【www.guakaob.com--中考】
2014年：
根据分数线的划定，襄阳四中、五中在各县（市）区指令生录取分区分数线从530.8分至572分不等。襄阳四中择校生录取分数线为551.8分，襄阳五中择校生录取分数线为543.5分。
襄阳一中指令生录取分数线为489.1分，择校生录取分数线为475分；襄阳三中指令生录取分数线508.7分，择校生录取分数线为499.9分。
襄阳市直其他省级、市级示范高中指令生和择校生录取分数线：致远中学469.9分，三十六中461.1分，襄阳八中350分，襄阳九中350分，东风中学350分，以上五所学校择校生录取最低控制分数线分别为各校指令生录取分数线下50分。凡填报了上述学校择校生志愿或愿意择校就读上述学校，中考成绩达到择校生录取最低控制分数线的考生，从高分到低分择优录取，额满为止。
中考成绩为A等的高分段学生，均在各高中招生录取分数线以上，志愿填报任何一所高中，都能以指令生资格录取。
襄阳四中、襄阳五中指令生录取分数线 县（市）区 学校及指令生录取分数线 襄城区 四中 567.5分 五中 564.3分 樊城区 四中 541.3分 五中 543.2分 高新区 四中 551.1分 五中 556.2分 东津区 四中 551分 五中 551分 襄州区 四中 550分 五中 530.8分 枣阳市 四中 572分 五中 560分 宜城市 四中 552.8分 五中 563分 老河口 四中 568.5分 五中 538.9分 南漳县 四中 543分 五中 544.7分 谷城县 四中 541.5分 五中 533.5分 保康县 四中 546.7分 五中 560.5分
2013年
襄阳四中、五中指令生录取分数线从569.6分至596.5分不等（详见附表）。襄阳四中择校生录取分数线为572.1分，襄阳五中择校生录取分数线为560.9分。
襄阳一中、三中、致远中学、三十六中指令生录取分数线分别为：528.2分、542.8分、506.2分、497.6分。这4所学校择校生录取最低控制分数线分别为各校指令生录取分数线下50分。凡填报这4所学校择校生志愿或愿意择校就读这4所学校、中考成绩达到择校生录取最低控制分数线的考生，从高分到低分择优录取，额满为止。
2012年
襄阳四中、襄阳五中指令生志愿填报资格线为490分。
襄阳一中、襄阳三中指令生志愿填报资格线为450分。
高考派—高考志愿填报专家
【襄阳职业技术学院专业】襄阳职业技术学院招生网站-襄阳职业技术学院分数线
襄阳职业技术学院重点专业:
襄阳职业技术学院全景地图:
襄阳职业技术学院历年分数线:
襄阳职业技术学院报考指南:
襄阳职业技术学院招生计划:
襄阳职业技术学院人气校友:
高考派—高考志愿填报专家
2010年学术型硕士研究生考研复试分数线
2009年考研国家复试基本分数线
考研教育网提示：箭头表示2009年与2008年考研国家复试分数线变化对比情况，↑表示上升，↓表示下降，无标注表示无变化。
2008年考研国家复试基本分数线
考研教育网提示：箭头表示2009年与2008年考研国家复试分数线变化对比情况，↑表示上升，↓表示下降，无标注表示无变化。
2007年考研国家复试基本分数线
2006年考研国家复试基本分数线
襄阳36中高一上学期期中测试
英语试卷
考试时间：120分钟；命题人：代小强
注意事项： 试卷类型：
A
1．答题前填写好自己的姓名、班级、考号等信息． 2.请将答案正确填写在答题卡上
第I卷（选择题）
第一部分：听力（共两节，满分30分）
做题时，先将答案划在试卷上。录音内容结束后，你将有两分钟的时间将试卷上的答案转涂到答题卡上。第一节（共5小题；每小题1.5分，满分7.5分）
听下面5段对话。每段对话后有一个小题，从题中所给的A、B、C三个选项中选出最佳选项，并标在试卷的相应位置。听完每段对话后，你都有10秒钟的时间来回答有关小题和阅读下一小题。每段对话仅读一遍。
1. Where does the woman live now?
A. In the heart of town. B. In the south of town. C. Near the center of town. 2. What color suit did the man wear yesterday?
