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小学数学公式及概念汇总

南江信望爱希望小学毕业复习资料

小学数学公式及概念分类汇总一、代数部分

(一)、整数:

1、自然数:表示物体的数量的数，最小的自然数是“0”

2、自然数也是整数。0是正整数与负整数的分界线。

3、质数:

一个数除了1和它本身，不再有其它的约数(因数)，这个数叫做质数(质数也叫做素数)。最小的质数是“2” ，50以内的质数:2、3、5、7、9、11、13、17、19、23、29、31、37、41、43、47.

4、合数

一个数除了1和它本身，还有别的约数，这个数叫做合数，最小的合数“4”

注意:1只有一个约数，就是它本身，1既不是质数，也不是合数。

最小的质数是2，也是质数中唯一的一个偶数(偶数解释见下)，其余的质数均为奇数(奇数解释见下)。

5、偶数

偶数就是可以被2整除的自然数(包括0)也叫做双数。偶数通常用“2k”表示。

6、奇数

奇数就是不能被2整除的自然数，也叫做单数。奇数通常用2k+1表示

注:偶数除了2以外都是合数。

7、互质数:只有公约数“1”的两个数。

8、最大公约数:几个数公有的约数，叫做这几个数的公约数。其中最大的一个，叫做最大公约数。

9、最小公倍数:几个数公有的倍数，叫做这几个数的公倍数，其中最小的一administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500-1000 punishment.

(5) significant near miss should be attempted as the case of responsible for the accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial number a 1 GB3323-2005 steel fusion welded butt joints, welding engineering-Ray lighting and quality rating of 2 GB11345-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-92 technical specification for welding of aluminium and its

alloys 5 low temperature steel welding procedure 6 SH3525-2004 petrochemical JB/ T4708-2000 of welding procedure qualification for

steel pressure vessels 7 JB/4709-2000 8 JB4730-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 1 GB150-98 2 GB50128-2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/ T4735-1997 steel welded atmospheric pressure vessel 4 GB50231-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-98

compressor, fan and pump installation engineering construction and acceptance specification for lifting 6

个叫做这几个数的最小公倍数。

10、互质数: 公约数只有1的两个数，叫做互质数。

11、质因数:把一个合数分解成几个质数相乘的形式，这几个质数叫作这个合数的质因数。

分解质因数:把一个合数分解成几个质数相乘的形式，这个过程叫做分解质因数。

12、能被2整除数的特征:个位上的数字是0，2，4，6，8

能被3整除数的特征:各位上的数字之和是3的倍数

能被5整除数的特征:个位上的数字是0，5

能被9整除数的特征:各位上的数字之和是9的倍数(

(二)、小数:

1、小数的基本性质:在小数末尾添上”0”或去掉”0”，小数的大小不变(

2、有限小数:小数部分的位数是有限的。

3、无限小数:小数部分的为数是无限的。无限循环小数:小数部分的数位有规律的. 无限不循环小数:小数部分没规律(又叫无理数)

4、纯循环小数:从小数部分第一位开始循环`

5、混循环小数:不是从小数部分第一位开始循环

6、循环节:从小数部分的某一位起.开是依次不断重复一个或几个数字.这些数字叫做循环节.

(三)、分数

1.分数:把单位“1”平均分成若干份，表示这样的一份或几分的数，叫做分数。

-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-ds manual methods of ultrasonic inspection and testing results for grade 3 GB5023689 steel wel-Ray lighting and quality rating of 2 GB11345-2005 steel fusion welded butt joints, welding engineering-mber a 1 GB3323ident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial nun team injuries acc1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and constructio-ative leadership of the criticism,

resulting in serious consequences, the pursuit of leadership, along with 500administrfication for lifting 698 compressor, fan and pump

installation engineering construction and acceptance speci-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-1997 steel welded atmospheric pressure vessel 4 GB50231-T4735 2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/-98 2 GB50128-GB150 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 12000 -2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2004 petrochemical JB/ T4708-5 low temperature steel welding procedure 6 SH352592 technical specification for welding of aluminium and its alloys 2

