2026秋小学数学四升五暑假专项提升训练17天（倍数问题应用题）

这是一份2026秋小学数学四升五暑假专项提升训练17天（倍数问题应用题），共5页。
解题核心：已知1倍量，求几倍量，用乘法计算（1倍量×倍数=几倍量），重点掌握基础数量关系，建立倍数模型认知。
1. 花园里有月季花28株，牡丹花的数量是月季花的3倍，牡丹花有多少株？
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2. 文具店卖出钢笔45支，卖出的圆珠笔数量是钢笔的4倍，卖出圆珠笔多少支？
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3. 小明每分钟走62米，爸爸每分钟走的路程是小明的2倍，爸爸每分钟走多少米？
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4. 果园里有梨树36棵，苹果树的棵数是梨树的5倍，苹果树有多少棵？
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5. 一个书包售价58元，一套运动服的价格是书包的6倍，这套运动服多少元？
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6. 养殖场有公鸡19只，母鸡的只数是公鸡的7倍，母鸡有多少只？
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7. 学校图书室有童话书86本，科普书的数量是童话书的2倍，科普书有多少本？
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8. 一辆自行车每小时行驶15千米，汽车每小时行驶的速度是自行车的8倍，汽车每小时行驶多少千米？
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9. 四年级有学生42人，五年级参加社团的人数是四年级的3倍，五年级参加社团的有多少人？
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10. 一箱橘子重24千克，一箱西瓜的重量是橘子的4倍，一箱西瓜重多少千克？
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第二天 基础巩固：简单倍数逆向应用题（求一个数是另一个数的几倍）
解题核心：已知两个数量，求倍数，用除法计算（几倍量÷1倍量=倍数），重点区分1倍量与几倍量，规范倍数表述。
1. 班级有男生36人，女生12人，男生人数是女生的几倍？
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2. 果园里有桃树72棵，梨树18棵，桃树的棵数是梨树的几倍？
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3. 文具店有笔记本90本，作业本30本，笔记本数量是作业本的几倍？
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4. 小明跳绳每分钟跳88下，小红每分钟跳22下，小明每分钟跳的数量是小红的几倍？
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5. 一辆货车载重4吨，一辆卡车载重20吨，卡车载重量是货车的几倍？
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6. 图书室有故事书126本，漫画书21本，故事书的数量是漫画书的几倍？
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7. 养殖场白兔56只，灰兔8只，白兔只数是灰兔的几倍？
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8. 超市运来苹果108千克，香蕉12千克，苹果重量是香蕉的几倍？
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9. 四年级植树64棵，三年级植树16棵，四年级植树数量是三年级的几倍？
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10. 一台空调售价2400元，一台风扇售价300元，空调价格是风扇的几倍？
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第三天 基础巩固：逆向倍数应用题（已知几倍量，求1倍量）
解题核心：已知几倍量和倍数，求1倍量，用除法计算（几倍量÷倍数=1倍量），突破逆向思维误区，找准标准量。
1. 果园里有苹果树144棵，是梨树的4倍，梨树有多少棵？
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2. 学校买来科技书252本，是童话书的6倍，童话书有多少本？
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3. 爸爸体重78千克，是小明体重的3倍，小明体重多少千克？
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4. 一辆汽车每小时行驶96千米，是电动车速度的8倍，电动车每小时行驶多少千米？
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5. 超市运来大米360千克，是面粉的5倍，面粉运来多少千克？
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6. 养殖场有母鸡133只，是公鸡的7倍，公鸡有多少只？
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7. 五年级参加运动会的人数是128人，是四年级的2倍，四年级参加运动会的有多少人？
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8. 一条公路长840米，是一条小路长度的4倍，小路长多少米？
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9. 一件外套售价198元，是一件短袖的9倍，一件短袖售价多少元？
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10. 鱼塘里有草鱼207条，是鲤鱼的3倍，鲤鱼有多少条？
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第四天 基础综合：三类基础倍数题型混合训练
解题核心：区分正向、逆向、求倍数三类题型，熟练判断1倍量、几倍量，灵活选用乘除法解题。
1. 小红有35块橡皮，小丽的橡皮数量是小红的2倍，小丽有多少块橡皮？
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2. 学校有篮球81个，足球9个，篮球数量是足球的几倍？
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3. 果园有樱桃树96棵，是李子树的8倍，李子树有多少棵？
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4. 每分钟流水32升，水龙头10分钟流水量是每分钟的10倍，10分钟流水多少升？
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5. 爸爸每月工资4800元，妈妈每月工资2400元，爸爸工资是妈妈的几倍？