A. Brown. B. Green. C. Gray. 3. How much does the man have to pay?
A. Five yuan. B. Ten yuan. C. Fifteen yuan. 4. What will the two speakers probably do next?
A. Go to Mary’s home. B. Go back home at once. C. Go and buy an umbrella. 5. What is the probable relationship between the two speakers?
A. Mother and babysitter (临时替人照看婴儿的人). B. Teacher and student. C. Husband and wife.
第二节（共 15 小题；每小题 1.5 分，满分 22.5 分）
听下面 5 段对话或独白。每段对话或独白后有几个小题，从题中所给的 A、B、C 三个选项中选出最佳选项，并标在试卷的相应位置。听每段对话或独白前，你将有时间阅读各个小题，每小题 5 秒钟；听完后，各小题将给出 5 秒钟的作答时间。每段对话或独白读两遍。 听第6段材料，回答第6、7题。
6. How will the man go to the station？
A. By subway. B. By taxi. C. By bus. 7. What will the woman do? A. Catch a train.
B. Visit her cousin. C. Go shopping.
襄阳36中高一上学期期中测试英语试卷 听第7段材料，回答第8、9题。
8. Where did the man probably work before?
A. In a hospital. B. In a language school. C. In a French company. 9. How long will the man work at his new job?
A. For about one year. B. For about two years. C. For about three years.
听第8段材料，回答第10至12题。
10. How many persons planned to spend the weekend with the man? A. Two. B. Three. C. Four. 11. Why can’t the woman go to Disneyland this weekend?
A. She has to prepare for a test. B. She plans to see some old friends. C. She wants to get some rest at home.
12. With whom will the man probably spend the weekend? A. Tom. B. Mike. C. Sam.
听第9段材料，回答第13至16题。
13. Why didn’t the woman answer the phone?
A. She didn’t take her phone with her. B. She didn’t hear the phone ringing. C. She wants to get some rest at home. 14. What day is it today?
A. Wednesday. B. Thursday. C. Friday. 15. What has the man prepared for Ann’s birthday?
A. A new CD. B. A special gift. C. A surprising party. 16. What will Ann’s pen friend do?
A. Come to see Ann. B. Go to France tomorrow. C. Buy Ann a plane ticket.
听第10段材料，回答第18至20题。
17. In which city did the speaker first meet Jenny?
A. New York City. B. Los Angeles. C. Chicago. 18. How long did Jenny stay in the speaker’s city?
A. For one year. B. For six years. C. For ten years. 19. How did the speaker and Jenny keep in touch first?
A. By writing letters. B. By chatting online. C. By making phone calls. 20. What happened to the speakers last month?
A. She came across Jenny. B. She lost touch with Jenny. C. She got in touch with Jenny online.
第二部分：词汇知识运用（共两节，满分30分）
第一节 多项填空（共10小题；每小题1分，满分10分）
21.When I entered, I found Tom_______ himself in a magazine and he even didn’t notice me. A. organizing B. enriching C. burying D. keeping
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22.Nobody knows the man killed in the accident, so it is difficult for the police to find out his_________.
A. thought B. height C. weight D. identity 23.Tom and Mike are good friends. They often_____each other from being punished by the teacher.
A. stop
B. shelter
C. prevent D. keep
24.The only wish of the hit-and-run driver after being arrested was to _________ apologize to the victim’s family for his misdeed. A. completely
B. gradually
C. secretly
D. sincerely
25.There are many ways to make you feel good. The most important thing is that you should learn to be ________ for what you have. A. sorry
B. concerned
C. grateful
D. upset
26.When you apologize, you’re telling someone that you’re sorry for the hurt you caused, even if you didn’t do it _________. A. by mistake
B. as usual C. on purpose D. by accident
27.After the storm, some houses in Taiwan lay ______; some had their roofs and chimneys blown
off.
A. in rags
B. in control C. in relief
D. in ruins
28.In our journey through life, we will ______ ups and downs. The most important thing is to keep a good state of mind. A. suffer from B. go through C. go over
D. look through 29.Jim ______ a better solution to the problem and all the people present were in favor of it.
A. got along with
B. got away with
C. came up with
D. caught up with
30.After chatting with his net-friend for a long time, they decided to meet each other, however, they were shocked to discover each other’s true ________.
