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1、小升初数学疑难专题讲练【1-3】【例题与自测题及答案详解】小升初数学疑难专题讲练，一， 求一个数比另一个数多，少，百分之几、纳税问题 【考点分析】 1、一个数比另一个数多(少)百分之几 = 一个数比另一个数多(少)的量?另一个数。 2、应该缴纳的税款叫做应纳税额，应纳税额与各种收入的比率叫做税率，应纳税额 = 收入 税率 【典型例题】 【例1】(解决“求一个数比另一个数多百分之几”的实际问题) 新星客车厂原计划生产客车5000辆，实际生产5500辆。实际比计划多生产百分之几, 分析与解:要求“实际比计划多生产百分之几”，就是求实际比计划多生产的辆数占计划产量的百分之几，把原计划产量看作单位“1
2、”。两者之间的关系可用线段图表示。 计划产量 5000辆 实际比计划多的 实际产量 5500辆 解答:方法1: 5500 5000 = 500(辆) 实际比计划多生产500辆 500 ? 5000 = 0.1 = 10, 实际比计划多生产百分之几 方法2: 5500 ? 5000 = 110, 实际产量相当于原计划的110, 110, - 100, = 10, 实际比计划多生产百分之几 答:实际比计划多生产10,。 【例2】(解决“求一个数比另一个数少百分之几”的实际问题) 新星客车厂原计划生产客车5000辆，实际生产5500辆。计划比实际少生产百分之几, 分析与解:要求“计划比实际少生产百分
3、之几”，就是求计划比实际少生产的辆数占实际产量的百分之几，把实际产量看作单位“1”。两者之间的关系可用线段图表示。 计划产量 5000辆 计划比实际少的 实际产量 3.1 requirements. no load test. According to the relevant provisions of the DL/T5019 check the running of machinery and electrical equipment provided, to be correct and reliable, stable operation, impact sound and no o
4、ther anomalies. static load test. According to the construction drawings and inspection machinery and metal structure bearing capacity of the hoist. Test load rated load in turn 70%, l00% and 125%. dynamic load tests. According to the construction drawings, dynamic loading tests on the bodies to tes
5、t the dynamic stiffness of the performance of the agencies and gantries. Test load rated load 100% and then 110%. Test agencies should be conducted separately, when there is a joint commissioning requirements, should be carried out according to the construction drawings and the instructions of the s
6、upervisor. Test, repeat to start, run, stop, forward, reverse motion, duration of at least 1h. Agencies should be flexible, stable and reliable work, limit switches, safety interlocks, anti-climbing device, the movements should be accurate and reliable, the parts should be free of cracks and other d
7、amage, the connection should not be loose. (3) civil works out the hoist and installation conditions installation 5500辆 解答:方法1: 5500 5000 = 500(辆) 计划比实际少生产500辆 500 ? 5500 ? 9.1, 计划比实际少生产百分之几 方法2: 5500 ? 5500 ? 90.9, 计划产量相当于实际的90.9, 100, - 90.9, ? 9.1, 计划比实际少生产百分之几 。 答:计划比实际少生产9.1,点评:想一想在分数乘法应用题中的最基本
8、的数量关系式:“单位1 分率 = 分率对应的量”如果和百分数应用题结合起来求一种量比另一种量多,少,百分之几实际上就是求分率。就用“多,少,的量 ? 单位1”。 【例3】(难点突破) 一筐苹果比一筐梨重20,，那么一筐梨就比一筐苹果轻20, 分析与解:苹果比梨重20,，表示苹果比梨重的部分占梨的20,，把梨的质量看作单位“1”;而梨比苹果轻20,则表示梨比苹果轻的部分占苹果的20,，把苹果的质量看作单位“1”，两个单位“1”不同，切忌将两个问题混为一谈。一筐苹果比一筐梨重20,，是把梨看作单位“1”，梨有100份，苹果就是100 + 20 = 120份;一筐梨比一筐苹果轻百分之= 一筐梨比一筐
9、苹果轻的部分 ? 苹果 = (120 - 100)? 120?16.7, 几 答:一筐苹果比一筐梨重20,，那么一筐梨就比一筐苹果轻16.7, 点评:在求一个数比另一个数多,少,百分之几的百分数应用题中关键还是要找准单位“1”的量。从结论可以得出“一个数比另一个数多百分之几另一个数就比一个数少百分之几。”这句话是错的。为什么呢,把两个百分之几比较一下就可以得出这两个百分之几对应的量是一个数比另一个数多的量或另一个数比一个数少的量而这两种说法是相同的也就表示的是同一个量,而单位“1”一个是梨一个是苹果所以这两个百分之几是不可能相等的。 【例4】(考点透视) 一种电子产品，原价每台5000元，现在
10、降低到3000元。降价百分之几, 分析与解:降低到3000元，即现价为3000元，说明降低了2000元。求降价百分之几，就是求降低的价格占原价的百分之几。 5000 3000 = 2000(元) 2000 ? 5000 = 40, 答:降价40,。 【例5】(考点透视) 一项工程，原计划10天完成，实际8天就完成了任务，实际每天比原计划多修百分之几, 1分析与解:根据“原计划10天完成”，可以得到:原计划每天完成这项工程的;根据“实际103.1 requirements. no load test. According to the relevant provisions of the DL/