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6. 书架上层有图书156本，是下层的3倍，下层有图书多少本？
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7. 四年级一班有44人，二班人数是一班的1.5倍（整数倍数简化，改为2倍），二班有多少人？
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8. 一辆大巴可坐60人，一辆小巴可坐15人，大巴载客量是小巴的几倍？
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9. 地里收获红薯420千克，收获的土豆重量是红薯的4倍，收获土豆多少千克？
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10. 商场运来运动鞋315双，是休闲鞋的5倍，休闲鞋运来多少双？
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第五天 进阶提升：倍数与加减法复合应用题（几倍多几、几倍少几）
解题核心：先算基础倍数，再结合“多几加、少几减”，理清复合数量关系，突破简单倍数局限。
1. 果园有桃树45棵，梨树的棵数比桃树的3倍多12棵，梨树有多少棵？
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2. 文具店有笔记本68本，作业本的数量比笔记本的2倍少15本，作业本有多少本？
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3. 小明收集邮票36枚，小红收集的邮票数量比小明的4倍多8枚，小红收集邮票多少枚？
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4. 学校有柳树52棵，杨树的棵数比柳树的5倍少20棵，杨树有多少棵？
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5. 一台电风扇售价125元，一台空调的价格比电风扇的18倍多60元，空调售价多少元？
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6. 四年级有学生85人，五年级人数比四年级的3倍少32人，五年级有多少人？
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7. 养殖场有鸭子76只，鸡的数量比鸭子的6倍多18只，鸡有多少只？
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8. 一本练习册售价18元，一套教辅资料的价格比练习册的12倍少25元，这套教辅资料多少元？
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9. 货车每小时行驶42千米，轿车速度比货车的2倍多15千米，轿车每小时行驶多少千米？
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10. 菜园有黄瓜93千克，西红柿重量比黄瓜的4倍少48千克，西红柿有多少千克？
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第六天 进阶提升：反向复合倍数应用题（几倍多几、几倍少几求1倍量）
解题核心：逆向推导，先“多去少补”还原标准倍数，再用除法求1倍量，锻炼逆向推理思维。
1. 果园有梨树147棵，梨树的棵数比桃树的3倍多12棵，桃树有多少棵？
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2. 学校有杨树240棵，杨树的棵数比柳树的5倍少20棵，柳树有多少棵？
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3. 小红收集邮票152枚，比小明的4倍多8枚，小明收集邮票多少枚？
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4. 文具店有作业本121本，比笔记本的2倍少15本，笔记本有多少本？
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5. 一台空调售价2310元，比电风扇的18倍多60元，电风扇售价多少元？
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6. 五年级有学生223人，比四年级的3倍少32人，四年级有多少人？
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7. 养殖场有鸡474只，比鸭子的6倍多18只，鸭子有多少只？
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8. 一套教辅资料售价191元，比练习册的12倍少25元，一本练习册售价多少元？
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9. 轿车每小时行驶99千米，比货车的2倍多15千米，货车每小时行驶多少千米？
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10. 菜园有西红柿324千克，比黄瓜的4倍少48千克，黄瓜有多少千克？
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第七天 专题突破：基础和倍问题（整数和倍，无余数）
解题核心：已知两个数的和与倍数关系，公式：1倍量=和÷（倍数+1），几倍量=和-1倍量，建立和倍解题模型。
1. 甲数和乙数的和是96，甲数是乙数的3倍，甲、乙两数各是多少？
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2. 果园里桃树和梨树共120棵，桃树棵数是梨树的5倍，桃树、梨树各有多少棵？
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3. 学校买来故事书和科普书共180本，科普书数量是故事书的2倍，两种书各买了多少本？
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4. 小明和小红共有零花钱140元，小明的零花钱是小红的4倍，两人各有多少零花钱？
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5. 养殖场有白兔和灰兔共150只，白兔只数是灰兔的9倍，白兔、灰兔各有多少只？
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6. 甲乙两个仓库共存粮食480吨，甲仓库粮食是乙仓库的3倍，两个仓库各存粮食多少吨？
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7. 四年级和五年级共有学生360人，五年级人数是四年级的2倍，两个年级各有多少人？
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8. 苹果和香蕉共重240千克，苹果重量是香蕉的7倍，苹果和香蕉各重多少千克？
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9. 钢笔和圆珠笔共90支，钢笔数量是圆珠笔的5倍，两种笔各有多少支？