2.分数的基本性质:分数的分子和分母同时乘以或除以同一个数(0除外)，分数的大小不变。

3.最简分数:分母与分子互质的时候(这个分数就叫最简分数(

4.将几个异分母的分数利用分数的基本性质将分母变成一样(这个过程叫通分(在分数大小的比较中会广泛遇到通分(

5. (分数大小的比较:同分母的分数相比较，分子大的大，分子小的小。异分母的分数相比较，先通分然后再比较;若分子相同，分母大的反而小。

6、分数的加、减法则:同分母的分数相加减，只把分子相加减，分母不变。异分母的分数相加减，先通分，然后再加减。

7(分数乘整数，用分数的分子和整数相乘的积作分子，分母不变。

8(分数乘分数，用分子相乘的积作分子，分母相乘的积作为分母。

9(分数除以整数(0除外)，等于分数乘以这个整数的倒数。

10(真分数:分子比分母小的分数叫做真分数,真分数小于1。

11(假分数:分子比分母大或者分子和分母相等的分数叫做假分数。假分数大于或等于1。

12(带分数:把假分数写成整数和真分数的形式，叫做带分数。

13(一个数除以分数，等于这个数乘以分数的倒数。

14(甲数除以乙数(0除外)，等于甲数乘以乙数的倒数。

(四)、百分数

1、百分数:表示一个数是另一个数的百分之几的数，叫做百分数。百分数也叫做百分率或百分比。

2、把小数化成百分数，只要把小数点向右移动两位，同时在后面添上百分号。其实，把小数化成百分数，只要把这个小数乘以100,就行了。

-steel pressure vessel NDT 9 JB/T4744 2005 pressure vessel welding procedures of-2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2004 petrochemical JB/ T4708-on for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH352592 technical specificati-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-89 steel welds manual methods of ultrasonic inspection and

testing results for grade 3 GB50236-nd quality rating of 2 GB11345Ray lighting a-2005 steel fusion welded butt joints, welding engineering-ion standards and specifications, serial number a 1 GB3323accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construct1000 punishment. (5) significant near miss should be attempted as the case of responsible for the -administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500gineering construction and acceptance specification for lifting 698 compressor,

fan and pump installation en-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-1997 steel welded atmospheric pressure vessel 4 GB50231-de for construction and acceptance of 3 JB/ T47352005 vertical cylindrical steel pressure vessel steel welded tank co-98 2 GB50128-ing 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineer3

3、把百分数化成小数，只要把百分号去掉，同时把小数点向左移动两位。

4、把分数化成百分数，通常先把分数化成小数(除不尽时，通常保留三位小数)，再把小数化成百分数。

5、把百分数化成分数，先把百分数改写成分数，能约分的要约成最简分数。

(五)、比及比例

1、什么叫比:两个数相除就叫做两个数的比。如:2?5或3:6或1/3

2、比的基本性质:比的前项和后项同时乘以或除以一个相同的数(0除外)，比值不变。

3、什么叫比例:表示两个比相等的式子叫做比例。如3:6,9:18

4、比例的基本性质:在比例里，两外项之积等于两内项之积。

5、解比例:求比例中的未知项，叫做解比例。如3:χ,9:18

6、正比例:两种相关联的量，一种量变化，另一种量也随着化，如果这两种量中相对应的的比值(也就是商k)一定，这两种量就叫做成正比例的量，它们的关系就叫做正比例关系。如:y/x=k( k一定)

7、反比例:两种相关联的量，一种量变化，另一种量也随着变化，如果这两种量中相对应的两个数的积一定，这两种量就叫做成反比例的量，它们的关系就叫做反比例关系。如:x×y = k( k一定)

(六)、数量关系

1、每份数×份数,总数总数?每份数,份数总数?份数,每份数

2、速度×时间,路程路程?速度,时间路程?时间,速度

3、单价×数量,总价总价?单价,数量总价?数量,单价

4、工作效率×工作时间,工作总量工作总量?工作效率,工作时间

inspection and testing results for grade 3 GB5023689 steel wel-Ray lighting and quality rating of 2 GB11345-2005 steel fusion welded butt joints, welding engineering-mber a 1 GB3323ident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial nun team injuries acc1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and constructio-ative leadership of the criticism,

resulting in serious consequences, the pursuit of leadership, along with 500administrfication for lifting 698 compressor, fan and pump