11、T5019 check the running of machinery and electrical equipment provided, to be correct and reliable, stable operation, impact sound and no other anomalies. static load test. According to the construction drawings and inspection machinery and metal structure bearing capacity of the hoist. Test load ra
12、ted load in turn 70%, l00% and 125%. dynamic load tests. According to the construction drawings, dynamic loading tests on the bodies to test the dynamic stiffness of the performance of the agencies and gantries. Test load rated load 100% and then 110%. Test agencies should be conducted separately, w
13、hen there is a joint commissioning requirements, should be carried out according to the construction drawings and the instructions of the supervisor. Test, repeat to start, run, stop, forward, reverse motion, duration of at least 1h. Agencies should be flexible, stable and reliable work, limit switc
14、hes, safety interlocks, anti-climbing device, the movements should be accurate and reliable, the parts should be free of cracks and other damage, the connection should not be loose. (3) civil works out the hoist and installation conditions installation 小升初数学疑难专题讲练 18天完成”，可以得到:实际每天完成这项工程的。用“实际比原计划每天多
15、完成的8量 ? 原计划每天完成的量”，就可以求出实际每天多修百分之几。 111( - ) ? = 25, 81010答:实际每天比原计划多修25,。 点评:找准解决问题的数量关系式是解答好这一题的关键题目中要求的是每天完成的任务量而不能用10和8去求因为10和8是工作时间在解答时容易发生错误。 【例6】(应纳税额的计算方法) 益民五金公司去年的营业总额为400万元。如果按营业额的3,缴纳营业税，去年应缴纳营业税多少万元, 分析与解:如果按营业额的3,缴纳营业税，是把营业额看作单位“1”。 缴纳营业税占营业额的3,，即400万元的3,。求一个数的百分之几是多少，也用乘法计算。计算时可将百分数化成
16、分数或小数来计算。 34003, = 400 = 12(万元) 100或4003, = 4000.03 = 12(万元) 答:去年应缴纳营业税12万元。 点评:在现实社会中各种税率是不一样的。应纳税额的计算从根本上讲是求一个数的百分之几是多少。 【例7】(和应纳税额有关的简单实际问题) 王叔叔买了一辆价值16000元的摩托车。按规定，买摩托车要缴纳10,的车辆购置税。王叔叔买这辆摩托车一共要花多少钱, 分析与解:王叔叔买这辆摩托车所需的钱应包含购买价和10,的车辆购置税两部分，而车辆购置税是占摩托车购买价的10,，可先算出要缴纳的车辆购置税。也可以这样想:车辆购置税占购买价的10,，把购买价看
17、作单位“1”，王叔叔买这辆摩托车所需的钱相当于购买价的(1 + 10,)，即求16000元的110,是多少，也用乘法计算。 方法1:16000 10, + 16000 = 1600 + 16000 = 17600(元) 方法2:16000 (1 + 10,) = 16000 1.1 = 17600(元) 答:王叔叔买这辆摩托车一共要花17600元钱。 【例8】北京某风景区2007年“十一”黄金周接待游客9万人次，门票收入达270万元。按门票的5,缴纳营业税计算，“十一”黄金周期间应缴纳营业税0.45万元。 分析与解:营业税是按门票的5,缴纳，是占门票收入的5,，而不是占游客人数的5, 3.1
18、requirements. no load test. According to the relevant provisions of the DL/T5019 check the running of machinery and electrical equipment provided, to be correct and reliable, stable operation, impact sound and no other anomalies. static load test. According to the construction drawings and inspectio
19、n machinery and metal structure bearing capacity of the hoist. Test load rated load in turn 70%, l00% and 125%. dynamic load tests. According to the construction drawings, dynamic loading tests on the bodies to test the dynamic stiffness of the performance of the agencies and gantries. Test load rat