A. item B. insurance C. identity D. introduction【襄阳教育网官网36分数线】
第二节：完型填空（共20小题；每小题1分，满分20分）
阅读下面短文，从短文后所给各题的四个选项（A、 B、 C和D）中，选出可以填入空白处的最佳选项，并在答题卡上将该项涂黑。
Love can be seen here and there in our daily life, and love will be passed on from person to .
One day, waiting for the airplane to take off , I was happy to get a seat by myself. Just then, an air hostess approached me and asked, “Would you mindyour seat? A couple would like to sit together.” The was next to a girl with her arms in casts (石膏绷带), a am I going to sit there, I thought immediately. But a soft voice spoke, “She needs help.” Finally , Imove to that seat.The girl was 襄阳36中高一上学期期中测试英语试卷 that Kathy would not be able to to feed her but hesitated（犹豫）Kathy’s need was morethan my We became closer and closer in a short period of time. By the end of the five–hour trip, my heart
I was very glad I had reached beyond my comfort zone to sit next to Kathy and feed her. flows beyond human borders（界线） 31. A. a girl B. help C. a seat D. love 32. A. losing B. taking C. changing
D. giving
33.A. suitable
B. comfortable
C. available（可利用的） D.favorable 34.A. No problem B. No way C. Nowhere D. No doubt 35.A. promised B. wanted C. regretted D. decided 36.A. was B. would be C. used to be D. had been 37.A. treatment B.pleasure C. travel D. business 38.A. know B. realize C. say D. recognize 39.A. eat B. feed C. choose D.support 40.A. offering B. needing C. stopping D. trying 41.A.impolite B. far C. close D.fast 42.A. girl B. neighbor C. passenger D. stranger 43.A. unusual B. direct C. important D. shameful 44.A. when B. although C. since D. as 45.A. refused B. wondered C. cried D. did 46.A. had warmed B. had jumped
C. had broken D.had cheered 47.A. life B. money C. time D.energy 48.A. seldom B. never
C. hardly D. sometimes 49.A. separate B.independent
C. silent
D. upset 50.A. happen B. stretch（张开） C. wait
D. continue
第三部分：阅读理解(共20小题；每小题2分，满分40分)
阅读下列短文，从每篇短文后所给各题的四个选项(A、B、C和D)中，选出最佳选项，并在答题卡上将该项涂黑。
A
Most people think zoos are safe for animals, where struggles such as difficulty in finding food and avoiding natural enemies don't exist. Without such problems, animals in zoos should live to
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an old age. But that may not be true for the largest land animals on earth. Scientists have known that elephants in zoos often suffer from poor health. They develop diseases and behaviour changes. Sometimes, they even become infertile, or unable to have babies.
To learn more about how elephants are affected, a team of international scientists compared the life spans of elephants born in zoos with those living outdoors in their native lands. Zoos keep detailed records of all the animals, such as birth dates, illnesses, weight and death. These records made it possible for the researchers to analyse 40 years of data on 800 African and Asian elephants in zoos across Europe. The team found that female African elephants born in zoos lived an average of 16.9 years while those in the wild lived an average of 56 years. Scientists don't yet know why wild elephants seem to be so much better than their zoo-raised elephants. Georgia Mason, a biologist who led the study, thinks stress and obesity (肥胖) may be to blame. Zoo elephants don't get the same kind of exercise they would in the wild, and most are fat.
Another finding from the study showed that Asian elephants born in zoos were more likely to die early than Asian elephants caught in the wild and brought to zoos. Mason suggests stress in the mothers in zoos might cause them to have babies that are less likely to survive. 51．Most people think that animals in the zoos ________． A.have difficulty in finding food
B.often struggle with each other
C.live longer than those in the wild D.will often fight with their enemies 52．What does the underlined word “infertile” mean? A.Without home to stay at. B.Without ability to give birth. C.Without friends to talk with.
D.Without anyone to turn to.
