# 双语数学概念（上）

2014-09-01

!exclamation 惊叹号 ?question mark 问号

￣ hyphen 连字符 'apostrophe 省略号;所有格符号

—dash 破折号 ‘ ’single quotation marks 单引号

“ ”double quotation marks 双引号 ...ellipsis 省略号

parentheses 圆括号 [ ]square brackets 方括号

《 》French quotes 法文引号;书名号 ¨ tandem colon 双点号

ditto 同上 ‖ parallel 双线号

/virgule 斜线号 & ampersand = and ～swung dash 代字号

§section; division 分节号 →arrow 箭号;参见号

plus sign 加号 minus sign 减号

+plus 加号;正号 -minus 减号;负号

±plus or minus 正负号 ×is multiplied by 乘号

÷is divided by 除号 =is equal to 等于号

≠is not equal to 不等于号 ≡is equivalent to 全等于号

≌is equal to or approximately equal to 等于或约等于号

≈is approximately equal to 约等于号

is more than 大于号

≮is not less than 不小于号 ≯is not more than 不大于号

≤is less than or equal to 小于或等于号 is more than or equal to 大于或等于号

等于 equals, is equal to, is equivalent to

大于 is greater than ;小于 is lesser than

大于等于 is equal or greater than ;小于等于 is equal or lesser than

运算符 operator

2+3=? 可表示为： How much is two plus three?

2+3=5

Two plus three is five. Two and three are equal to five.

Two and three make five. Two added to three equals five.

If we add two to/and three, we get five.

commutative property of addition加法交换率:changing the order of the addends does not change the sum..

associative property of addition: If a,b and c are real numbers ,then +c=a+.changing the manner of combining addends doesn’t change the sum.

3. “减”用 minus或 take from表示 minuend被减数,subtrahend减数 difference差

减 minus, subtract, subtraction

10-6=? How much is ten minus six?

10-6=4 Ten minus six is four.

Take six from ten and the remainder is four.

Six from ten is four.十减去六等于四

4. “乘”用time(动词)或multiply表示

乘 times, multiply, multiplication;被乘数 multiplicand, faciend ;因数factors,乘数 multiplicator; multiplier;积 product

3X4=? How much is three times four?

3X4=12 Three times four is twelve.

Multiply three by four，we get twelve.

Three multiplied by four makes twelve. 三乘以四等于十二

In a multiplication equation, these are the two numbers which are multiplied together.

Any number multiplied by 1 is itself.

To multiply a number by ten, simply add a zero at the end of the original number.

0和任何数相乘都得0。

Commutative property of multiplication乘法交换率:If a and b are real numbers, then a×b=b×a，changing the order of the factors does not change the product.

Is subtraction commutative ?

Is multiplication commutative ?

Is division commutative ?

associative property of multiplication结合率:If a,b and c are real numbers ,then a=c. changing the grouping of multiplying factors does not change the product.

distributive property of multiplication over addition 乘法对加法的分配率：If a,b and c are real numbers ,then a=ab+ac.

For every real number ”a”:a+0=a.0 is the identity element for addition.

For every real number “a”:a×1=a. 1 is the identity element for multiplication.

5. “除”用divide的过去分词形式表示

除 divided by, divide, division

可被整除的数 divisible;被整除divided evenly;被除数 dividend ;除数 divisor ;余数remainder;商 quotient

16÷4=? How much is sixteen divided by four?

16÷4=4 Sixteen divided by four is four.

Sixteen divided by four equals/gives/makes four.

6. 表示“n次方”的说法：指数用序数词，底数用基数词。

10的7次方 the seventh power of ten(ten to the seventh power)

6的10次方 the tenth power of six(six to the tenth power)

A zero factor always gives a zero product.

The product of two real numbers may be 0 only if one factor is 0.

Dividing by zero is not difined.a/0 and a÷0 are not defined.

Zero divided by any non-zero real number equals zero .

For the pair of numbers ,select the correct symbol fill in the blank.

One is less than one hundred.

Forty-four is greater than six.

Nine equals three times three.

7、The order of operations regarding addition, subtraction, multiplication etc运算顺序：

1) parentheses: do calculations within grouping symbols such as: []{}.