工作总量?工作时间,工作效率

5、加数，加数,和和,一个加数,另一个加数

6、被减数,减数,差被减数,差,减数差，减数,被减数

7、因数×因数,积积?一个因数,另一个因数 8、被除数?除数,商被除数?商,除数商×除数,被除数

9、相遇问题

相遇路程,速度和×相遇时间

相遇时间,相遇路程?速度和

速度和,相遇路程?相遇时间

10、追及问题

追及距离,速度差×追及时间

追及时间,追及距离?速度差

速度差,追及距离?追及时间

11、流水问题

顺流速度,静水速度，水流速度

逆流速度,静水速度,水流速度

静水速度,(顺流速度，逆流速度)?2

水流速度,(顺流速度,逆流速度)?2

12、浓度问题

溶质的重量，溶剂的重量,溶液的重量溶质的重量?溶液的重量×100%,浓度溶液的重量×浓度,溶质的重量

溶质的重量?浓度,溶液的重量

13、利润与折扣问题

-ing 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineer-steel pressure vessel NDT 9 JB/T4744 2005 pressure vessel welding procedures of-2000 8 JB4730-2000 of welding procedure

qualification for steel pressure vessels 7 JB/4709-2004 petrochemical

JB/ T4708-on for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH352592 technical specificati-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-nd quality rating of 2 GB11345Ray lighting a-2005 steel fusion welded butt joints, welding engineering-ion standards and specifications, serial number a 1

GB3323accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construct1000 punishment. (5) significant near miss should be attempted as the case of responsible for the -administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500gineering construction and acceptance specification for lifting 698 compressor, fan and pump installation en-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-1997 steel welded atmospheric pressure vessel 4 GB50231-de for construction and acceptance of 3 JB/ T47352005 vertical cylindrical

steel pressure vessel steel welded tank co-98 2 GB501285 利润,售出价,成本

利润率,利润?成本×100%,(售出价?成本,1)×100%

涨跌金额,本金×涨跌百分比

折扣,实际售价?原售价×100%(折扣,1)

利息,本金×利率×时间

税后利息,本金×利率×时间×(1,5%)(注:教育储蓄和购国库券不收利息税)

(七)、简便运算

1(加法交换律:两数相加交换加数的位置，和不变。a+b=b+a

2(加法结合律:三个数相加，先把前两个数相加，或先把后两个数相加，再同

第

三个数相加，和不变。(a+b)+c=a+(b+c)

3(乘法交换律:两数相乘，交换因数的位置，积不变。a.b=b.a

4(乘法结合律:三个数相乘，先把前两个数相乘，或先把后两个数相乘，再和

第三个数相乘，它们的积不变。(a.b).c=a.(b.c)

5(乘法分配律:两个数的和同一个数相乘，可以把两个加数分别同这个数相

乘，再把两个积相加，结果不变。(a+b).c=a.c+b.c

6、一个数连续减两个数，可以先把后两个数相加，然后再减，结果不变。

例:78-29-11,78-(29+11)

7、一个数连续除以两个数，可以先把后两个数相乘，再用它们的积去除这个数，结果不变。例:90?5?6,90?(5×6)

-2005 pressure vessel welding procedures of steel pressure vessel NDT 9 JB/T4744-2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2004 petrochemical JB/ T4708-5 low temperature steel welding procedure 6 SH352592 technical specification for welding of aluminium and its alloys -2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-ds manual methods of ultrasonic inspection and testing results

for grade 3 GB5023689 steel wel-Ray lighting and quality rating of 2

GB11345-2005 steel fusion welded butt joints, welding engineering-mber a

1 GB3323ident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial nun team injuries acc1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and constructio-ative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500administrfication for lifting 698 compressor, fan and pump installation engineering construction and acceptance speci-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-1997 steel welded atmospheric pressure vessel 4 GB50231-T4735 2005 vertical cylindrical steel pressure vessel steel welded tank code for construction and acceptance of 3 JB/-98

