小数乘法简便运算（专项训练）-2026-2027学年五年级上册数学人教版

**基本信息** 以“运算定律一致性”为核心，通过“万能三步走”框架系统整合六大题型，构建从基础凑整到高阶构造的思维训练体系，培养抽象能力与运算能力。 **专项设计** |模块|题量/典例|方法提炼|知识逻辑| |----|-----------|----------|----------| |交换律+结合律|基础10+变式10+思维10|黄金搭档凑整（2.5×4等）、拆数结合|从连乘特征到多层拆分，体现运算顺序优化| |分配律正逆用|正向30+逆用30|正向去括号不漏乘、逆用提取公因数（含隐藏×1）|从公式直接应用到符号与数字特征分析| |拆分凑整|基础10+变式10+思维10|9.9=10-0.1等拆数建模|从简单拆分到构造相同因数的推理训练| |积不变规律|基础10+变式10+思维10|因数缩放成对移动小数点|建立小数变形与公因数构造的关联| |整体代换|基础10+变式10+思维10|大数拆整（如2026×2025.2025）|从具体运算到代数换元思想的过渡|

五上小数乘法简便运算·全题型综合练习 核心信念：小数和整数运算定律完全一样，只是多了小数点。 三大基石：乘法交换律、乘法结合律、乘法分配律。 公式总表（背熟） 定律 字母公式 关键提醒 交换律 a × b = b × a 交换两个乘数的位置 结合律 (a×b)×c = a×(b×c) 改变运算顺序，只适合连乘 分配律 (a+b)×c = a×c + b×c (a-b)×c = a×c - b×c 乘加、乘减才用，每个数都要乘外面的数 区分核心：分配律是乘加/乘减；结合律只有乘法，没有加减号！ 做题“万能三步走”（拿到题先看这3步） 1.看符号定方向： ①全是×（连乘）→ 优先交换律、结合律（找 2.5、1.25 凑整）。 ②有乘有加/减 → 优先乘法分配律（找相同因数，或看能否拆数）。 2.看数字找特征： ①有没有 9.9、10.1？ → 拆成整十/整百±小数。 ②两个乘法算式有没有相同因数？ → 提取公因数。 ③没有相同因数？ → 用 “积不变规律” 变出一个公因数。 3.动笔算，查符号：注意小数点位置，检查有没有漏乘。 类型一：交换律 + 结合律（连乘凑整） 黄金搭档：0.25×4=1，1.25×8=10，0.125×8=1，2.5×4=10 【基础题】（直接交换或结合） ① 0.25 × 4.7 × 4 ② 1.25 × 0.8 × 6.3 ③ 0.5 × 2.3 × 0.2 ④ 2.5 × 3.9 × 0.4 ⑤ 0.125 × 7.2 × 8 ⑥ 4.7 × 0.25 × 4 ⑦ 1.25 × 5.6 × 8 ⑧ 0.25 × 1.6 × 0.4 ⑨ 12.5 × 0.7 × 0.8 ⑩ 0.4 × 2.5 × 0.8 【变式题】（需拆一个数再结合） ① 2.5 × 3.2 × 1.25  ② 0.25 × 4.8 × 1.25  ③ 1.25 × 2.5 × 1.6  ④ 0.125 × 0.25 × 3.2  ⑤ 2.5 × 0.32 × 1.25  ⑥ 0.4 × 2.5 × 1.25 × 8 ⑦ 1.25 × 0.8 × 2.5 × 0.4 ⑧ 0.125 × 8 × 0.25 × 40 ⑨ 2.5 × 0.8 × 12.5 × 4 ⑩ 0.25 × 1.25 × 3.2 × 2.5 【思维题】（多层拆分+换元思想） ① 0.125 × 0.25 × 0.5 × 64  ② 1.25 × 2.5 × 32 × 0.25 ③ 0.625 × 1.6 × 0.25  ④ 3.2 × 1.25 × 2.5 × 0.5 ⑤ 1.28 × 2.5 × 0.125 ⑥ 0.75 × 0.4 × 2.5 × 1.6 ⑦ 0.16 × 1.25 × 5 × 0.4 ⑧ 2.5 × 0.77 × 0.4 × 2 ⑨ 1.25 × 0.88 × 8 ⑩ 0.125 × 9.6 × 0.25 类型二：乘法分配律正向用（去括号） 格式：(a±b)×c = a×c ± b×c，括号里每个数都要乘外面的数！ 【基础题】 ① (10 + 0.2) × 4.5 ② (10 - 0.2) × 3.2 ③ (100 + 0.5) × 0.8 ④ (20 + 0.3) × 6.7 ⑤ (30 - 0.1) × 5.1 ⑥ (40 + 0.8) × 2.5 ⑦ (8 + 0.4) × 1.25 ⑧ (4 - 0.04) × 0.25 ⑨ (10 + 0.5) × 7.6 ⑩ (10 - 0.3) × 9.3 【变式题】（括号内三项） ① (4 + 0.4 + 0.04) × 0.25 ② (8 + 0.8 - 0.08) × 1.25 ③ (4 - 0.4 + 0.2) × 2.5 ④ (80 + 8 + 0.8) × 0.125 ⑤ (10 + 0.2 - 0.02) × 4.8 ⑥ (5 + 0.5 - 0.05) × 3.6 ⑦ (20 - 0.4 + 0.02) × 0.5 ⑧ (10 - 0.1 + 0.01) × 7.2 ⑨ (50 + 0.5 - 0.05) × 1.6 ⑩ (25 - 0.5 + 0.05) × 0.4 【思维题】（四项展开 + 需拆开括号外乘数） ①(80 + 8 + 0.8 + 0.08) × 0.125 ②(40 + 4 + 0.4 + 0.04) × 2.5 ③(4 + 0.8 - 0.04 - 0.004) × 0.25 ④(8 - 0.8 + 0.08 - 0.008) × 1.25 ⑤(10 + 0.2) × 3.6 + (10 - 0.2) × 3.6 ⑥(10 - 0.1) × 4.8 - (5 + 0.2) × 4.8 ⑦(50 + 0.3) × 2.4 + (50 - 0.3) × 2.4 ⑧(20 + 0.3) × 5.2 - (10 - 0.1) × 5.2 ⑨(100 + 0.2 + 0.03) × 0.78 ⑩(5 + 0.2 - 0.01) × 1.6 题型三：乘法分配律逆用（提取公因数） --考试重难点 格式：a×c ± b×c = c×(a±b) 隐藏×1：单独一个数 a = a×1 【基础题】 ① 5.6 × 3.8 + 4.4 × 3.8 ② 2.5 × 1.3 + 2.5 × 6.7 ③ 0.6 × 4.7 + 0.6 × 5.3 ④ 1.2 × 9.8 - 1.2 × 8.8 ⑤ 7.5 × 2.4 + 2.5 × 2.4 ⑥ 4.6 × 7.2 - 4.6 × 6.2 ⑦ 3.8 × 5.5 + 6.2 × 5.5 ⑧ 9.9 × 6.4 - 9.9 × 5.4 ⑨ 0.45 × 3.6 + 0.55 × 3.6 ⑩ 8.3 × 4.7 - 8.3 × 3.7 【变式题】（隐藏×1） ①7.8 × 4.2 + 7.8 × 5.8 - 7.8 ②3.5 × 4.6 + 3.5 × 6.4 - 3.5 ③4.2 × 1.01 + 4.2 × 0.99 - 4.2 × 0.1 ④9.9 × 8.1 + 9.9 × 1.9 - 9.9 ⑤6.3 × 5.4 + 6.3 × 4.6 - 6.3 ⑥2.8 × 3.7 + 2.8 × 6.3 - 2.8 ⑦0.72 × 4.5 + 0.72 × 6.5 - 0.72 ⑧5.6 × 7.4 + 5.6 × 2.6 - 5.6 ⑨1.25 × 4.3 + 1.25 × 5.7 - 1.25 ⑩0.96 × 6.7 + 0.96 × 3.3- 0.96 【思维题】 ① 8.9 × 1.1 + 1.1 × 1.1 - 11 ② 3.6 × 2.7 + 7.4 × 3.6 - 3.6 ③ 4.8 × 0.7 + 0.52 × 7  ④ 2.7 × 4.8 + 7.3 × 4.8 - 4.8 ⑤ 6.5×3.8 + 3.5×3.8 - 3.8×2 ⑥ 9.4 × 2.5 + 0.6 × 2.5 - 2.5 ⑦ 3.8×6.7+6.2×6.7-6.7×5 ⑧ 0.85×2.4 +0.15×2.4 - 2.4×0.1 ⑨ 12.5×3.2 -2.5×3.2+3.2 ⑩ 4.6×7.5+5.4×7.5-7.5×10 类型四：拆分凑整（高频必考） 核心：9.9=10-0.1，10.1=10+0.1，99=100-1，101=100+1 【基础题】 ① 9.9 × 6.7 ② 10.1 × 3.4 ③ 0.99 × 8.5 ④ 1.01 × 2.8 ⑤ 9.99 × 5.6  ⑥ 10.01 × 4.7  ⑦ 0.98 × 7.3  ⑧ 1.02 × 6.4  ⑨ 9.8 × 3.6  ⑩ 10.2 × 5.5  【变式题】（拆数后配合提公因数） ① 9.9 × 7.8 + 0.78 ② 10.1 × 4.5 - 0.45 ③ 0.99 × 6.4 + 0.064 ④ 1.01 × 3.7 - 0.037 ⑤ 9.8 × 5.2 + 1.04 ⑥ 10.2 × 2.6 - 0.52 ⑦ 9.9 × 8.3 + 0.83 ⑧ 10.1 × 6.8 - 0.68 ⑨ 0.98 × 4.5 + 0.09 ⑩ 1.02 × 3.6 - 0.072 【思维题】（构造相同因数） ① 9.9 × 9.9 + 0.99  ② 10.1 × 10.1 - 1.01 ③ 99.9 × 6.6 + 6.66 ④ 9.99 × 8.8 + 0.088 ⑤ 10.01 × 7.7 - 0.077 ⑥ 0.999 × 6.4 + 0.0064 ⑦ 1.001 × 5.5 - 0.0055 ⑧ 9.9 × 4.8 + 4.8 × 0.1 ⑨ 10.1 × 3.2 - 3.2 × 0.1 ⑩ 9.99 × 7.5 + 7.5 × 0.01 类型五：积不变规律（变形构造公因数)--必考难点 核心：两个乘法没有一模一样因数，利用 “积不变规律” 变出公因数。a×b 中，一个因数×10，另一个÷10，积不变。 规律：一个因数扩大几倍，另一个因数缩小相同倍数，积不变。 