53.The scientists carried out a research so that they could know ________． A.how long the elephants live B.how the elephants are affected C.how the elephants can be fed D.how the elephants should be kept 54．In order to let the elephants in the zoos live longer, people should ________． A.give them a good diet B.keep their living place clean and tidy C.get them to exercise as in the wild
D.try to keep as quiet as possible
B
The old man walked with a cane (拐杖) slowly into the restaurant. His poor jacket, patched (打补
丁的) trousers, and worn-out shoes made him stand out from the usual Saturday morning breakfast
crowd. Unforgettable were his pale blue eyes that sparkled like diamonds, large rosy cheeks, and thin lips that held a steady smile.
He walked toward a table by the window. A young waitress watched him and ran over to him, saying, “Here, Sir. Let me give you a hand with that chair.”
Without a word, he smiled and nodded a thank you. She pulled the chair away from the table. Supporting him with one arm, she helped him move in front of the chair, and get comfortably
襄阳36中高一上学期期中测试英语试卷 seated. Then she pushed the table up close to him, and leaned his cane against the table where he could reach it.
In a soft, clear voice he said, “Thank you, Miss.”
“You’re welcome, Sir.” She replied. “My name is Mary. I’ll be back in a moment. If you need anything, just wave at me.”
After he had finished a hearty meal of pancakes, bacon, and hot lemon tea, Mary brought him the change, helping him up from his chair and out from behind the table. She handed him his cane, and walked with him to the front door. Holding the door open for him, she said, “Come back and see us, Sir!”
He nodded a thank you and said softly with a smile, “You are very kind!”
When Mary went to clean his table, she was shocked. Under his plate she found a business card and a note written on the napkin, under which was a $ 100 bill.
The note on the napkin read, “Dear Mary, I respect you very much, and you respect yourself, too. It shows by the way you treat others. You have found the secret of happiness. Your kind gestures will shine through those who meet you.”
The man she had served was the owner of the restaurant. This was the first time that she, or any of his employees, had seen him in person. 55.Mary ran over to the old man because _____. A.the old man was the boss of the restaurant
B.she was worried that the old man might cause trouble to the restaurant C.she saw the old man had some difficulty moving and taking a seat D.the old man had asked her to wait on him 56.The man came to the restaurant ______. A.to have breakfast
B.to see his employees
C.to find out how his restaurant was working D.to see how Mary served customers 57.The words the man left on the napkin suggested that _____. A.respecting others means respecting oneself B.serving others is a respectable job
C.Mary would get a rise as a result of her kindness D.Mary’s kind service would bring in more money for her 58.Which of the following titles goes best with the story? A.A kind- hearted Girl
B.Shining Kindness C.Kindness Means Opportunities
D.A Special Customer
C
Many people tend to complain about not having good friends in their lives. Sadly, they seem to think that their own company is not enough to make them happy. Nothing could be further from the truth, though. In order to get along with others, the first thing you need to do is learn to get
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along with yourself. Only in this way will you succeed in developing healthy, solid relationships with others.
Listen to your inner voice. Remember that inner voice that keeps whispering to you what you listening to it. In order to get to know yourself in depth, it is important to learn and accept what you want and what you do not want.
Learn to enjoy your own company. You will be surprised to find out how many things you can do by yourself and actually have fun in the process. Reading romantic novels, poetry or science fiction is only a few of the things that you can do by yourself, which not only can offer you hours of enjoyment, but also the chance to get to know yourself better.
Satisfy yourself. Pay special attention to your personal hygiene(卫生). Do your hair and nails often and experiment with new styles. Follow a healthy diet and exercise regularly to stay in good shape. No matter how busy your daily schedule is, always find at least an hour per day for yourself, when you can either relax doing absolutely nothing, or doing something that you enjoy. Learn to respect your own boundaries(分界线). Find out what your boundaries are and learn to respect them. You are the only one who knows what you can and what you cannot accept. 59. If you want to have a good relationship with others, you should first ________. A. get into the habit of living alone
B. make many friends in society C. always tell the truth
D. learn to be your own best friend 60. What is the purpose of listening to your inner voice? A. To keep a good state of mind.
