the equation balanced. For the equation 2x + 3 = 11, first subtract 3 from both sides to get 2x = 8, then divide both sides by 2 to get x = 4.

方程是表示两个表达式相等的语句。目标是找到使该语句成立的未知数的值。使用逆运算来分离变量，同时保持方程平衡。对于方程 2x + 3 = 11，首先两边减 3 得到 2x = 8，然后两边除以 2 得到 x = 4。

Always check your solution

Published by TutorHao | Mathematics Revision Series | aleveler.com

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