例：4.8 × 0.35 = 0.48 × 3.5 【基础题】 ① 3.6 × 4.5 + 0.36 × 55 ② 4.8 × 7.5 + 0.48 × 25 ③ 0.79 × 1.2 + 7.9 × 0.08 ④ 6.3 × 2.8 + 0.63 × 72 ⑤ 2.4 × 3.6 + 0.24 × 64 ⑥ 1.25 × 3.4 + 0.125 × 66 ⑦ 5.6 × 4.2 + 0.56 × 58 ⑧ 7.2 × 5.3 + 0.72 × 47 ⑨ 3.8 × 6.1 + 0.38 × 39 ⑩ 9.4 × 5.7 + 0.94 × 43 【变式题】 ① 4.2 × 6.8 + 0.42 × 32 ② 3.6 × 7.4 + 0.36 × 26 ③ 0.78 × 3.5 + 7.8 × 0.65 ④ 1.6 × 4.5 + 0.16 × 55 ⑤ 8.5 × 2.3 + 0.85 × 77 ⑥ 2.7 × 6.4 + 0.27 × 36 ⑦ 0.96 × 4.8 + 9.6 × 0.52 ⑧ 5.4 × 3.7 + 0.54 × 63 ⑨ 7.6 × 2.5 + 0.76 × 75 ⑩ 3.2 × 5.6 + 0.32 × 44 【思维题】（三项移位 + 多次变换） ① 2.4 × 3.6 + 0.24 × 14 + 36 × 0.076 ② 3.6 × 4.5 + 0.36 × 55 - 0.036 × 10 ③ 0.8 × 3.7 + 0.08 × 63 ④ 1.25 × 4.6 + 0.125 × 54 ⑤ 2.5 × 5.8 + 0.25 × 42 ⑥ 0.6 × 7.3 + 6 × 0.27 ⑦ 0.35 × 4.6 + 3.5 × 0.54 ⑧ 4.4 × 2.5 + 44 × 0.75 ⑨ 1.6 × 9.7 + 16 × 0.03 ⑩ 0.28 × 3.9 + 2.8 × 0.61 类型六：整体代换与构造（思维巅峰） 核心：无直接公因数，通过“拆大数”或“换元”强行构造。 经典代表：2026 × 2025.2025 - 2025 × 2026.2026 【基础题】（构造“×1”思想） ① 101 × 4.8 - 4.8 ② 202 × 3.6 - 3.6 × 2 ③ 303 × 2.5 - 2.5 × 3 ④ 1001 × 5.6 - 5.6 ⑤ 99 × 7.2 + 7.2 ⑥ 199 × 4.5 + 4.5 ⑦ 98 × 6.3 + 6.3 × 2 ⑧ 97 × 8.4 + 8.4 × 3 ⑨ 102 × 3.7 - 3.7 × 2 ⑩ 1002 × 2.6 - 2.6 × 2 【变式题】 ① 101 × 4.8 - 4.8 × 0.1 ② 99 × 5.6 + 5.6 × 1.1 ③ 202 × 3.7 - 3.7 × 2.02 ④ 100.1 × 6.5 - 0.65  ⑤ 99.9 × 7.8 + 7.8 × 0.1 ⑥ 100.01 × 4.5 - 0.045 ⑦ 9.9 × 5.6 + 0.56 ⑧ 10.1 × 8.7 - 0.87 ⑨ 101.01 × 3.2 - 3.2 × 0.01 ⑩ 99.99 × 2.5 + 2.5 × 0.01 【思维题】 ① 2026 × 2025.2025 - 2025 × 2026.2026 ② 2025 × 2026.2026 - 2026 × 2025.2025 ③ 31.4 × 6.7 + 3.14 × 33 ④ 28.6 × 4.5 + 2.86 × 55 ⑤ 7.2 × 5.3 + 0.72 × 47 ⑥ 6.8 × 3.9 + 0.68 × 61 ⑦ 4.5 × 7.6 + 0.45 × 24 ⑧ 9.6 × 2.8 + 0.96 × 72 ⑨ 5.4 × 8.7 + 0.54 × 13 ⑩ 3.7 × 6.2 + 0.37 × 38 五年级高频易错点汇总（考前必看） 序号 易错点 正确做法 1 混淆结合律和分配律 (2.5×4)×0.8 只有乘法，用结合律； (2.5+4)×0.8 有加号，用分配律，每个数都要乘0.8。 2 分配律漏乘 括号里每一个数，都要乘外面的数。 ❌ (10-0.2)×0.5 = 10×0.5 - 0.2 ✅ = 10×0.5 - 0.2×0.5 3 符号看错 括号内是减号，展开后还是减号；提取公因数时，括号内符号与原式一一对应。 4 拆数用错方法 连乘拆数要拆成乘法（3.2=4×0.8），不要拆成加减（3+0.2），除非用分配律。 5 隐藏的×1 看到单独一个数 a，马上想到 a × 1，提公因数时千万别漏掉它！ 6 小数位数点错 做完简便运算，对照原式估算一下，检查小数点位置是否合理。 7 移小数点只移一边 用“积不变”变公因数时，一个因数×10，另一个必须÷10，要成对移动！ 