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六年级上册数学试题提升爬坡题北京版(2014秋)(附解析)

六年级上册数学试题提升爬坡题北京版(2014秋)(附解析)
六年级上册数学试题提升爬坡题北京版(2014秋)(附解析)

6数上-爬坡题

第一单元 分数乘法

【例1】挂钟几时就敲几下,半时敲一下,凌晨4时挂钟2秒敲完,早上7时挂钟几秒敲完? 解析:凌晨4时挂钟敲4下,这4下之间有3个间隔,用时2秒,即每相邻两下之间的时间

间隔是

32秒,早上7时挂钟敲7下,这7下之间有6个间隔,也就是6个3

2

秒。 解答: 2÷(4一1)=3

2

(秒) 7一1=6 3

2

×6=4(秒) 答:早上7时挂钟4秒敲完。

【例2】瓶子中装有一种孢子,每小时分裂一次,每分裂一次体积增大一倍。如果最初孢子的体积占瓶子的

32

3

,那么3小时后,孢子的体积占瓶子的几分之几? 解析:孢子每小时分裂一次,每分裂一次体积增大一倍,也就是说孢子每经过一小时体积就扩大到原来的2倍,

况,如下表:

求3小时后孢子的体积占瓶子的几分之几,就是求

32

的(2×2×2)倍是多少,用乘法计算。 解答:2×2×2=8

323×8=4

3 答:孢子的体积占瓶子的4

3

【例3】□里最小应填自然数几?

26□×2>2712 38□×9>39

18 思路分析 先将分数乘整数的算式写成整数和分子相乘作分子的形式,再根据“>”左右两边分数分母的大小关系来判断□里最小应填自然几。如26□×2=262?□>27

12

,26<27,当分子是12时,262?□才大于27

12

,推出□里最大应填6。 正确解答

×2>

27

12

×9>

39

18

【例4】两根相同的长3米的绳子,第一根剪去

31,第二根剪去3

1

米,哪根绳子剪去的多? 解析:此题是对求一个数的几分之几是多少的解题方法的全面考查。第一根绳子剪去的是3米的

31,也就是3×31=1(米),第二根绳子剪去31米,1米>3

1

米,因此第一根绳子剪去的多。我们还可以这样思考:第一根绳子剪去的是3米的

31,第二根绳子剪去的是3

1

米,相当于1米的

3

1

,3米>1米,因此第一根绳子剪去的多。 解答: 第一根绳子剪去的多

【例5】先计算,再比较每道算式中因数与积的大小,从中你能发现什么规律? 24×

21= 24×1= 24×34= 24×4

1= 解析:先计算出每道算式的结果,再比较积与因数的大小,从中找出规律。

24×

21=12 24×1=24 24×34=32 24×41=6 21<1 1=1 34>1 4

1<1 12<24 24=24 32>24 6<24

解答: 24×

21

=12 24×1=24 24×34=32 24×4

1

=6

【例6】有两袋面粉,甲袋面粉的质量是30千克,乙袋面粉的质量是甲袋的6

5

,要使两袋面粉同样重,应从甲袋中取出多少千克面粉放人乙袋? 解析: 观察示意图可知,乙袋面粉的质量是甲袋的6

5

,则乙袋 面粉的质量是30×

6

5

=25(千克),甲袋比乙袋多30-25=5(千 克),因为要从甲袋取出一部分放入乙袋,并使两袋一样重,所

以取出的是它们质量差的一半。 解答: 30×6

5

=25(千克) 30-25=5(千克)

2

1

=2.5(千克) 答:应从甲袋中取出2.5千克面粉放人乙袋。 【例7】甲数是乙数的52,丙数是甲数的41

,丙数是乙数的几分之几?

解析:“甲数是乙数的5

2

”是把乙数看作单位“1”,把乙数平均分成5份,甲数是这样的2

份,如图一。“丙数是甲数的4

1

”是把甲数看作单位“1”,把甲数平均分成4份,丙数是这

样的1份,如图二。由此可以看出丙数是乙数的52的4

1

图一 图二 解答:

52×41=101 答:丙数是乙数的10

1

。 第二单元 分数除法

【例1】 小丽在计算一道除法算式时,把除以6按照乘6去计算了,结果得3

2

。正确的结果应该是多少?

