章节大纲

  • 常规

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  • 合并对面数字

    Number Types
    ::数量类型

    By now,  you  probably  know what fractions and whole numbers are. The set of  Whole Numbers   includes all positive numbers and zero, without fractions or decimals.
    ::现在,你可能知道什么是分数和整数。全数包括所有正数和零,没有分数或小数。

    The set of Whole N umbers includes the Natural Numbers and zero . T he set of Natural Numbers   is sometimes referred to as the set of counting numbers, because they are all the numbers you would use to count whole things (fingers, dogs, rocks, trees, and so on).
    ::完整数字集包括自然数字和零。自然数字集有时被称为数数组,因为它们是用于计算整个事物的所有数字(鱼、狗、石头、树等等)。

    Another  group of numbers is  the   Integers . The Integers are all the Whole Numbers  and their negatives . Again, no decimals or fractions, just {...-4, -3, -2, -1, 0, 1, 2, 3, 4, ...}. Whole numbers are known as a subset of integers (they are within the set of Integers).  
    ::另一个数字组是整数组。整数组是整数组及其负数组。同样,没有小数组或小数组,只有 {...-4,3,2,2,1,0,1,2,3,4,......}。整数组被称为整数组(在整数组之内)。

    The last set of numbers this book will address are rational numbers. A rational number is any number that can be written as a fraction . This includes terminating decimals (decimals that end, like 0.5) and repeating decimals (decimals that repeat in a pattern , 0.5858585858..., also written 0. 58 ¯ ). All whole numbers and integers can also be written as fractions.  For example,  − 16 4 = − 4.
    ::这本书将处理的最后一组数字是理性数字。 理性数字是可以作为一个分数写入的任何数字。 这包括终止小数( 结束的十进制, 如0. 5) 和重复小数( 在模式中重复的十进制, 0. 58585858..., 也写为 0. 5858 .) 。 所有的整数和整数也可以作为分数写入 。 例如, - 164\\ 4 。

     

    Place the Number
    ::移动数字

    Below is a mapping of the rational numbers.
    ::下面是合理数字的图示。

    Drag the the numbers to their correct subset. Be as specific as possible.
    ::将数字拖到正确的子集。尽可能具体。

    O pposite numbers are the same number with opposite signs. All opposite numbers are called additive inverses . All additive inverses have a sum of zero, as you discovered in the interactive. If you were to place the number 'a' and it's opposite, '-a', on a number line, you would see they are the same distance away from zero.
    ::对面数字是相同的数字,有相反的符号。所有相反的数字都称为添加反函数。所有添加反函数都有零之和,正如您在互动中发现的那样。如果您在数字行中将数字“a”放在数字上,而数字线上的数字是相反的,“-a”就会看到它们与零的距离相同。

    Number line showing that 3 and -3 are opposites, both 3 units from zero.
    Opposites on a number line

    Both 3 and -3 are 3 units away from zero, making them additive inverses and opposites. The distance away from zero is also called the absolute value of a number.  Absolute value is always positive because distance is always positive. Absolute value is marked with  vertical lines on either side of the number.
    ::3 和 - 3 均为距离零的3 个单位, 使得它们相互反向和反向。 离零的距离也称为数字的绝对值。 绝对值总是正值, 因为距离总是正值。 绝对值在数字的两侧都标有垂直线 。

    | − 12 | = 12 | 4.5 | = 4.5

    Fence Painting
    ::栅栏绘画

    Peter is painting his wooden fence white. T reat the flower as location zero. Any pickets on the right represent a positive number or movement in the positive direction. Any pickets on the left of the flower represent a negative number or movement in the negative direction. Drag the red dot back and forth to paint the fence.  
    ::Peter将木制栅栏涂成白色。 将花朵当作零位置。 右侧的任何纠察点代表一个正数或正方向的移动。 花叶左侧的任何纠察点代表一个负数或负方向的移动。 将红点前后拖来拉去画栅栏 。

    Dance Moves
    ::舞蹈动作

    Juan really wants to impress the girls at the next school dance , so he decides to take dance lessons. He notices that dancing is just a series of steps; move two steps forward, two steps back, one to the left, one to the right, etc. At the school dance, Juan creates his own series of moves . Here is a list of the steps:
    ::Juan想在下一次学校舞蹈中给女孩留下深刻的印象,所以他决定去上舞蹈课。他注意到舞蹈只是一系列步骤;向后走两步,向后走两步,向左走一步,向右走一步,等等。在学校舞蹈中,Juan创造了自己的一系列步骤。下面列出一系列步骤:

    • 3 steps to the left
      ::左向左3 步
    • 2 steps to the right
      ::向右两步
    • 4 steps to the left
      ::左向左4 步
    • 3 steps to the right
      ::向右3个步骤

    T hen he repeats. If his starting position is zero on the number line, where does he end up after one cycle? Use the number line and Juan's feet to help you towards your answer. 
    ::然后他重复。如果他的起点在数字线上是零,那么他在一个周期后会到哪里去?使用数字线和胡安的脚来帮助你找到答案。

    Discussion Question
    ::讨论问题

    Discuss other types of situations that you could use a number line to help you with.  
    ::讨论其它类型您可以使用数字线来帮助您处理的情况 。

    for other examples of number lines!
    ::数字线的其他例子!

       Summary
    ::摘要

    • Whole numbers are positive numbers without fractional or decimal parts, including zero.
      ::整数是正数,不含分数或小数部分,包括零。
    • Integers are whole numbers that are positive and negative. Whole numbers are a part of the set of integers.
      ::整数是正数和负数的整数。整数是整数组的一部分。
    • Rational numbers are all numbers that can be written as a fraction, including whole numbers, integers, fractions, terminating decimals, and repeating decimals.
      ::理性数字是指可以作为一个分数书写的所有数字,包括整数、整数、分数、终止小数和重复小数。
    • The absolute value of a number is its distance from zero on the number line. Distance is always positive, therefore, so is the absolute value.
      ::数字的绝对值是数字线上与零的距离。 距离总是正数, 因此绝对值也是正数 。
    • Two numbers are opposites of each other, or additive inverses, if  their sum is zero.
      ::两个数字是相反的,或者如果其总和为零,则两个数字是相互对立的,或者加法反差。