全题型对照总表（复习索引） 题型 特征 核心方法 易错预警 ①交换+结合 全是× 找 2.5/1.25 凑整 只能用于连乘，有加减号不能用 ②正向分配 (a±b)×c 括号内各项分别乘c 不能漏乘任何一项 ③凑整拆数 9.9、10.1 拆成整十/百±小数 拆数后要加括号，注意符号 ④提取公因数 a×c±b×c 提相同因数 注意隐藏的×1，符号要跟上 ⑤构造公因数 无相同因数 用“积不变”变出来 小数点移动要成对（一扩一缩） ⑥整体构造 大数换元 拆成 整数×1.0001 等 整体代入，抵消时仔细 五上小数乘法简便运算·全题型综合练习（含完整简算步骤+答案） 类型一：交换律 + 结合律（连乘凑整） 基础题 ① 0.25 × 4.7 × 4 =0.25×4×4.7 =1×4.7 =4.7 ② 1.25 × 0.8 × 6.3 =1×6.3 =6.3 ③ 0.5 × 2.3 × 0.2 =0.5×0.2×2.3 =0.1×2.3 =0.23 ④ 2.5 × 3.9 × 0.4 =2.5×0.4×3.9 =1×3.9 =39 ⑤ 0.125 × 7.2 × 8 =0.125×8×7.2 =1×7.2 =7.2 ⑥ 4.7 × 0.25 × 4 =4.7×(0.25×4) =4.7×1 =4.7 ⑦ 1.25 × 5.6 × 8 =1.25×8×5.6 =10×5.6 =56 ⑧ 0.25 × 1.6 × 0.4 =0.25×0.4×1.6 =0.1×1.6 =0.16 ⑨ 12.5 × 0.7 × 0.8 =12.5×0.8×0.7 =10×0.7 =7 ⑩ 0.4 × 2.5 × 0.8 =1×0.8 =0.8 变式题 ① 2.5 × 3.2 × 1.25 =2.5×(0.4×8)×1.25 =(2.5×0.4)×(8×1.25) =1×10=10 ② 0.25 × 4.8 × 1.25 =0.25×0.6×8×1.25 =(0.25×0.6)×(8×1.25) =0.15×10 =1.5 ③ 1.25 × 2.5 × 1.6 =1.25×2.5×0.2×8 =(1.25×8)×(2.5×0.2) =10×0.5 =5 ④ 0.125 × 0.25 × 3.2 =0.125×0.25×0.4×8 =(0.125×8)×(0.25×0.4) =1×0.1 =0.1 ⑤ 2.5 × 0.32 × 1.25 =2.5×0.4×0.8×1.25 =1×1 =1 ⑥ 0.4 × 2.5 × 1.25 × 8 =(0.4×2.5)×(1.25×8) =1×10 =10 ⑦ 1.25 × 0.8 × 2.5 × 0.4 =( 1.25 × 0.8 )×（ 2.5 × 0.4） =1×1 =1 ⑧ 0.125 × 8 × 0.25 × 40 =（0.125 × 8）×（0.25 × 40） =1×10 =10 ⑨ 2.5 × 0.8 × 12.5 × 4 =(2.5×4)×(0.8×12.5) =10×10 =100 ⑩ 0.25 × 1.25 × 3.2 × 2.5 =0.25×1.25×0.4×8×2.5 =(0.25×0.4)×(1.25×8)×2.5 =0.1×10×2.5 =2.5 思维题 ① 0.125 × 0.25 × 0.5 × 64 =0.125×0.25×0.5×8×4×2 =(0.125×8)×(0.25×4)×(0.5×2) =1×1×1 =1 ② 1.25 × 2.5 × 32 × 0.25 =1.25×2.5×8×4×0.25 =(1.25×8)×2.5×(4×0.25) =10×2.5×1 =25 ③ 0.625 × 1.6 × 0.25 =0.625×0.4×4×0.25 =0.25×1 =0.25 ④ 3.2 × 1.25 × 2.5 × 0.5 =0.8×4×1.25×2.5×0.5 =(0.8×1.25)×(4×2.5)×0.5 =1×10×0.5 =5 ⑤ 1.28 × 2.5 × 0.125 =0.16×8×2.5×0.125 =(8×0.125)×(0.16×2.5) =1×0.4 =0.4 ⑥ 0.75 × 0.4 × 2.5 × 1.6 =0.75×0.4×2.5×4×0.4 =0.75×(0.4×2.5×4)×0.4 =0.75×4×0.4 =1.2 ⑦ 0.16 × 1.25 × 5 × 0.4 =0.2×0.8×1.25×5×0.4 =0.2×(0.8×1.25)×(5×0.4) =0.2×1×2 =0.4 ⑧ 2.5 × 0.77 × 0.4 × 2 =(2.5×0.4)×0.77×2 =1×1.54 =1.54 ⑨ 1.25 × 0.88 × 8 =1.25×8×0.88 =10×0.88 =8.8 ⑩ 0.125 × 9.6 × 0.25 =0.125×8×1.2×0.25 =1×0.3 =0.3 类型二：乘法分配律正向用（去括号） 基础题 ① (10 + 0.2) × 4.5 =10×4.5+0.2×4.5 =45+0.9 =45.9 ② (10 - 0.2) × 3.2 =10×3.2-0.2×3.2 =32-0.64 =31.36 ③ (100 + 0.5) × 