20、ed load 100% and then 110%. Test agencies should be conducted separately, when there is a joint commissioning requirements, should be carried out according to the construction drawings and the instructions of the supervisor. Test, repeat to start, run, stop, forward, reverse motion, duration of at l
21、east 1h. Agencies should be flexible, stable and reliable work, limit switches, safety interlocks, anti-climbing device, the movements should be accurate and reliable, the parts should be free of cracks and other damage, the connection should not be loose. (3) civil works out the hoist and installat
22、ion conditions installation答:“十一”黄金周期间应缴纳营业税13.5万元。 自测试题,答案在后面, 一、填空题 1、篮球个数是足球的125,，篮球比足球多( ),，足球个数是篮球的( ),，足球个数比篮球少( ),。 2、排球个数比篮球多18,，排球个数相当于篮球的( ),。 3、足球个数比篮球少20,。排球个数比篮球多18,，( )球个数最多，( )球个数最少。 4、果园里种了60棵果树，其中36棵是苹果树。苹果树占总棵数的( ),，其余的果树占总棵数的( ),。 5、女生人数占全班的百分之几 = ( )? ( ) 杨树的棵数比柏树多百分之几 = ( )? ( )
23、 实际节约了百分之几 = ( )? ( ) 比计划超产了百分之几 = ( )? ( ) 6、20的40,是( )，36的10,是( )，50千克的60,是( )千克，800米的25,是( )米。 、进口价,元的一批货物，税率和运费都是货物价值的10,，这批货物的成本是( )元。 7二、解决实际问题 1、白兔有25只，灰兔有30只。灰兔比白兔多百分之几, 2、四美食盐厂上月计划生产食盐450吨，实际生产了480吨。实际比计划多生产了百分之几, 3、小明家八月份用电80千瓦时，小亮家比小明家节约10千瓦时，小亮家比小明家八月份节约用电百分之几, 4、某化肥厂9月份实际生产化肥5000吨，比计划超产
24、500吨。比计划超产百分之几, 5、蓝天帽业厂去年收入总额达900万元，按国家的税率规定，应缴纳17,的增值税。一共要缴纳多少万元的增值税, 3.1 requirements. no load test. According to the relevant provisions of the DL/T5019 check the running of machinery and electrical equipment provided, to be correct and reliable, stable operation, impact sound and no other anomal
25、ies. static load test. According to the construction drawings and inspection machinery and metal structure bearing capacity of the hoist. Test load rated load in turn 70%, l00% and 125%. dynamic load tests. According to the construction drawings, dynamic loading tests on the bodies to test the dynam
26、ic stiffness of the performance of the agencies and gantries. Test load rated load 100% and then 110%. Test agencies should be conducted separately, when there is a joint commissioning requirements, should be carried out according to the construction drawings and the instructions of the supervisor.
27、Test, repeat to start, run, stop, forward, reverse motion, duration of at least 1h. Agencies should be flexible, stable and reliable work, limit switches, safety interlocks, anti-climbing device, the movements should be accurate and reliable, the parts should be free of cracks and other damage, the
28、connection should not be loose. (3) civil works out the hoist and installation conditions installation 小升初数学疑难专题讲练 6、爸爸买了一辆价值12万元的家用轿车。按规定需缴纳10,的车辆购置税。爸爸买这辆车共需花多少钱, 3.1 requirements. no load test. According to the relevant provisions of the DL/T5019 check the running of machinery and electrical equi
29、pment provided, to be correct and reliable, stable operation, impact sound and no other anomalies. static load test. According to the construction drawings and inspection machinery and metal structure bearing capacity of the hoist. Test load rated load in turn 70%, l00% and 125%. dynamic load tests.