2 GB50128-GB150 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineering 12000 6

(八)、方程

1(除法的性质(商不变性质):在除法里，被除数和除数同时扩大(或缩小)相同的倍数，商不变。0除以任何不是0的数都得0。

2(等式:等号左边的数值与等号右边的数值相等的式子叫做等式。 3.等式的基本性质:等式两边同时乘以(或除以)一个相同的数，等式仍然成立。

4(方程式:含有未知数的等式叫方程式。

5(一元一次方程式:含有一个未知数，并且未知数的次数是一次的等式叫做一元一次方程式。

(九)、植树问题

1 非封闭线路上的植树问题主要可分为以下三种情形: ?如果在非封闭线路的

两端都要植树,那么:

株数,段数，1,全长?株距,1

全长,株距×(株数,1) 株距,全长?(株数,1) ?如果在非封闭线路的一端要植树,另一端不要植树,那么: 株数,段数,全长?株距

全长,株距×株数株距,全长?株数 ?如果在非封闭线路的两端都不要植树,那么:

株数,段数,1,全长?株距,1

全长,株距×(株数，1) 株距,全长?(株数，1) 2 封闭线路上的植树问题的数

量关系如下

株数,段数,全长?株距

全长,株距×株数株距,全长?株数

ing 1 GB1502000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineer-

steel pressure vessel NDT 9 JB/T4744 2005 pressure vessel welding procedures of-2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2004 petrochemical JB/ T4708-on for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH352592 technical specificati-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-89 steel welds manual methods of ultrasonic inspection and

construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construct1000 punishment. (5) significant near miss should be attempted as the case of responsible for the -administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500gineering construction and acceptance specification for lifting 698 compressor,

(十)、单位换算

重量单位换算

1吨=1000 千克

1千克=1000克

1千克=1公斤

人民币单位换算

1元=10角

1角=10分

1元=100分

时间单位换算

1世纪=100年 1年=12月

大月(31天)有:1\3\5\7\8\10\12月小月(30天)的有:4\6\9\11月平年2月

28天, 闰年2月29天平年全年365天, 闰年全年366天 1日=24小时 1时=60

分

1分=60秒 1时=3600秒

92 technical specification for welding of aluminium and its alloys -2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-ds manual methods of ultrasonic inspection and testing results for grade 3 GB5023689 steel wel-Ray lighting and quality rating of 2 GB11345-2005 steel fusion welded butt joints, welding engineering-mber a 1 GB3323ident penalty provisions, mutatis mutandis. Eight, should perform in the construction standards and specifications, serial nun team injuries acc1000 punishment. (5) significant near miss should be attempted as the case of responsible for the accident and constructio-ative leadership of the criticism,

resulting in serious consequences, the pursuit of leadership, along with 500administrfication for lifting 698 compressor, fan and pump

NDT 9 JB/T4744-2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2004 petrochemical JB/ T4708-5 low temperature steel welding procedure 6 SH35258

二、几何部分

(一)、公式

1 、正方形: C周长， S面积， a边长，周长,边长×4 C=4a

面积=边长×边长 S=a

2 、长方形

C周长， S面积，a边长

周长=(长+宽)×2 C=2(a+b) 面积=长×宽 S=ab

23 、正方体 V:体积 a:棱长表面积=棱长×棱长×6 s表= a×6

体积=棱长×棱长×棱长 V=a

4 、长方体

V:体积 s:面积 a:长 b: 宽 h:高

(1)表面积(长×宽+长×高+宽×高)×2 S=2(ab+ah+bh)