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10. 甲乙两数和为210，甲数是乙数的6倍，甲乙两数分别是多少？
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第八天 专题突破：进阶和倍问题（带余数、多量和倍）
解题核心：处理和倍变式，先去掉多余数量、补足缺少数量，转化为标准和倍问题，掌握多量倍数关系分析方法。
1. 桃树和梨树共132棵，桃树棵数比梨树的3倍多12棵，桃树、梨树各有多少棵？
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2. 故事书和漫画书共205本，故事书数量比漫画书的4倍少15本，两种书各有多少本？
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3. 小明和小红共有零花钱168元，小明的零花钱比小红的5倍多18元，两人各有多少零花钱？
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4. 白兔和黑兔共186只，白兔只数比黑兔的6倍少24只，白兔、黑兔各有多少只？
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5. 甲乙丙三个数的和是180，乙数是丙数的2倍，甲数是丙数的3倍，三个数各是多少？
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6. 学校购进篮球、足球、排球共240个，足球数量是排球的2倍，篮球数量是排球的3倍，三种球各购进多少个？
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7. 大米和面粉共430千克，大米重量比面粉的4倍多30千克，大米和面粉各重多少千克？
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8. 四年级三个班共有学生315人，二班人数是一班的2倍，三班人数是一班的4倍，三个班各有多少人？
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9. 钢笔、中性笔、铅笔共120支，中性笔数量是铅笔的3倍，钢笔数量是铅笔的2倍，三种笔各有多少支？
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10. 甲乙两数和为248，甲数比乙数的7倍少32，甲乙两数各是多少？
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第九天 专题突破：基础差倍问题（整数差倍，无余数）
解题核心：已知两个数的差与倍数关系，公式：1倍量=差÷（倍数-1），几倍量=1倍量+差，建立差倍解题模型。
1. 甲数比乙数多72，甲数是乙数的5倍，甲、乙两数各是多少？
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2. 桃树比梨树多96棵，桃树棵数是梨树的4倍，桃树、梨树各有多少棵？
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3. 科普书比故事书多120本，科普书数量是故事书的3倍，两种书各有多少本？
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4. 小明零花钱比小红多105元，小明零花钱是小红的6倍，两人各有多少零花钱？
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5. 白兔比灰兔多135只，白兔只数是灰兔的10倍，白兔、灰兔各有多少只？
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6. 甲仓库粮食比乙仓库多320吨，甲仓库粮食是乙仓库的5倍，两个仓库各存粮多少吨？
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7. 五年级人数比四年级多120人，五年级人数是四年级的3倍，两个年级各有多少人？
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8. 苹果比香蕉多180千克，苹果重量是香蕉的8倍，苹果和香蕉各重多少千克？
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9. 钢笔比圆珠笔多72支，钢笔数量是圆珠笔的7倍，两种笔各有多少支？
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10. 甲数比乙数多175，甲数是乙数的8倍，甲乙两数分别是多少？
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第十天 专题突破：进阶差倍问题（变式差倍）
解题核心：处理差倍变式题型，修正多余、缺少数量，转化为标准差倍模型，精准分析数量差值与倍数的对应关系。
1. 桃树比梨树多84棵，桃树棵数比梨树的4倍少12棵，桃树、梨树各有多少棵？
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2. 科普书比故事书多95本，科普书数量比故事书的3倍多5本，两种书各有多少本？
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3. 小明零花钱比小红多98元，小明零花钱比小红的5倍少2元，两人各有多少零花钱？
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4. 白兔比黑兔多112只，白兔只数比黑兔的7倍少8只，白兔、黑兔各有多少只？
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5. 甲仓库比乙仓库多290吨粮食，甲仓库粮食比乙仓库的4倍多20吨，两个仓库各存粮多少吨？
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6. 五年级比四年级多108人，五年级人数比四年级的3倍少12人，两个年级各有多少人？
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7. 苹果比香蕉多156千克，苹果重量比香蕉的6倍多6千克，苹果和香蕉各重多少千克？
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8. 钢笔比圆珠笔多63支，钢笔数量比圆珠笔的8倍少7支，两种笔各有多少支？
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9. 甲数比乙数多124，甲数比乙数的5倍少16，甲乙两数各是多少？
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10. 长方形长比宽多48厘米，长是宽的7倍，长方形的长和宽各是多少厘米？
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第十一天 综合训练：和倍、差倍混合辨析（基础变式）
解题核心：精准区分和倍、差倍题型，根据题干“和”“差”关键词，快速匹配对应解题模型，避免题型混淆。
1. 甲乙两数和为135，甲数是乙数的4倍，甲乙两数各是多少？
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2. 甲乙两数差为108，甲数是乙数的7倍，甲乙两数各是多少？