2) Multiplication Division from left to right. 3)Addition Subtraction from left to right.

记“Please Excuse My Dear Aunt Sally”(括号、指数、乘法、除法、加法、减法)

Hint: Remember “Please Excuse My Dear Aunt Sally”

Express the following, using mathematical phrases:用数学语言表达

1) Ten increased by the product of six and three

2) Eight decreased by the quotient of four and two.

3) The product of six and five decreased by the sum of eight and four.

8、explain how to round numbers.解释如何四舍五入

近似值approximation 估算estimation

To give an approximate value .即取一个近似值。

将一个整数四舍五入到所要求的位数值，若所要求位数右边的数字小于5，则将其约去，若大于或等于5，则进一位。When rounding a number to a given place value :if the digit to the right of the one given is less than or equal to five ,you round up.

Example: round 67 to the nearest ten’s place .”7”is greater than “5”,so round “67”up to “70”.

Round the number 5842 to the nearest hundred. The four in the ten’s place is less than five, so you round down to 5800.

进位 carry

截尾 truncation

四舍五入 round

下舍入 round down

上舍入 round up

有效数字 significant digit

无效数字 insignificant digit

9、验算How can you use multiplication to check the result of a division problem?example:41/9=

1) multiply the quotient by the divisor4x9=36

2)add the remainder to the product of item 1 above 36+5=41

二、整数

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1、数

数字 digit;零 null, zero, nought, nil

数 number ;整数 whole number ，integer

正 positive ;正数positive number;正整数positive whole number

负 negative (a number that is less than zero);负数negative number ;非负的nonnegative ;负整数negative whole number ;opposite numbers相反数;

real numbers实数 ;number line数轴; origin原点

Arithmetic算术 algebra代数 geometry几何 generated 旋转 average平均数

natural number自然数：The same as a counting number . It is a member of the set {0，1，2，3，4……｝

rational number有理数：A number that can be represented by a fraction. This includes all terminating and repeating decimals.

整数integer：Any positive or negative number or zero. A member of the set {…,-3,-2,-1,0，1，2，3，…｝.

整数whole numbers ：All the “natural numbers” plus zero.

irrational number无理数: A non-repeating (无限),non-terminating(不循环) decimal.

实数real number：Any rational or irrational number.

连续整数consecutive number

Counting or natural numbers(自然数):

The numbers you count with.:1,2,3,…

Even numbers; even integer,偶数: Whole numbers divisible by two .0,2,4,…

Odd numbers ;odd integer,奇数 : Whole numbers not divisible by two.

prime number质数：A number which has no factors other than itself or 1.

List all of the non-prime numbers between 15 and 30

prime number 质数：A number which has exactly two whole number factors ?one and itself.

prime factor质因数:A factor of a number which is also a prime number. 49 has factors of 1,7,49.

合数Composite number e.g. 4,6,8,9,10,12,14,15…

list the digits in our numbers system列出数字系统中的阿拉伯数字。There are ten:0,1,2,3,4,5,6,7,8,9。

Combinations of these are used to make up all numbers 这些阿拉伯数字构成了所有的数。

2、十进制decimal system

二进制 binary system

一位数1-digit number 两位数2-digit number

list place values for the following number:123456789列出下面这个数各位数字的位值。

Place values tell us by which power of 10 to multiply a digit位值的意思是，一个数的相邻两位之间相差10倍。

9—one’s place个位

8—ten’s place十位，8 is in the tens place

7—hundred’s place

6—thousand’s place

5—ten thousand’s place, 5 is in the ten thousands place

4—100thousand’s place

3—million’s place

2—10million’s place

1—100million’s place亿位

3、正负数

如何用正负数来表示相反的情况?

How are signed numbers used to represent opposing situations?

1) Opposites such as up and down or left and right can be represented by “+”and “-”.If up is represented by “+”, then down can be represented by “-”.

2) Even though the distance is represented as +25 and ?15 ,the total miles traveled is 40.

→

←(-15)

3) A deposit or increase is represented as +

4) Street level is considered zero .Traveling down one level would be expressed as ?1.