B. To know more about yourself. C. To enjoy the time by yourself.
D. To form a relationship with others.
61. In order to please yourself, the writer gives some suggestions EXCEPT ________.
A. eating healthily
B. exercising regularly C. experimenting with new hair style
D. keeping on struggling
62. What is the structure of the passage?
D
The weather is getting hotter. You are thirsty（口渴的） playing basketball or riding home from school. A cold drink may be just the thing. But be careful what you are drinking. Something that looks cool may not be good for your health. There are plenty of “energy drinks” on the market. Most of them have beautiful colors and cool names. The lists on them tell you they are helpful to your health. Sounds great!
But after a careful check you may find that most energy drinks have lots of caffeine(咖啡碱)in
襄阳36中高一上学期期中测试英语试卷 them. These drinks are especially aimed at young people, students, busy people and sports players. Makers sometimes say their drinks make you better at sports and can keep you awake. But be careful not to drink too much. Caffeine makes your heart beat fast. Because of this, the International Olympic Committee(IOC)（国际奥委会） has limited its use. Caffeine in most energy drinks is at least as strong as that in a cup of coffee or tea. Possible health dangers have something to do with energy drinks. Just one box of energy drink can make you nervous, have difficulty sleeping and can even cause heart problems. Scientists say that teenagers should be discouraged from taking drinks with a lot of caffeine in them. 63.Which of the following can be the best title of the passage? ______
A. What’s the Use of Energy Drinks? B. Who Can Drink Energy Drinks? C. What’s that in Energy Drinks? D. Why Can’t We Buy Energy Drinks? 64.The underlined word “discouraged” can be replaced(替换) with ______. A. disliked B. helped
C. stopped D. encouraged
65.From the passage we can know that ______. A. energy drinks are especially aimed at teenagers B. energy drinks are helpful to teenagers’ study C. sports players need to drink a lot of energy drinks
D. advertisements are important in getting people to buy energy drinks
66.Many people like drinking energy drinks because of the following EXCEPT that ______. A.they have beautiful colors and cool names B.they have lots of caffeine
C.they can keep them awake and better at sports D. they are said to be helpful to health
E
Several years ago, I worked as a truck driver for a company. On Saturdays I usually spent several hours doing something to keep my truck in good condition.
One Saturday, as I was cleaning my truck, I noticed the boss’s elderly father came out to ask his grandson to take him fishing after work. The grandson told him all about how much he would love to do that, but he just couldn’t because he had other plans already. The old man hobbled (蹒跚) off to the house.
Then I heard the grandson telling his dad, "I’m not taking that old man fishing! It’s worse than
taking a kid."
That just broke my heart.
I quit working immediately and went home to fetch my fishing gear (渔具) and a chair. Then I came back and invited the old man to go fishing. He accepted happily.
When we got to the river, I let him sit in the chair at the edge of the water. It wasn’t long before he got a fish. He got one fish after another. His eyes were shining like a child. About half an hour later, he told me he was tired and needed to go home. So I took him and the fish home. Two weeks later, the old man died. His family told me later that all he talked about during that time was his fishing trip. I am satisfied that I have taken an old man on his last fishing trip, but I
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am sorry that his family have lost their last chance. Whenever you get the chance, don’t forget about taking Grandpa fishing. Someday, you may be in the same place and you’ll want your family to care about you, too.
67. The writer wrote the passage mainly to ________.
A. tell us something about his work B. tell us about a fishing experience C. persuade us to take Grandpa fishing D. persuade us to care about the elderly 68. The old man’s Grandson refused to fish with him because ______.
A. he had something more important to do that day B. he didn’t like to fish with an old man C. he was tired of his job and he wanted to rest D. he preferred fishing with a child 69. What’s the possible meaning of the underlined word "quit"?