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3. 红花和黄花共160朵，红花数量是黄花的3倍，两种花各有多少朵？
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4. 红花比黄花多120朵，红花数量是黄花的4倍，两种花各有多少朵？
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5. 玩具车和玩具飞机共210个，玩具飞机数量是玩具车的6倍，两种玩具各有多少个？
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6. 玩具飞机比玩具车多150个，玩具飞机数量是玩具车的4倍，两种玩具各有多少个？
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7. 跳绳和踢毽子的学生共184人，跳绳人数是踢毽子的3倍，两类学生各有多少人？
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8. 跳绳人数比踢毽子多92人，跳绳人数是踢毽子的3倍，两类学生各有多少人？
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9. 大米和小米共320千克，大米重量是小米的7倍，大米、小米各重多少千克？
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10. 大米比小米多240千克，大米重量是小米的4倍，大米、小米各重多少千克？
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第十二天 思维拓展：隐藏条件倍数应用题
解题核心：挖掘题干隐藏数量关系（总数、差值、不变量），补全条件后再用倍数模型解题，培养审题挖掘能力。
1. 两数相除商是6，被除数与除数的和是140，被除数、除数各是多少？
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2. 两数相除商是8，被除数比除数多126，被除数、除数各是多少？
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3. 一个长方形周长是120厘米，长是宽的5倍，长方形的长和宽各是多少厘米？
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4. 一个长方形周长是96厘米，长比宽多24厘米，长是宽的几倍？长和宽各是多少？
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5. 甲乙两个数的商是7，两数和为168，甲乙两数各是多少？
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6. 甲乙两个数的商是9，两数差为144，甲乙两数各是多少？
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7. 把一根长180厘米的铁丝围成一个长方形，长是宽的2倍，长和宽分别是多少厘米？
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8. 两数相除商是5，余数是0，被除数比除数多80，被除数和除数各是多少？
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9. 甲乙两数之和是192，甲数除以乙数商是3，甲乙两数各是多少？
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10. 甲乙两数之差是136，甲数除以乙数商是17，甲乙两数各是多少？
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第十三天 生活应用：购物场景倍数应用题
解题核心：结合购物价格、数量、总价场景，运用倍数关系解决实际消费问题，贴合生活实际，强化建模应用。
1. 一支钢笔售价16元，一套文具礼盒的价格是钢笔的12倍，一套文具礼盒多少元？
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2. 一个书包售价192元，一个笔袋售价24元，书包价格是笔袋的几倍？
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3. 一双运动鞋售价268元，一双皮鞋的价格比运动鞋的3倍多45元，皮鞋售价多少元？
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4. 一台学习机售价1560元，比一台点读笔的6倍少60元，点读笔售价多少元？
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5. 超市运来牛奶和酸奶共360箱，牛奶箱数是酸奶的5倍，牛奶和酸奶各运来多少箱？
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6. 洗衣液比洗洁精多126瓶，洗衣液数量是洗洁精的4倍，洗衣液和洗洁精各有多少瓶？
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7. 买3本笔记本花费27元，一套工具书的价格是一本笔记本的48倍，一套工具书多少元？
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8. 一件连衣裙售价246元，比一件T恤的4倍多26元，一件T恤售价多少元？
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9. 超市零食区和饮料区共有商品420件，零食数量是饮料的6倍，零食和饮料各有多少件？
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10. 保温杯比玻璃杯贵90元，保温杯价格是玻璃杯的6倍，两种杯子各多少元？
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第十四天 生活应用：行程、工程场景倍数应用题
解题核心：结合速度、路程、时间、工作量场景，融合倍数关系，解决复合型实际问题，提升综合分析能力。
1. 小明步行每分钟走45米，骑车的速度是步行的4倍，小明骑车每分钟走多少米？
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2. 汽车每小时行驶78千米，电动车每小时行驶13千米，汽车速度是电动车的几倍？
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3. 工程队第一天修路56米，第二天修的路程比第一天的3倍少18米，第二天修路多少米？
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4. 火车每小时行驶192千米，比高铁速度的2倍少48千米，高铁每小时行驶多少千米？
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5. 甲乙两队修路，两队共修路480米，甲队修路长度是乙队的3倍，甲乙两队各修路多少米？
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6. 快车比慢车每小时多行驶60千米，快车速度是慢车的4倍，快慢车每小时各行驶多少千米？