0.8 =100×0.8+0.5×0.8 =80+0.4 =80.4 ④ (20 + 0.3) × 6.7 =20×6.7+0.3×6.7 =134+2.01 =136.01 ⑤ (30 - 0.1) × 5.1 =30×5.1-0.1×5.1 =153-0.51 =152.49 ⑥ (40 + 0.8) × 2.5 =40×2.5+0.8×2.5 =100+2 =102 ⑦ (8 + 0.4) × 1.25 =8×1.25+0.4×1.25 =10+0.5 =10.5 ⑧ (4 - 0.04) × 0.25 =4×0.25-0.04×0.25 =1-0.01 =0.99 ⑨ (10 + 0.5) × 7.6 =10×7.6+0.5×7.6 =76+3.8 =79.8 ⑩ (10 - 0.3) × 9.3 =10×9.3-0.3×9.3 =93-2.79 =90.21 变式题 ① (4 + 0.4 + 0.04) × 0.25 =4×0.25+0.4×0.25+0.04×0.25 =1+0.1+0.01 =1.11 ② (8 + 0.8 - 0.08) × 1.25 =8×1.25+0.8×1.25-0.08×1.25 =10+1-0.1 =10.9 ③ (4 - 0.4 + 0.2) × 2.5 =4×2.5-0.4×2.5+0.2×2.5 =10-1+0.5 =9.5 ④ (80 + 8 + 0.8) × 0.125 =80×0.125+8×0.125+0.8×0.125 =10+1+0.1 =11.1 ⑤ (10 + 0.2 - 0.02) × 4.8 =10×4.8+0.2×4.8-0.02×4.8 =48+0.96-0.096 =48.864 ⑥ (5 + 0.5 - 0.05) × 3.6 =5×3.6+0.5×3.6-0.05×3.6 =18+1.8-0.18 =19.62 ⑦ (20 - 0.4 + 0.02) × 0.5 =20×0.5-0.4×0.5+0.02×0.5 =10-0.2+0.01 =9.81 ⑧ (10 - 0.1 + 0.01) × 7.2 =10×7.2-0.1×7.2+0.01×7.2 =72-0.72+0.072 =71.352 ⑨ (50 + 0.5 - 0.05) × 1.6 =50×1.6+0.5×1.6-0.05×1.6 =80+0.8-0.08 =80.72 ⑩ (25 - 0.5 + 0.05) × 0.4 =25×0.4-0.5×0.4+0.05×0.4 =10-0.2+0.02 =9.82 思维题 ①(80 + 8 + 0.8 + 0.08) × 0.125 =80×0.125+8×0.125+0.8×0.125+0.08×0.125 =10+1+0.1+0.01 =11.11 ②(40 + 4 + 0.4 + 0.04) × 2.5 =40×2.5+4×2.5+0.4×2.5+0.04×2.5 =100+10+1+0.1 =111.1 ③(4 + 0.8 - 0.04 - 0.004) × 0.25 =4×0.25+0.8×0.25-0.04×0.25-0.004×0.25 =1+0.2-0.01-0.001 =1.189 ④(8 - 0.8 + 0.08 - 0.008) × 1.25 =8×1.25-0.8×1.25+0.08×1.25-0.008×1.25 =10-1+0.1-0.01=9.09 ⑤(10 + 0.2) × 3.6 + (10 - 0.2) × 3.6 =3.6×(10+0.2+10-0.2) =3.6×20 =72 ⑥(10 - 0.1) × 4.8 - (5 + 0.2) × 4.8 =4.8×(10-0.1-5-0.2) =4.8×4.7 =22.56 ⑦(50 + 0.3) × 2.4 + (50 - 0.3) × 2.4 =2.4×(50+0.3+50-0.3) =2.4×100 =240 ⑧(20 + 0.3) × 5.2 - (10 - 0.1) × 5.2 =5.2×(20+0.3-10+0.1) =5.2×10.4 =54.08 ⑨(100 + 0.2 + 0.03) × 0.78 =100×0.78+0.2×0.78+0.03×0.78 =78+0.156+0.0234 =78.1794 ⑩(5 + 0.2 - 0.01) × 1.6 =5×1.6+0.2×1.6-0.01×1.6 =8+0.32-0.016 =8.304 题型三：乘法分配律逆用（提取公因数） 基础题 ① 5.6 × 3.8 + 4.4 × 3.8 =3.8×(5.6+4.4) =3.8×10 =38 ② 2.5 × 1.3 + 2.5 × 6.7 =2.5×(1.3+6.7) =2.5×8 =20 ③ 0.6 × 4.7 + 0.6 × 5.3 =0.6×(4.7+5.3) =0.6×10 =6 ④ 1.2 × 9.8 - 1.2 × 8.8 =1.2×(9.8-8.8) =1.2×1 =1.2 ⑤ 7.5 × 2.4 + 2.5 × 2.4 =2.4×(7.5+2.5) =2.4×10=24 ⑥ 4.6 × 7.2 - 4.6 × 6.2 =4.6×(7.2-6.2) =4.6×1 =4.6 ⑦ 3.8 × 5.5 + 6.2 × 5.5 =5.5×(3.8+6.2) =5.5×10 =55 ⑧ 9.9 × 6.4 - 9.9 × 5.4 =9.9×(6.4-5.4) =9.9×1 =9.9 ⑨ 0.45 × 3.6 + 0.55 × 3.6 =3.6×(0.45+0.55) =3.6×1 =3.6 ⑩ 8.3 × 4.7 - 8.3 × 3.7 =8.3×(4.7-3.7) =8.3×1 =8.3 变式题（隐藏×1） ①7.8 × 4.2 + 7.8 × 5.8 - 7.8 =7.8×(4.2+5.8-1) =7.8×9 =70.2 ②3.5 × 4.6 + 3.5 × 6.4 - 3.5 =3.5×(4.6+6.4-1) =3.5×10 =35 ③4.2 × 1.01 + 4.2 × 0.99 - 4.2 × 0.1 =4.2×(1.01+0.99-0.1) =4.2×1.9 =7.98 ④9.9 × 8.1 + 9.9 × 1.9 - 9.9 =9.9×(8.1+1.9-1) =9.9×9 =89.1 ⑤6.3 × 5.4 + 6.3 × 4.6 - 6.3 =6.3×(5.4+4.6-1) =6.3×9 =56.7 ⑥2.8 × 3.7 + 2.8 × 6.3 - 2.8 =2.8×(3.7+6.3-1) =2.8×9 =25.2 ⑦0.72 × 4.5 + 0.72 × 6.5 - 0.72 =0.72×(4.5+6.5-1) =0.72×10=7.2 ⑧5.6 × 7.4 + 5.6 × 2.6 - 5.6 =5.6×(7.4+2.6-1) =5.6×9=50.4 ⑨1.25 × 4.3 + 1.25 × 5.7 - 1.25 =1.25×(4.3+5.7-1) =1.25×9=11.25 ⑩0.96 × 6.7 + 0.96 × 3.3- 0.96 =0.96×(6.7+3.3-1) =0.96×9 =8.64 思维题 ① 8.9 × 1.1 + 1.1 × 1.1 - 11 =1.1×(8.9+1.1)-11 =1.1×10-11 =11-11=0 ② 3.6 × 2.7 + 7.4 × 3.6 - 3.6 =3.6×(2.7+7.4-1) =3.6×9.1 =32.76 ③ 4.8 × 0.7 + 0.52 × 7 =0.48×7+0.52×7 =7×(0.48+0.52) =7×1=7 ④ 2.7 × 4.8 + 7.3 × 4.8 - 4.8 =4.8×(2.7+7.3-1) =4.8×9=43.2 ⑤ 6.5×3.8 + 3.5×3.8 - 3.8×2 =3.8×(6.5+3.5-2) =3.8×8=30.4 ⑥ 9.4 × 2.5 + 0.6 × 2.5 - 2.5 =2.5×(9.4+0.6-1) =2.5×9=22.5 ⑦ 3.8×6.7+6.2×6.7-6.7×5 =6.7×(3.8+6.2-5) =6.7×5=33.5 ⑧ 0.85×2.4 +0.15×2.4 - 2.4×0.1 =2.4×(0.85+0.15-0.1) =2.4×0.9=2.16 ⑨ 12.5×3.2 -2.5×3.2+3.2 =3.2×(12.5-2.5+1) =3.2×11=35.2 ⑩ 4.6×7.5+5.4×7.5-7.5×10 =7.5×(4.6+5.4-10) =7.5×0=0 类型四：拆分凑整（高频必考） 基础题 ① 9.9 × 6.7 =(10-0.1)×6.7 =67-0.67=66.33 ② 10.1 × 3.4 =(10+0.1)×3.4 =34+0.34=34.34 ③ 0.99 × 8.5 =(1-0.01)×8.5 =8.5-0.085=8.415 ④ 1.01 × 2.8 =(1+0.01)×2.8 =2.8+0.028=2.828 ⑤ 9.99 × 5.6 =(10-0.01)×5.6 =56-0.056=55.944 ⑥ 10.01 × 4.7 =(10+0.01)×4.7 =47+0.047=47.047 ⑦ 0.98 × 7.3 =(1-0.02)×7.3 =7.3-0.146=7.154 ⑧ 1.02 × 6.4 =(1+0.02)×6.4 =6.4+0.128=6.528 ⑨ 9.8 × 3.6 =(10-0.2)×3.6 =36-0.72=35.28 ⑩ 10.2 × 5.5 =(10+0.2)×5.5 =55+1.1=56.1 变式题 ① 9.9 × 7.8 + 0.78 =9.9×7.8+7.8×0.1 =7.8×(9.9+0.1) =7.8×10=78 ② 10.1 × 4.5 - 0.45 =10.1×4.5-4.5×0.1 =4.5×10=45 ③ 0.99 × 6.4 + 0.064 =0.99×6.4+6.4×0.01 =6.4×1=6.4 ④ 1.01 × 3.7 - 0.037 =1.01×3.7-3.7×0.01 =3.7×1=3.7 ⑤ 9.8 × 5.2 + 1.04 =9.8×5.2+5.2×0.2 =5.2×10=52 ⑥ 10.2 × 2.6 - 0.52 =10.2×2.6-2.6×0.2 =2.6×10=26 ⑦ 9.9 × 8.3 + 0.83 =9.9×8.3+8.3×0.1 =8.3×10=83 ⑧ 10.1 × 6.8 - 0.68 =10.1×6.8-6.8×0.1 =6.8×10=68 ⑨ 0.98 × 4.5 + 0.09 =0.98×4.5+4.5×0.02 =4.5×1=4.5 ⑩ 1.02 × 3.6 - 0.072 =1.02×3.6-3.6×0.02 =3.6×1=3.6 思维题 ① 9.9 × 9.9 + 0.99 =9.9×9.9+9.9×0.1 =9.9×10=99 ② 10.1 × 10.1 - 1.01 =10.1×10.1-10.1×0.1 =10.1×10=101 ③ 99.9 × 6.6 + 6.66 =0.9×111×6×1.1+666×0.01 =666×0.99+666×0.01 =666×（0.99+0.01） =666×1=666 ④ 9.99 × 8.8 + 0.088 =9.99×8.8+8.8×0.01 =8.8×10=88 ⑤ 10.01 × 7.7 - 0.077 =10.01×7.7-7.7×0.01 =7.7×10=77 ⑥ 0.999 × 6.4 + 0.0064 =0.999×6.4+6.4×0.001 =6.4×1=6.4 ⑦ 1.001 × 5.5 - 0.0055 =1.001×5.5-5.5×0.001 =5.5×1=5.5 ⑧ 9.9 × 4.8 + 4.8 × 0.1 =4.8×(9.9+0.1) =4.8×10=48 ⑨ 10.1 × 3.2 - 3.2 × 0.1 =3.2×(10.1-0.1) =3.2×10=32 ⑩ 9.99 × 7.5 + 7.5 × 0.01 =7.5×(9.99+0.01) =7.5×10=75 类型五：积不变规律 基础题 ① 3.6 × 4.5 + 0.36 × 55 =3.6×4.5+3.6×5.5 =3.6×10=36 ② 4.8 × 7.5 + 0.48 × 25 =4.8×7.5+4.8×2.5 =4.8×10=48 ③ 0.79 × 1.2 + 7.9 × 0.08 =7.9×0.12+7.9×0.08 =7.9×0.2=1.58 ④ 6.3 × 2.8 + 0.63 × 72 =6.3×2.8+6.3×7.2 =6.3×10=63 ⑤ 2.4 × 3.6 + 0.24 × 64 =2.4×3.6+2.4×6.4 =2.4×10=24 ⑥ 1.25 × 3.4 + 0.125 × 66 =1.25×3.4+1.25×6.6 =1.25×10=12.5 ⑦ 5.6 × 4.2 + 0.56 × 58 =5.6×4.2+5.6×5.8 =5.6×10=56 ⑧ 7.2 × 5.3 + 0.72 × 47 =7.2×5.3+7.2×4.7 =7.2×10=72 ⑨ 3.8 × 6.1 + 0.38 × 39 =3.8×6.1+3.8×3.9 =3.8×10=38 ⑩ 9.4 × 5.7 + 0.94 × 43 =9.4×5.7+9.4×4.3 =9.4×10=94 变式题 ① 4.2 × 6.8 + 0.42 × 32 =4.2×6.8+4.2×3.2 =4.2×10=42 ② 3.6 × 7.4 + 0.36 × 26 =3.6×7.4+3.6×2.6 =3.6×10=36 ③ 0.78 × 3.5 + 7.8 × 0.65 =7.8×0.35+7.8×0.65 =7.8×1=7.8 ④ 1.6 × 4.5 + 0.16 × 55 =1.6×4.5+1.6×5.5 =1.6×10=16 ⑤ 8.5 × 2.3 + 0.85 × 77 =8.5×2.3+8.5×7.7 =8.5×10=85 ⑥ 2.7 × 6.4 + 0.27 × 36 =2.7×6.4+2.7×3.6 =2.7×10=27 ⑦ 0.96 × 4.8 + 9.6 × 0.52 =9.6×0.48+9.6×0.52 =9.6×1=9.6 ⑧ 5.4 × 3.7 + 0.54 × 63 =5.4×3.7+5.4×6.3 =5.4×10=54 ⑨ 7.6 × 2.5 + 0.76 × 75 =7.6×2.5+7.6×7.5 =7.6×10=76 ⑩ 3.2 × 5.6 + 0.32 × 44 =3.2×5.6+3.2×4.4 =3.2×10=32 思维题 ① 2.4 × 3.6 + 0.24 × 14 + 36 × 0.076 =2.4×3.6+2.4×1.4+3.6×0.76 =2.4×5 + 3.6×0.76 =12+2.736=14.736 ② 