A. start B. stop C. imagine D. try 70. According to the passage, we can infer（推断） that the author is _______.
A. willing to make his boss happy B. in need of care from his family C. prefers fishing to his work D. kind and warm-hearted
第II卷（非选择题）
第一节 完成句子（20分）
, which made the teacher angry. (late) 这是他这个星期第三次迟到了，这让老师很生气。 made him so upset? (it) 到底是什么让他如此不安？
73. Don’t believe him; he ____________________. (change) 不要相信他。他总是改变主意。
74. It is commanded that all the stolen items ________________before the show is on. (recover) 据命令，所有被偷的物品都要在展览前找回来。
75. ___________________ his accent, he comes from a small town in northern England. (judge) 从他的口音判断，他来自英国北部的一个小镇。
76. Once __________________ reading a book, he will forget everything around him. (bury) 一旦专注于读书，他就会忘了周围的一切。
77. With ____________________, the party went like clockwork. (organize) 每件事都组织好了，这台晚会进展很顺利。
我考试又失败了，我本该努力学习。
襄阳36中高一上学期期中测试英语试卷 79. before he came. (it) 不久后他来了。
那段时间人们遭受了沉重的损失。 第二节 书面表达（30 分）
请根据以下提示，并结合事例，用英语写一篇短文。
The promise is such an important thing that all of us should keep it. You should think about your promise before you make it.
注意：①无需写标题，不得照抄英语提示语；
②除诗歌外，文体不限；
③内容必须结合自己生活或学习中的一个事例； ④词数不少于120。
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五年级数学上册复习资料
一、倍数与因数
1、自然数与整数
正整数：像1、2、3
自然数
负整数：像-1、-2、-3、-4…
2、倍数与因数
倍数和因数是相互依存的，不能单独地说谁是倍数，谁是因数，只能说谁是谁
的倍数，谁是谁的因数。
如：4×5=20（或20÷4=5）
4和5是20的因数，20是4和5的倍数。但不能说4和5是因数，20是倍数。
3、找倍数
找一个数倍数的方法：就是用这个数乘1、乘2、乘3……依次去找。
一个数倍数的个数是无限的，一个数没有最大的倍数，最小的倍数是它本身。
4、 2、3、5倍数的特征
个位是0、2、4、6、8的数是2的倍数；个位是0、5的数是5的倍数；
各个数位上数字之和是3的倍数，这个数就是3的倍数；同时是2、5的倍数的
数个位一定是0；各个数位上数字之和是9的倍数，这个数就是9的倍数。
5、奇数和偶数
一个自然数按是不是2的倍数可分为奇数和偶数。
是2的倍数的就是偶数；不是2的倍数的就是奇数。
6、质数与合数
一个自然数（除0外）按因数的个数可分为质数、1、合数。
1只有一个因数；只有1和它本身两个因数的数叫质数；有三个或三个以上因数
的数叫合数。
7、找因数
（1）找一个合数的因数的方法：把一个合数分解成两个自然数的积，可按乘法
口诀从1开始一一成对找；还可以把这个合数依次除以自然数1、2、3、……所
得商如果也是自然数，那么这个商和除数都是合数的因数。
（2）一个数的因数的个数是有限的，最小的因数是1，最大的因数是它本身。
