Cambridge Lower Secondary Mathematics Workbook 7: Answers & Key Concepts Explained | 剑桥初中数学练习册7：答案与知识点精讲

📚 Cambridge Lower Secondary Mathematics Workbook 7: Answers & Key Concepts Explained | 剑桥初中数学练习册7：答案与知识点精讲

This comprehensive guide unpacks the essential topics found in Cambridge Lower Secondary Mathematics Workbook 7, linking worked answers to clear explanations. Mastering these concepts will build a strong foundation for further study and boost your confidence in tackling exam-style questions.

本指南深度解析剑桥初中数学练习册7的核心主题，将精选答案与清晰的概念讲解紧密结合，帮你夯实基础，从容应对各类考题。

1. Integers and Place Value | 整数与位值

In Workbook 7, you are often asked to read and write large numbers. Understanding place value helps you break down 5,620,481 as 5 million + 6 hundred thousands + 2 ten thousands + 0 thousands + 4 hundreds + 8 tens + 1 one. This skill is essential for ordering and comparing integers and for grasping the structure of our number system.

练习册7中经常要求读写大数。理解位值有助于你将5,620,481分解为5个百万、6个十万、2个万、0个千、4个百、8个十和1个一。这一技能对排序和比较整数、以及掌握计数体系的结构至关重要。

Negative numbers are introduced on the number line. To arrange −9, −3, −1, 2, 0 in ascending order, remember that −9 < −3 < −1 < 0 < 2. In answer keys, you may see questions requiring you to find the difference between temperatures, e.g., −4°C and 3°C gives a difference of 7°C.

负数在数轴上引入。要将−9、−3、−1、2、0按升序排列，需记住−9 < −3 < −1 < 0 < 2。答案中常出现温度差的计算，例如−4°C和3°C相差7°C。

2. Factors, Multiples and Primes | 因数、倍数与质数

One common workbook task is finding the Highest Common Factor (HCF) and Lowest Common Multiple (LCM). For 18 and 24, list factors: 18 (1,2,3,6,9,18); 24 (1,2,3,4,6,8,12,24). HCF = 6. Multiples: 18 (18,36,54,72…); 24 (24,48,72…). LCM = 72. Use prime factorisation to verify: 18 = 2 × 3²; 24 = 2³ × 3.

常见的练习是找最大公因数（HCF）和最小公倍数（LCM）。对于18和24，列出因数：18（1,2,3,6,9,18）；24（1,2,3,4,6,8,12,24）。HCF=6。倍数：18 (18,36,54,72…); 24 (24,48,72…)。LCM=72。可用质因数分解验证：18=2×3²；24=2³×3。

Prime numbers are numbers greater than 1 with exactly two factors. The first ten primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Workbook 7 includes sieve of Eratosthenes activities. Knowing primes helps with simplifying fractions, finding HCF/LCM, and understanding number properties.

质数是大于1且只有两个因数的数。前十个质数为2、3、5、7、11、13、17、19、23、29。练习册7包含埃拉托色尼筛法活动。认识质数有助于约分、求HCF和LCM，以及理解数的性质。

3. Fractions: Operations and Simplification | 分数：运算与化简

Adding and subtracting fractions requires a common denominator. For 2/5 + 1/3, the LCM of 5 and 3 is 15. Convert: 2/5 = 6/15, 1/3 = 5/15, so sum = 11/15. Always simplify your answer: 12/16 = 3/4. Mixed numbers should be turned into improper fractions before adding.

分数加减需要通分。以2/5+1/3为例，5和3的最小公倍数是15。转换：2/5=6/15，1/3=5/15，和为11/15。最后一定要化简：12/16=3/4。带分数需先化为假分数再相加减。

Multiplication and division: multiply numerators and denominators. 3/4 × 2/5 = 6/20 = 3/10. For division, flip the second fraction: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. The rule ‘invert and multiply’ is essential for fraction division answers.

乘除法：分子乘分子、分母乘分母。3/4 × 2/5 = 6/20 = 3/10。除法时将第二个分数取倒数：3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8。“颠倒相乘”规则是分数除法答题的关键。

4. Decimals: Place Value and Calculations | 小数：位值与计算

Multiplying decimals: ignore decimal points initially. For 0.6 × 0.4, do 6 × 4 = 24. Count total decimal places (1 + 1 = 2), so the answer is 0.24. For division, 1.2

Published by TutorHao | Mathematics Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）