解析:此题是对分数除以整数的计算方法的全面考查。一个数乘6,结果是3

2

,可以逆推,用

3

2

除以6,求得这个数,也就是除法算式的被除数,然后用被除数除以6,求得正确的答案。一定注意解答此类题时,可以采用逆推法,先从错误的结果入手,分析错误的原因,再利用积、商的变化得到正确的算式,然后求出正确的结果。 解答:

32÷6=32×61=91 91÷6=91×61=541 答:正确的结果应该是54

1。 【例2】小敏看一本书,第一天看了全书的5

2,第二天看了全书的41

,两天一共看了91页。

这本书一共有多少页?

解析:由题意可知,两个分数对应的单位“1”的量均是全书的总页数。题中的数量关系可以用线段图表示如下:

这本书一共有?页

根据线段图可以得出等量关系式:第一天看的页数十第二天看的页数=两天一共看的页数。根据等量关系式列方程解答。 解答:设这本书一共有χ页。

5

2χ十41

χ=91

20

13

χ=91 χ=140 答:这本书一共有140页。

【例3】简算:

175×249+179×24

7。 解析:这个算式可以看成两组算式相加,每组算式中的每个因数都不相同,但两组算式中分数的分母都相同,分子中都有9,根据乘法的性质和乘法交换律在两组算式中转化出一个相同的因数,然后根据乘法分配律简算。根据上面的思路转化算式。

两个分数的分子调换位置 两个分数的分母调换位置

175×249=241795??=241795??714259??=179×245或175×249=71429

5??=245×17

9 179×245和245×179都与175×249有相同的因数17

9。

同样也可以调换179×247中分数的分子或分母的位置,使调换后的算式与 17

5

×

249有相同的因数24

9。 解答: 175×249+179×247 175×249+179×247

=179×245+179×247 =175×249十177×249

=179×(245+247) =(175十177)×24

9

179×21 =1712×249 =349 =34

9

【例4】 计算:22÷23

22

22。

解析: 通过观察发现,除数是一个带分数,它的整数部分和分数部分的分子都和被除数相同,都是22,所以可以利用商不变的规律进行转化,使计算简便。 正确解答 22÷232222=(22÷22)÷(232222÷22)=1÷2311=24

23

【例5】晶晶文化用品商店购进一批日记本,第一周售出的本数比总数的一半还多12本,结果剩下36本,这批日记本一共有多少本?

解析: 画图分析题意,如图所示:

从图中可以看出,用剩下的本数加上12

解答: 12+36=48(本) 48÷2

1

=96(本) 答:这批日记本一共有96本。

第三单元 百分数

【例1】下列哪些分数可以用百分数表示?

(1)预计到2050年,我国60岁及60岁以上的老年人口约占总人口的100

31。 (2)1袋盐的质量是10050kg 。

(3)空气中的氧气含量约占100

21。

解析:因为百分数表示两个数量之间的倍比关系。所以:

100

31表示我国60岁及60岁以上的老年人口与我国 人口总数之间的倍比关系,能用百分数表示。

100

50

kg 表示l 袋盐的质量,不能用百分数表示。 100

21表示氧气含量与空气总量之间的倍比关系,能用百分数表示。

解答:(1)和(3)中的分数,可以用百分数表示。

【例2】有甲、乙两杯糖水,甲杯糖水为100克,含糖20克;乙杯糖水为300克,含糖42克,哪杯糖水更甜些?

解析:要知道哪杯糖水更甜些,就要比较那杯水的20÷100=10020,42÷300=30042,把300

42

都化成分母是100的分数进行比较。30042=10014 因为10020>10014,所以10020>300

42

。由

此得出:甲杯糖水更甜些。 解答:甲杯糖水更甜些。

【例3】 实验一小的优秀教师人数占全校教师人数的10%,实验二小的优秀教师人数占全校教师人数的15%。哪个学校的优秀教师人数多?