特别注意：一个数的最小倍数和最大因数都是它本身。一个数的倍数都是大于
它的因数。（╳）
（3）找因数的应用：
把50个苹果分成堆，每堆苹果的个数相同，有几种分法？运用列表法。
8、数的奇偶性
同性相加减结果是偶数；异性相加减结果是奇数。
用数的奇偶性解决生活中问题时要注意：（1）开始的状态。（2）变化奇数次和
偶数次的规律。
教室里的灯是亮着的，突然停电，小明连续按了10下开关，那么来电时灯是（ ）
的。灯开始是亮的，按奇数次开关，灯是关的；按偶数次开关，灯是亮的。所
以按10下开关，来电时灯应是亮。
二、分数
1、分数的认识
把整体1平均分成若干份，表示这样的一份或几份的数，叫做分数。
1一本书已看了 ，刚好看了20页，这本书有（ ）页。 4
1 表示整体1一本书平均分成4份，已看了这样的1份。已看了20页即1份4
是20页，那么这本书是4份，也就是80页。）
同一个分数对应的整体1不同，所表示的具体数量也不同。只有整体1和其对
应的分率都相同，所表示的具体数量才相同，否则不会相同。
111①甲的和乙的一定相同吗？（甲和乙不一定相同，那么他们的也不一定444
相同。）
1111②甲的 和乙的一定不同吗？（甲和乙不知道，甲的和乙的不一定不同。） 5454
111③如果甲的和乙的 相同，那么甲和乙哪个大？（甲的 是表示把甲平均分454
1成4份，取这样的1份，乙的 是表示把乙平均分成5份，取这样的1份。要5
使甲的1份和乙的1份相等，那么甲一定小于乙。）
2、真分数和假分数
分子比分母小的分数叫真分数，真分数小于1；
分子比分母大或分子和分母相等的分数叫假分数。假分数大于或等于1。带分数
是假分数的另一种表现形式，带分数大于1。
ab（1）把整数化成指定分母的假分数： ；（2）把假分数化成带分数或整数：a
用假分数的分子除以分母，所得的整数商作为带分数的整数部分，余数作为带
ad分数的分数部分的分子，分母不变。 =a÷b=c……d=c；（3）带分数化成假bb
cab+c分数，用整数乘分母加分子作为假分数的分子，分母不变，a =。 bb
a3、分数与除法：a÷b= b
分数的分子相当于除法中被除数，分数线相当于除号，分母相当于除数。
（1）把3米长绳子平均分成7段，每段是（ ）米，每段是全长的（ ）。 （ ）
每份的数量=总数量÷平均分的份数；每份的分数=整体1÷平均分的份数。
3（）1即每段长=3÷7=米，每段是全长的÷7= 。 7（）7
（2）小明30分钟走了2千米路。
1①每分钟走了（）千米（求每分钟走的千米就用总路程÷时间，即2÷ 千15
米）；
②走1千米需（）分钟（求每千米需要的时间就用总时间÷路程，即30÷2=15
分钟）。
（3）求一个数是另一个数的几分之几，用一个数÷另个数。
（ ）（ ）一种盐水中盐10克，水100克。盐是水的 ，盐是盐水的 ，（ ）（ ）
水是盐水的（ ）。 （ ）
盐÷水
=10÷100 （用除法）
10=（写成分数） 100
=1 （化成最简分数） 10
4、分数的基本性质
分数的分子和分母都乘或除以相同的数（0除外），分数的大小不变。【襄阳教育网官网36分数线】
分数的分母（分子）扩大或缩小几倍，要使分数的大小不变，分子（分母）也
应该扩大或缩小相同的倍数。39（） = =（）÷25 5 （） 20
5、找最大公因数
方法：（1）列表法
先找几个数的因数，再找几个数的公因数，最后找几个数的最大公因数。
（2）图示法 A的因数B的因数A、B的最大公因数是
6、找最小公倍数
（
1）列表法
（2）图示法
A、B的最小公倍数是
（3） 用短除法
求两个数的最大公因数和最小公倍数， 连续用这两个数的公因数去除，
除到最后的商只有公因数1为止。两个数最大公因数是所有除数的积，两个数最小公倍数是所有除数的积×所有商的积 。
2 18 24
3 9 12
3 4
18、24的最大公因数=2×3=6；18、24的最小公倍数=2×3×3×4=72。
求两个数最大公因数和最小公倍数的特例：
（1）两个数如果较大数是较小数的倍数，那么它们的最小公倍数就是较大数，
它们的最大公因数就是较小数。
（2）两个数如果只有公因数1，那么它们的最小公倍数就是这两个数乘积，它
们的最大公因数就是1。
求三个数的最小公倍数。
（1）如果三个数中最大数是另外两个数的倍数，那么最大数就是这三个数的
最小公倍数。
如：3、5和15的最小公倍数。15同时是3和5的倍数，所以它们的最小公倍
数是15。