将下列正负数按从小到大顺序排列

Place these signed numbers in order from most negative to most positive .

On a number line the values of negative numbers decrease from the origin to the left . the values of positive numbers increase from the origin to the right.

absolute value绝对值：

The distance between a number and zero on a number line.

What is the symbol for absolute value?

The symbol │x│ means absolute value of the term x inside.

4、代数

expression表达式：A relationship represented with numbers and/or symbols.

equation等式：A sentence that uses the symbol “=” to stats that the result of the expressions on the left side is the same as the result of the expressions on the right side.

inequality不等于：Two numbers that are not equal to each other. One number may be greater than the other number or less than the other number.

Express as an equation列方程式

A number increased by six equals 63.What is the number?

三、 分数fraction

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3----分子numerator

——----分数线 fraction stroke or fraction line

4-----分母denominator

1. 分数是由基数词和序数词一起来表示的。基数词作分子，序数词作分母，除了分子是“1”以外，其它情况下序数词都要用复数形式。

3/4 three fourths或 three quarters

1/3 one third或a third

24/25 twenty-four twenty-fifths

3 1/4 three and one fourth或 three and one quarter

1/2 a half

1/4 one quarter或a quarter

1 1/2 one and a half

1 1/4 one and a quarter

2. 当分数后面接名词时，如果分数表示的值大于1，名词用复数;小于1，名词用单数。

1 1/2 hours 一个半小时(读作 one and a half hours)

2 3/4 meters 二又四分之三米(读作two and three-fourths meters)

4/5 meter 五分之四米

5/6 inch 六分之五英寸

真分数proper fraction ;假分数improper fraction ;

带分数mixed number :whole part整数部分;fraction part分数部分

simplify this mixed number 化简带分数

普通分数vulgar fraction，common fraction;简分数simple fraction

繁分数complex fraction

四分之一quarter

公分母common denominator

公约数common divisor

倍数multiple ;公倍数common multiple

因子 factor

公因子common factor

least common multiple 最小公倍数:the expression with fewest factors divisible by each number.

least common denominator最小公分母: the LCD of the denominators.

Find the least common denominator for these fractions 1/2,3/4.

Because 2 is a factor of 4 the least common denominator is 4.

Reciprocal倒数：When the product of two fractions is 1 then the fraction are reciprocals.

To find the reciprocal, exchange the numerator for the denominator.

Find the reciprocal of 4.

The reciprocal of a whole number is 1 over that number.

Find the reciprocal of 0: 0=0/1;reciprocal is 1/0;not defined无意义!The reciprocal of 0 is not defined because no 0’s are allowed in a fraction’s denominator.

For every real, non-zero number“a”: a and 1/a are reciprocals .

Rule for addition of fractions with the same denominator分母相同的分数加法法则： When adding two fractions with the same denominator add the numbers and put the result over the denominator.

What is the rule for subtraction of like fractions?两分母相同的分数减法法则

When subtracting fractions with the same denominator, subtract the numerators and put the result over the denominator.

如何运算分母相同分式的加、减法?What is the procedure for adding or subtracting fractions that have the same denominator?

1) The numerator of the result is the sum or difference of the numerators of the given fractions.

2) The denominator is the common denominator of the given fractions.

3) Reduce the result to the lowest terms.

如何运算分母不同的分式的加、减法?What is the procedure for adding or subtracting fractions that have different denominators?

1) Factor each denominator to find the lowest common denominator.

2) Make each fraction an equivalent ,so all fractions have the same LCD.

3) Perform the addition or subtraction.

4) Reduce to lowest terms.

异分母分数加法法则：

1) find the LCD for both fractions .

2)convert to like fractions.

3) add the numerators of like fractions

4)simplify when possible.

异分母分数减法法则：subtract unlike fractions 1/2-2/7

1) find the LCD for both fractions .

2)convert fractions to the same denominator .

3)subtract numerators.

multiplication rule for fractions分数的乘法法则：To multiply fractions you multiply the numerators together and then the denominators.

State the rules for multiplying fractions描述分子相乘的规则：

1) 积的分子是分子之积：The product’s numerator is the product of the numerators of the given fractions.