3.6 × 4.5 + 0.36 × 55 - 0.036 × 10 =3.6×4.5+3.6×5.5-3.6×0.1 =3.6×9.9=35.64 ③ 0.8 × 3.7 + 0.08 × 63 =0.8×3.7+0.8×6.3 =0.8×10=8 ④ 1.25 × 4.6 + 0.125 × 54 =1.25×4.6+1.25×5.4 =1.25×10=12.5 ⑤ 2.5 × 5.8 + 0.25 × 42 =2.5×5.8+2.5×4.2 =2.5×10=25 ⑥ 0.6 × 7.3 + 6 × 0.27 =6×0.73+6×0.27 =6×1=6 ⑦ 0.35 × 4.6 + 3.5 × 0.54 =3.5×0.46+3.5×0.54 =3.5×1=3.5 ⑧ 4.4 × 2.5 + 44 × 0.75 =44×0.25+44×0.75 =44×1=44 ⑨ 1.6 × 9.7 + 16 × 0.03 =1.6×9.7+1.6×0.3 =1.6×10=16 ⑩ 0.28 × 3.9 + 2.8 × 0.61 =2.8×0.39+2.8×0.61 =2.8×1=2.8 类型六：整体代换与构造 基础题 ① 101 × 4.8 - 4.8 =4.8×(101-1) =4.8×100=480 ② 202 × 3.6 - 3.6 × 2 =3.6×(202-2) =3.6×200=720 ③ 303 × 2.5 - 2.5 × 3 =2.5×(303-3) =2.5×300=750 ④ 1001 × 5.6 - 5.6 =5.6×(1001-1) =5.6×1000=5600 ⑤ 99 × 7.2 + 7.2 =7.2×(99+1) =7.2×100=720 ⑥ 199 × 4.5 + 4.5 =4.5×(199+1) =4.5×200=900 ⑦ 98 × 6.3 + 6.3 × 2 =6.3×(98+2) =6.3×100=630 ⑧ 97 × 8.4 + 8.4 × 3 =8.4×(97+3) =8.4×100=840 ⑨ 102 × 3.7 - 3.7 × 2 =3.7×(102-2) =3.7×100=370 ⑩ 1002 × 2.6 - 2.6 × 2 =2.6×(1002-2) =2.6×1000=2600 变式题 ① 101 × 4.8 - 4.8 × 0.1 =4.8×(101-0.1) =4.8×100.9=484.32 ② 99 × 5.6 + 5.6 × 1.1 =5.6×(99+1.1) =5.6×100.1=560.56 ③ 202 × 3.7 - 3.7 × 2.02 =3.7×(202-2.02) =3.7×199.98=739.926 ④ 100.1 × 6.5 - 0.65 =100.1×6.5-6.5×0.1 =6.5×100=650 ⑤ 99.9 × 7.8 + 7.8 × 0.1 =7.8×(99.9+0.1) =7.8×100=780 ⑥ 100.01 × 4.5 - 0.045 =100.01×4.5-4.5×0.01 =4.5×100=450 ⑦ 9.9 × 5.6 + 0.56 =9.9×5.6+5.6×0.1 =5.6×10=56 ⑧ 10.1 × 8.7 - 0.87 =10.1×8.7-8.7×0.1 =8.7×10=87 ⑨ 101.01 × 3.2 - 3.2 × 0.01 =3.2×(101.01-0.01) =3.2×101=323.2 ⑩ 99.99 × 2.5 + 2.5 × 0.01 =2.5×(99.99+0.01) =2.5×100=250 思维题 ①2026 × 2025.2025 - 2025 × 2026.2026 =2026×2025×1.0001-2025×2026×1.0001 =0 ②2025 × 2026.2026 - 2026 × 2025.2025 =2025×2026×1.0001-2026×2025×1.0001 =0 ③31.4 × 6.7 + 3.14 × 33 =31.4×6.7+31.4×3.3 =31.4×10=314 ④28.6 × 4.5 + 2.86 × 55 =28.6×4.5+28.6×5.5 =28.6×10=286 ⑤7.2 × 5.3 + 0.72 × 47 =7.2×5.3+7.2×4.7 =7.2×10=72 ⑥6.8 × 3.9 + 0.68 × 61 =6.8×3.9+6.8×6.1 =6.8×10=68 ⑦4.5 × 7.6 + 0.45 × 24 =4.5×7.6+4.5×2.4 =4.5×10=45 ⑧9.6 × 2.8 + 0.96 × 72 =9.6×2.8+9.6×7.2 =9.6×10=96 ⑨5.4 × 8.7 + 0.54 × 13 =5.4×8.7+5.4×1.3 =5.4×10=54 ⑩3.7 × 6.2 + 0.37 × 38 =3.7×6.2+3.7×3.8=3.7×10=37 学科网（北京）股份有限公司 $