解析:假设两个学校的教师人数都是100人,那么实验一小有10人是优秀教师,实验二小有15人是优秀教师,所以实验二小的优秀教师人数多。假设实验一小有教师200人,实验二小有教师100人,那么实验一小有20人是优秀教师,实验二小有15人是优秀教师,所以实验一小的优秀教师人数多。同理,还有两个学校优秀教师人数相等的可能。

解答 在没有具体给出两个学校的教师总人数时,无法判断哪个学校的优秀教师人数多,哪个学校的优秀教师人数少。

【例4】全世界胡杨的90%在中国,中国胡杨的90%在新疆,新疆胡杨的90%在塔里木。塔里木的胡杨占全世界胡杨的百分之几? 解析:根据题意画图如下:

从图中可知:塔里木的胡杨占全世界胡杨的90%×90%×90%。 解答: 90%×90%×90%=0.729=72.9% 答:塔里木的胡杨占全世界胡杨的72.9%。 【例5】在0.85、85.1%、651

、8

7

和l.85这五个数中,最大的数是多少?最小的数是多少? 解析:把题中要比较的几个数分成大、小两组,先在各组中找出最大或最小的数,再采用大

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2014国乙2014国乙07 2014国乙08 2014国乙09 2014国乙10 2014国乙11 2014国乙12 2014国乙13 2014国乙26 2014国乙27 2014国乙28 2014国乙36 2014国乙37 2014国乙38 2014国甲2014国甲07 2014国甲08 2014国甲09 2014国甲10 2014国甲11 2014国甲12 2014国甲13 2014国甲26 2014国甲27 2014国甲28 2014国甲36 2014国甲37 2014国甲38 2014北京2014北京06 2014北京07 2014北京08 2014北京09 2014北京10 2014北京11 2014北京12 2014北京252014北京26 2014北京27 2014北京28 2014山东 2014山东07 2014山东08 2014山东09 2014山东10 2014山东11 2014山东12 2014山东13 2014山东29 2014山东30 2014山东31 2014山东32 2014山东33 2014山东34 2014 浙江 2014 浙江07 2014 浙江08 2014 浙江09 2014 浙江10 2014 浙江11 2014 浙江12 2014 浙江13 2014 浙江26 2014 浙江27 2014 浙江28 2014 浙江29 2014福建 2014福建06 2014福建07 2014福建08 2014福建09 2014福建10 2014福建11 2014福建12 2014福建23 2014福建24 2014福建25 2014福建31 2014福建32 2014安徽 2014安徽07 2014安徽08 2014安徽09 2014安徽10 2014安徽11 2014安徽12 2014安徽13 2014安徽25 2014安徽26 2014安徽27 2014安徽28 2014天津 2014天津01 2014天津02 2014天津03 2014天津04 2014天津05 2014天津06 2014天津07 2014天津08 2014天津09 2014天津10 2014重庆 2014重庆01 2014重庆02 2014重庆03 2014重庆04 2014重庆05 2014重庆06 2014重庆07 2014重庆08 2014重庆09 2014重庆10 2014重庆11 2014四川 2014四川01 2014四川02 2014四川03 2014四川04 2014四川05 2014四川06 2014四川07 2014四川08 2014四川09 2014四川10 2014四川11 2014广东 2014广东07 2014广东08 2014广东09 2014广东10 2014广东11 2014广东12 2014广东22 2014广东23 2014广东30 2014广东31 2014广东32 2014广东33 2014海南 2014海南01 2014海南02 2014海南03 2014海南04 2014海南05 2014海南06 2014海南07 2014海南08 2014海南09 2014海南10 2014海南11 2014海南12 2014海南13 2014海南14 2014海南15 2014海南16 2014海南17 2014海南18 2014海南19 2014海南20 2014江苏 2014江苏01 2014江苏02 2014江苏03 2014江苏04 2014江苏05 2014江苏06 2014江苏07 2014江苏08 2014江苏09 2014江苏10 2014江苏11 2014江苏12 2014江苏13 2014江苏14 2014江苏15 2014江苏16 2014江苏17 2014江苏18 2014江苏19 2014江苏20 2014江苏21 【鸣谢整理人员:2014国乙(2中林书雄)2014国甲(协和周丽萍)2014北京(协和周丽萍)2014山东(麒麟梁晓燕)2014浙江(麒麟梁晓燕)2014福建(麒麟梁晓燕)2014安徽(麒麟梁晓燕)2014天津(协和周丽萍)2014重庆(麒麟梁晓燕)2014四川(协和周丽萍)2014广东(麒麟梁晓燕)2014海南(2中林书雄)2014江苏(2中林书雄)】

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