2) 积的分母是分母之积：The product’s denominator is the product of the denominators of the given fractions.

Division rule for fractions分数的除法法则：To divide fractions, change the divisor to its reciprocal and multiply.

The rule for dividing algebraic fractions分数除法的规则：除以分式，就是用除数的倒数乘被除数：To divide by an algebraic fraction, multiply the dividend by the reciprocal of the divisor.

四、 小数

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小数decimal 小数点decimal point

1、Identify the value of each digit in the following number :0.987654

9—9/10---tenths;

8—8/100—hundredths;

7—thousandths;

6---ten thousandths

5—hundred thousandths;

4—millionths;

3--ten millionths;

2---hundred millionths;

1--billionths

2. 小数用基数词来表示，以小数点为界，小数点左首的数字为一个单位，表示整数，数字合起来读;小数点右首的数字为一个单位，表示小数，数字分开来读;小数点读作 point，0读作 zero或o[ou]，整数部分为零时，可以省略不读。

0.4 zero point four或point four 零点四

10.23 ten point two three 十点二三

25.67 twenty-five point six seven 二十五点六七

l.03 one point o three 一点零三

当数字值大于1时，小数后面的名词用复数，数字值小于1时，小数后面的名词用单数。

1.03 meters 一点零三米

0.49 ton 零点四九吨

l.5 tons 一点五吨

小数 decimal ;小数点 decimal point ;纯小数decimal fraction ;无穷小数Infinite decimal

write the following in fractions form :0.004

write the following in fraction form :0.000009

round the decimal 4.0897 to the nearest hundredth.

Rename the following decimal as a fraction in simplest form :0.056

Rename the following decimal as an improper fraction in simplest form :1.2

Convert fraction to decimal :To convert a fraction t a decimal ,the denominator becomes the divisor and the numerator becomes the dividend .divide as usual .

Terminating decimal有限小数 :A decimal which ends at a given place.

1/3=0.3333…The “…”means that the pattern of “3”continues infinitely .the decimal is NOT-TERMINATING.表示循环节3无限地循环下去。该小数是无限小数。

Repeating decimal 循环小数:A decimal which repeats a series of numbers forever.无限重复的一组数字的小数

To subtract decimals, line up in vertical form, give each decimal the same number of places and subtract as usual.

Simple rules for multiplying decimals:小数乘法的简单法则

1) List in vertical form.

2) Multiply like whole numbers.

3) Put in decimal place by counting over from the right the total number of decimal spaces as in the factors.

To multiply a decimal by 1000, move the decimal point to the right three spaces ?the same number of zeros in 1000.

Rules for dividing decimals小数除法的法则

1) If the divisor is a decimal ,multiply the divisor and the dividend by the same power of 10 to make the divisor a whole number.若除数是个小数，它与被除数同时乘一个10的倍数，使两者都变为整数

2) divide like whole numbers.像整数一样相除

To divide by 100,move the decimal two spaces to the left, the same number of zeros in 100.

How do you find the AVERAGE of a group of numbers?

1) Add all the numbers together.

2) Divide the sum by the quantity of numbers you added together.

3、百分数Percent: A part of a whole or a part of 100.

The symbol is “%” and means “divided by 100”

Rewrite 50% as a fraction.

Rewrite the following as a percent :1/3

百分数用基数+percent表示

50% fifty percent 百分之五十; 3% three percent 百分之三

0.12% zero point one two percent 百分之零点一二

这里的percent前半部per表示“每一”，cent这一后半部分表示“百”，所以百分之几中percent不用复数形式。

amount = percent× number分量=百分比×总量

What is 10% of 30?

6 is what percent of 24?

2 is 60% of what number?

%per cent 百分之… ‰per mille 千分之…

Rate of interest 利率:The percentage rate on which your interest payment is based.

Time period存款期限:The amount of time your money must remain in the account to earn the specified interest.

Simple interest利息:Interest that is paid to you based on your principal(本金) only .

百分数应用题：Percent problem

Use the formula p=rb

p= the percentage (百分数)

r= the rate

b= the base amount