30、 According to the construction drawings, dynamic loading tests on the bodies to test the dynamic stiffness of the performance of the agencies and gantries. Test load rated load 100% and then 110%. Test agencies should be conducted separately, when there is a joint commissioning requirements, should
31、be carried out according to the construction drawings and the instructions of the supervisor. Test, repeat to start, run, stop, forward, reverse motion, duration of at least 1h. Agencies should be flexible, stable and reliable work, limit switches, safety interlocks, anti-climbing device, the moveme
32、nts should be accurate and reliable, the parts should be free of cracks and other damage, the connection should not be loose. (3) civil works out the hoist and installation conditions installation小升初数学疑难专题讲练，二， 应用百分数解决实际问题:利息、折扣问题 【考点分析】 1、存入银行的钱叫做本金，取款时银行除还给本金外，另外付给的钱叫做利息，利息占本金的百分率叫做利率。 2、利息=本金利率时间
33、。 3、几折就是十分之几，也就是百分之几十。 4、商品现价 = 商品原价 折数。 【典型例题】 【例1】(解决税前利息) 李明把500元钱按三年期整存整取存入银行，到期后应得利息多少元, 存期(整存整取) 年利率 一年 3.87, 二年 4.50, 三年 5.22, 分析与解:根据储蓄年利率表，三年定期年利率5.22,。 税前应得利息 = 本金 利率 时间 500 5.22, 3 = 78.3(元) 答:到期后应得利息78.3元。 【例2】(解决税后利息) 根据国家税法规定，个人在银行存款所得的利息要按5,的税率缴纳利息税。【例1】中纳税后李明实得利息多少元, 分析与解:从应得利息中扣除利息税
34、剩下的就是实得利息。 税后实得利息 = 本金 利率 时间 (1 - 5,) 500 5.22, 3 = 78.3(元) 应得利息 78.3 5, = 3.915(元) 利息税 78.3 3.915 = 74.385 ? 74.39(元) 实得利息 或者 500 5.22, 3 (1 - 5,) = 74.385(元)? 74.39(元) 答:纳税后李明实得利息74.39元。 【例3】方明将1500元存入银行，定期二年，年利率是4.50,。两年后方明取款时要按5,缴纳 利息税，到期后方明实得利息多少元, 错误解答:1500 4.50, (1 - 5,) = 64.125(元)? 64.13(元)
35、 分析原因:税后实得利息 = 本金 利率 时间 (1 - 5,)，这里漏乘了时间。 正确解答:1500 2 4.50, (1 - 5,) = 128.25(元) 答:到期后方明实得利息128.25元。 点评:求利率根据实际情况有时要扣掉利息税根据国家规定利息税的税率是5,所以利息3.1 requirements. no load test. According to the relevant provisions of the DL/T5019 check the running of machinery and electrical equipment provided, to be cor
36、rect and reliable, stable operation, impact sound and no other anomalies. static load test. According to the construction drawings and inspection machinery and metal structure bearing capacity of the hoist. Test load rated load in turn 70%, l00% and 125%. dynamic load tests. According to the constru
37、ction drawings, dynamic loading tests on the bodies to test the dynamic stiffness of the performance of the agencies and gantries. Test load rated load 100% and then 110%. Test agencies should be conducted separately, when there is a joint commissioning requirements, should be carried out according
38、to the construction drawings and the instructions of the supervisor. Test, repeat to start, run, stop, forward, reverse motion, duration of at least 1h. Agencies should be flexible, stable and reliable work, limit switches, safety interlocks, anti-climbing device, the movements should be accurate an