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7. 工人师傅每小时加工零件32个，师傅加工零件的速度是徒弟的2倍，徒弟每小时加工多少个零件？
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8. 甲工程队比乙工程队多修路145米，甲队修路长度比乙队的6倍少5米，两队各修路多少米？
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9. 一辆货车3小时行驶180千米，一辆客车每小时速度是货车的2倍，客车每小时行驶多少千米？
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10. 师徒二人每小时共加工零件96个，师傅加工数量是徒弟的5倍，师徒每小时各加工多少个零件？
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第十五天 拔高训练：多步复合倍数应用题
解题核心：三步及以上复合运算，融合倍数、加减、归一问题，锻炼分步解题、层层推理的思维能力。
1. 商店运来24箱苹果，每箱18千克，运来的梨的总重量是苹果的3倍，运来梨多少千克？
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2. 小明每天读书15页，读了8天，小红读书的总页数是小明的2倍少36页，小红读了多少页？
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3. 养殖场有4笼兔子，每笼12只，鸭子的数量比兔子的5倍多28只，鸭子有多少只？
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4. 工厂每天生产零件45个，生产6天后，总产量比计划的2倍少80个，计划生产多少个零件？
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5. 学校买来6捆树苗，每捆15棵，栽种的柳树数量是树苗总数的4倍，柳树有多少棵？
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6. 小红每分钟跳绳24下，跳了12分钟，小丽跳绳总数比小红的3倍多42下，小丽跳了多少下？
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7. 货车每次运货32吨，运了5次，卡车运货总量是货车的2倍少45吨，卡车运货多少吨？
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8. 四年级4个班，每班48人，五年级总人数比四年级的2倍多32人，五年级有多少人？
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9. 超市每天卖出饮料36箱，7天后剩余饮料是卖出的2倍，超市原有饮料多少箱？
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10. 工人每天加工28个配件，9天完成任务，改良工艺后总产量是原来的3倍少120个，改良后加工多少个配件？
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第十六天 拔高训练：变量不变倍数应用题（和不变、差不变）
解题核心：抓住“总量不变、差值不变”核心规律，分析数量变化后的新倍数关系，突破动态变式难点。
1. 甲乙两个书架共有图书360本，甲书架图书数量是乙书架的2倍，如果从甲书架取走若干本，两个书架总数不变，要使甲书架是乙书架的3倍，乙书架应有多少本图书？
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2. 甲乙两数差为90，甲数是乙数的4倍，若甲乙两数同时增加15，现在甲数是乙数的几倍？
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3. 兄弟两人共有零花钱240元，哥哥钱数是弟弟的5倍，两人各花掉20元后，兄弟两人各剩多少零花钱？此时哥哥钱数是弟弟的几倍？
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4. 白兔和黑兔相差84只，白兔是黑兔的8倍，各卖出6只后，白兔比黑兔多多少只？现在白兔是黑兔的几倍？
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5. 两个仓库共存粮食450吨，甲仓库存粮是乙仓库的4倍，从甲仓库运出一部分到乙仓库，使两个仓库粮食相等，需要运出多少吨？
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6. 甲乙两数和为280，甲数是乙数的3倍，若乙数增加20，要使倍数关系不变，甲数应增加多少？
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7. 红球比白球多72个，红球数量是白球的7倍，各放入8个球后，红球和白球各有多少个？差值是否变化？
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8. 四年级和五年级共400人，五年级人数是四年级的4倍，新学期转入相同人数的学生，两个年级总人数增加60人，现在两个年级各有多少人？
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9. 两根绳子，长绳比短绳长54厘米，长绳长度是短绳的7倍，两根绳子同时剪掉18厘米，现在长绳是短绳的几倍？
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10. 甲乙两个水箱共蓄水320升，甲水箱蓄水量是乙水箱的3倍，放出相同水量后，乙水箱剩40升，甲乙现在各蓄水多少升？
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第十七天 综合拔高：四则运算+倍数综合应用题
解题核心：融合加减乘除四则运算与倍数关系，多步骤分层解题，全面提升综合运算与逻辑推理能力。
1. 商店有钢笔85支，圆珠笔比钢笔多35支，铅笔的数量是圆珠笔的4倍，铅笔有多少支？
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2. 果园有梨树62棵，桃树比梨树少18棵，苹果树的棵数是桃树的5倍，苹果树有多少棵？
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3. 小明有58元零花钱，妈妈又给了他32元，现在小明的钱数是小红的3倍，小红有多少元？
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4. 工厂原有工人126人，辞退26人后，又招聘新人，现在总人数是原来的2倍，招聘新人多少人？
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5. 一箱苹果重48千克，卖出一半后，剩下的苹果重量是一箱橘子的3倍，一箱橘子重多少千克？
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6. 四年级植树78棵，五年级植树棵数是四年级的2倍，六年级比四、五年级总数少45棵，六年级植树多少棵？
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