（2）如果三个数中每两个数都只有公因数1，那么这三个数的乘积就是它们的
最小公倍数。
如：求3、4和5的最小公倍数。我们发现3和4，4和5
3和5都只有公因数1，所以它们的最小公倍数就是3×4×5=60【襄阳教育网官网36分数线】
（3）找三个数最小公倍数，可以先找最大数的倍数，再看看这个最大数的倍
数是不是同时是另外两个数的倍数。
如：求9、15和30的最小公倍数。可先找30的倍数，30的1倍是30，30是
15的倍数但不是9的倍数；30的2倍是60，60是15的倍数但不是9的
倍数；30的3倍是90，90同时9和15的倍数。所以90就是它们的最小
公倍数。
7、最大公因数和最小公倍数的实际应用。
（1）把长30厘米，宽24厘米的长方形木板锯成大小相等的小正方形，每个小
正方形的边长最长是几厘米？能锯成多少块？
（分析：每个小正方形的边长既是长方形长的因数也宽的因数，即是长和宽的
公因数，每个小正方形的最长边长就是长和宽的最大公因数。因为30和24的
最大公因数是6，所以每个小正方形的最长边长是6厘米；能锯成（30×24）÷
（6×6）=20块。）
（2）、人民公园是1路、3路汽车的起点站。1路汽车每3分钟发车1次，3路
汽车每5分钟发车1次，这两路汽车同时发车以后，至少再经过多少分钟又同
时发车？
（分析：这两路车同时发车的时间既是3的倍数又是5的倍数，即是3和5的
公倍数，再次同时发车的最小时间是3和5的最小公倍数。因为3 和5的最小
公倍数是3×5=15，所以至少再经过15分钟又同时发车。）
（3）有一盒铅笔，平均分给4个小朋友余1支，平均分给5个小朋友也余下1
支，如果平均分给6个小朋友还余下1支。这盒铅笔至少有多少支？
（分析：把这盒铅笔平均分给4、5、6个小朋友都是余下1支，那么把这盒铅
笔的总数减1支，就刚好是4、5、6的公
倍数，这盒铅笔的最少支数就是4、5、6的最小公倍数。 A、B的公倍数
因为4、5、6的最小公倍数是60，所以这盒铅笔最少有 60+1=61支。）
8、约分
（1）先观察分数的分子、分母，找出它们的公因数，用分子、分母同时除以公因数，一次一次地约，一直约到最简分数为止。
（2）找出分子、分母的最大公因数，用分子、分母同时除以最大公因数，一次得到最简分数。
（3）如果分数的分子和分母具有倍数关系，就用分数的分子和分母同时除以分子和分母中较小的那个数，就能得到最简分数。
9、最简分数：分子和分母只有公因数1。
判断：分子和分母没有公因数的分数就是最简分数。（）分子和分母都是偶数的分数，一定不是最简分数。（） 分子和分母都是奇数的分数，一定是最简分数。（） 分子和分母都是质数的分数，一定是最简分数。（） 分子和分母都是合数的分数，一定不是最简分数。（）
10、分数的大小：同分母分数，分子越大，分数越大。同分子分数，分母越小，分数越大。
11通分
意义：把分母不相同的分数化成和原来分数相等，并且分母相同的分数，这个过程叫做通分。通分时要根据分数的基本性质运算。通分的一般方法：先求出原来几个分母的最小公倍数，也可用几个分母的公倍数，但一般用最小公倍数。然后把各分母分别化成用这个最小公倍数作公分母的分数。
12、做同一件事，时间用得少，速度就快。
4王师傅加工一个零件用36秒，李师傅加工同一个零件用 分，谁的速度快？ 7
化：36秒=36÷60=
43 < 75
三、分数的加减法
1、计算同分母分数加减法的方法：分母不变，分子相加减。
2、计算异分母分数加减法的方法：先通分，化成相同的分母，再按照同分母分数相加减的方法进行计算。
3、分数加减法对计算结果的要求：能约分的要约成最简分数。
4、分数加减法混合运算的顺序与整数加减法混合运算的顺序相同。
（1）只有加减法，按照从左往右的顺序进行计算。（2）有小括号的，先算小括号里面的。
5、在一个没有括号的算式中，分数连加、连减或加减混合，可一次通分。
6、分数加减法的简算：
（1）分数连加，同分母的，能凑整的可运用加法的交换律和结合律进行简算。
33523532 + +（）+ + ） 85858855
（2）分数连减，如果几个减数的和能凑整，可运用减法的性质进行简算。
35A-B-C=A-（B+C） 2- -88
（3）分数加减混合，交换运算顺序结果不变；注意连运算符号一起交换。 3633214202021分 比较： ∵ ∴6055357353535
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