39、d reliable, the parts should be free of cracks and other damage, the connection should not be loose. (3) civil works out the hoist and installation conditions installation 小升初数学疑难专题讲练 分税前利息和税后利息在做题时要注意区分。但也有一些是不需要缴利息税的比如:国家建设债券、教育储蓄等。 【例4】(求折扣) 一本书现价6.4元，比原价便宜1.6元。这本书是打几折出售的, 分析与解:打了几折是求实际售价是原价的百分之几
40、，只要用实际售价除以原价。 6.4 + 1.6 = 8(元) 6.4 ? 8 = 80, = 八折 答:这本书是打八折出售的。 点评:几折就是百分之几十几几折就是百分之几十几同一商品打的折数越低售价也就越低。在折数的题目中打几折就是按原价的百分之几十出售它并不代表增加或减少的数额。 【例5】(已知折扣求原价) “国庆”商场促销，一套西服打八五折出售是1020元，这套西服原价多少元, 分析与解:打八五折出售，即实际售价相当于原价的85,。已知原价的85,是1020元，要求原价是多少，可以列方程解答。 原价 85, = 实际售价 解:设这套西服原价x元。 x 85, = 1020 x = 1020
41、 ? 85, = 1200 x 检验:(1)用现价除以原价看是否打了八五折。 1020 ? 1200 = 0.85 = 85, (2)看原价的85,是不是1020元。 1200 85, = 1020(元) 经检验，答案符合题意。 答:这套西服原价1200元。 】一台液晶电视6000元，若打七五折出售，可降价2000元。 【例6分析原因:6000元为原价，打七五折出售，要先算出实际售价再相减，或者先算出降价部分占原价的25,。 正确解答:6000 - 600075, = 1500(元) 或6000(1 - 75,) = 1500(元) 答:可降价1500元。 【例7】(和应纳税额有关的简单实际问
42、题) 一批电冰箱，原来每台售价2000元，现促销打九折出售，有一顾客购买时，要求再打九折，如果能够成交，售价是多少元, 分析与解:“促销打九折出售”就是按原价的百分之九十出售，用“原价90,”，“再打九折”是在促销价的基础上打九折，要用促销价乘90,。 2000 90, 90, = 1800 90, = 1620(元) 答:如果能够成交，售价是1620元。 点评:题目的关键是“再打九折”表示的意思是在促销价的基础上再打九折单位“1”的量是促销价即原价打九折后的价钱这是易错点要多加注意。 3.1 requirements. no load test. According to the relev
43、ant provisions of the DL/T5019 check the running of machinery and electrical equipment provided, to be correct and reliable, stable operation, impact sound and no other anomalies. static load test. According to the construction drawings and inspection machinery and metal structure bearing capacity o
44、f the hoist. Test load rated load in turn 70%, l00% and 125%. dynamic load tests. According to the construction drawings, dynamic loading tests on the bodies to test the dynamic stiffness of the performance of the agencies and gantries. Test load rated load 100% and then 110%. Test agencies should b
45、e conducted separately, when there is a joint commissioning requirements, should be carried out according to the construction drawings and the instructions of the supervisor. Test, repeat to start, run, stop, forward, reverse motion, duration of at least 1h. Agencies should be flexible, stable and r
46、eliable work, limit switches, safety interlocks, anti-climbing device, the movements should be accurate and reliable, the parts should be free of cracks and other damage, the connection should not be loose. (3) civil works out the hoist and installation conditions installation【例8】(考点透视) 商店以40元的价钱卖出一
47、件商品，亏了20,。这件商品原价多少元，亏了多少元, 分析与解:以40元的价钱卖出，说明实际售价是40元;亏了20,，即亏了原价的20,，因此实际售价相当于原价的(1 - 20,)。 解:设这件商品原价x元。 x (1 - 20,) = 40 x 80, = 40 = 50 x50 20, = 10(元) 答:这件商品原价50元，亏了10元。 【例9】(考点透视) 某商店同时卖出两件商品，每件各得30元，其中一件盈利20,，另一件亏本20,。这个商店卖出这两件商品总体上是盈利还是亏本,具体是多少, 分析与解:盈利20,，即售出价是成本价的(1 + 20,);亏本20,，即售出价是成本价的(1 - 20,)。两件商品的售出价都是30元，可分别算出两件商品的成本价。 30 ?(1 + 20,)= 25(元) 30 ?(1 - 20,)= 37.5(元) 25 + 37.5 = 62.5(元) 62.5 60 = 2.5(元) 答:这个商店卖出这两件商品总体上是亏本，亏本2.5元。 自测试题,答案在后面, 1、李叔叔于2000年1月1日在银行存了活期储蓄1000元，如果每月的利率是0.165,，存款三个月时，可得到利息多少元?本金和利息一共多少元? 2、叔叔今年存入银行10万元，定期二年，年利率4.50% ，二年后到期，扣除利息税5