(2)体积=长×宽×高 V=abh

5 三角形(内角和:三角形的内角和,180度。)

s面积 a底 h高面积=底×高?2 s=ah?2 6 平行四边形

s面积 a底 h高面积=底×高 s=ah 7 梯形

s:面积 a:上底 b:下底 h:高面积=(上底+下底)×高?2

S=(a+b)h?2

8 圆形

S:面积 C:周长 d:直径 r:半径

(1)周长=直径×π=2×π×半径C=πd=2πr

(2)面积=半径×π s=πr

2000 steel pressure vessel products mechanical properties test of welded plate II, mechanical equipment installation engineer-steel pressure vessel NDT 9 JB/T4744 2005 pressure vessel welding procedures of-2000 8 JB4730-2000 of welding procedure qualification for steel pressure vessels 7 JB/4709-2004 petrochemical JB/ T4708-on for welding of aluminium and its alloys 5 low temperature steel welding procedure 6 SH352592 technical specificati-2002 industrial pipe welding engineering code for construction and acceptance of field equipment 4 HGJ222-89 steel welds manual methods of ultrasonic inspection and testing results for grade 3 GB50236-nd quality rating of 2 GB11345Ray lighting a-2005 steel fusion welded butt joints, welding engineering-ion standards and specifications, serial number a 1 GB3323accident and construction team injuries accident penalty provisions, mutatis mutandis. Eight, should perform in the construct1000 punishment. (5) significant near miss should be attempted as the case of responsible for the -administrative leadership of the criticism, resulting in serious consequences, the pursuit of leadership, along with 500gineering construction and acceptance specification for lifting 698 compressor, fan and pump installation en-2009 mechanical equipment installation engineering construction and acceptance specification for 5 GB50275-1997 steel

welded atmospheric pressure vessel 4 GB50231-de for construction and acceptance of 3 JB/ T47352005 vertical cylindrical steel pressure vessel steel welded tank co-98 2 GB50128-ing 1 GB1509

9 圆柱体

v:体积 h:高 s:底面积 r:底面半径 c:底面周长

(1)侧面积=底面周长×高 s侧,ch

(2)表面积=侧面积+底面积×2 s表,s侧 +2s底

(3)体积=底面积×高V,sh=πrh

10 圆锥体

v:体积 h:高 s;底面积 r:底面半径

2111体积=底面积×高×/ V,/sh=/πrh 333

(二)、单位换算

长度单位换算

1千米=1000米 1米=10分米 1分米=10厘米 1米=100厘米 1厘米=10毫米面积单位换算

1平方千米=100公顷 1公顷=10000平方米

1平方米=100平方分米 1平方分米=100平方厘米体(容)积单位换算

1立方米=1000立方分米 1立方分米=1000立方厘米 1立方分米=1升 1立方厘米=1毫升 1升,1000毫升 1立方米=1000升

(三)、基本概念

1、一个封闭式图形,将他的周围围上1圈,这个圈的长度是他的周长.

2、一个物体所占平面的大小叫做这个物体的面积.

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3、一个物体所占空间的大小叫做这个物体的体积.

4、一个物体所能容纳别的物体的体积叫做这个物体的容积

5、一个物体表面的面积叫表面积

6、三角形的内角和是180度.四边形的内角和是360度.N边形的内角和是(边长-2)×180度.

7、外角:1条边的反向延长线与相邻的一条边所夹的角叫做外角.三角形的外角是不相邻的两个内角之和,

8、任何封闭式的图形的外角和都是360度

线:

1、直线:没有端点,没有长度,无限延长

2、射线:有一个端点,没有长度,无限延长

3、线段:有两个端点,有长度.

4、由一个点引出的两条射线,这两条射线所夹的这个部分叫做角,而那个点叫做顶点.角分为几种角:锐角(大于0度小于90度),直角(等于90度),钝角(大于90度小于180度),平角(等于180度),周角(等于360度)

5、由1点做一条线段的垂线,这个点叫做垂足.

6、当两条直线永远不相交时,就说明这两条直线互相平行.

平面图形:

1、三角形:

, 三角形中最大的角是钝角的话这个三角形叫钝角三角形.

, 三角形中最大的角是直角的话这个三角形叫直角三角形

, 三角形中最大的角是锐角的话这个三角形叫锐角三角形

, 从顶点做与他对边的垂线段.这个垂线段的长度叫做这个三角形的高，1个三角形有三条高.