章节大纲

  • Marbled Ratios
    ::混合比率

    Lindsey is crazy about organizing her marbles. She has 3 red, 6 blue, and 5 green marbles. Drag the marbles into the white boxes to help to answer the questions below the interactive.
    ::Lindsey疯狂于整理弹珠。 她有3个红色、6个蓝色和5个绿色弹珠。 将弹珠拖入白箱, 帮助回答互动下的问题 。

     

    INTERACTIVE
    Lindsey's Marbles
    minimize icon

    Lindsey is organizing her marbles.  She has 3 red, 6 blue, and 5 green marbles. 
    ::Lindsey正在整理弹珠 她有3颗红色 6颗蓝色 5颗绿色弹珠

    • Move the colored marbles onto the boxes to find different ratios between them.
      ::将彩色弹珠移到框中,以发现它们之间的比例不同。
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    Progress
    0 / 5
    1.

    Drag the red marbles into the top box (above the fraction bar) and the blue marbles into the bottom box (below the fraction bar).
    ::将红色大理石块拖到顶部框(在分数栏上方),将蓝色大理石块拖到底部框(在分数栏下方)。

    What is the ratio of red to blue marbles? Can the fraction representing the ratio be reduced?
    ::红色和蓝色弹珠的比例是多少?代表比例的分数能否降低?

    a

    The ratio is @$\begin{align*}\tfrac{3}{6}\end{align*}@$ and reduces to @$\begin{align*}\tfrac{1}{2}.\end{align*}@$
    ::比例为 @ $\ begin{ align} tfrac{ 3\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\Al\\\\\\\\Al\\\\\\\\\\\\\\\\\\

    b

    The ratio is @$\begin{align*}\tfrac{3}{6}\end{align*}@$ and reduces to @$\begin{align*}2.\end{align*}@$
    ::比例是 @ $\ begin{ align} tfrac{ 3\\\\\\\\\\\\\\\\\\\\\\\end{ end{ ALign\\\\$, 降为 @ $\\ begin{ aliign}\\\\\\\\\end{ leign\\\\\\\\\\\\\$

    c

    The ratio is @$\begin{align*}\tfrac{6}{3}\end{align*}@$ and cannot be reduced.
    ::比例是 @$\ begin{ align} tfrac{ 6} @\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ end{align\\\\\\$, 无法降低 。

    d

    The ratio is @$\begin{align*}\tfrac{3}{6}\end{align*}@$ and cannot be reduced.
    ::比例是 @$\ begin{ align} tfrac{ 3}\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ end{align\\\\\$, 不能降低 。

     

    From the marbles interactive, you know that order matters for any ratio. In the next interactive, you will explore what happens when the ratio has two different units of measurement.
    ::从弹珠互动中,您知道任何比例的顺序都很重要。在下一次互动中,您将探索当比例有两个不同的测量单位时会发生什么。

     

    Buying Oranges  
    ::购买橙子

    Carlos is at the grocery store shopping for oranges. He buys 4 pounds of oranges for $3.20. When he returns home, he realizes that he actually needed to buy 9 pounds of oranges, so he plans to return to the store to buy more oranges so that in total he has 9 pounds.
    ::Carlos在杂货店买橘子,他买了4磅橙子,价格是3.20美元。当他回家时,他意识到他实际上需要买9磅橙子,所以他计划回到商店买更多的橙子,这样他总共就有9磅。

     

    INTERACTIVE
    Exploring Unit Rates
    minimize icon
    • Move the red point to change the cost of 4 pounds of oranges.
      ::移动红点以改变4磅橙子的成本。
    • Click on the grey points to change how many pounds Carlos buys.
      ::点击灰色点以改变Carlos买多少英镑。
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    A rate is a ratio where one unit is compared to another. In the orange problem above, the rate was cost per pound, also written $ / lb (the "/" means per, like division). Use the next  activity  to determine which units are also written as .
    ::A 是一个单位与另一个单位比较的比率。在以上橙色问题中,该比率是每磅的成本,也写为 $ / lb (“/”指每个单位,如分区)。使用下一项活动来确定哪些单位也写为 。

     

    State the Rates
    ::州 州 利率

    Which blocks contain rates?
    ::哪些区块含有速率?

    Drag only the rates into the white area, then answer the questions below the interactive.
    ::只将速率拖到白色区域,然后回答交互式区域下面的问题。

     

    INTERACTIVE
    Choose the Rates
    minimize icon
    • Move only the rates into the box on the right.
      ::只将利率移动到右边的框中。
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    A unit rate takes any rate and makes it so that the denominator is one.
    ::单位率以任何速率计算,使分母为一。

    Discussion Question
    ::讨论问题

    Describe  other situations that use different types of rates?
    ::描述使用不同类型汇率的其他情况?

    for examples!
    ::举个例子!

    Driving for Miles and Miles
    ::为迈尔斯和迈尔斯开车

    If a car travels 300 miles in 5 hours, how far does it travel in 1 hour? How far does a car travel in 1 hour if it ravels 350 miles in 5 hours?
    ::如果一辆汽车在5小时内行驶300英里,1小时内行驶多远?如果一辆汽车在5小时内行驶350英里,在1小时内行驶多远?如果一辆汽车在5小时内行驶350英里,行驶多远?

    Drag the car back and forth to determine how many miles the car drives in one hour.  When looking at the point value for the car, the x − value is the hours, and the y − value is the miles.
    ::拖动汽车前后以确定汽车驱动器在1小时内的英里数。 当查看汽车的点值时, x - 值是小时数, Y - 值是英里数 。

     

    INTERACTIVE
    Car Speed
    minimize icon
    • Move the red point to change the rate of speed for the car.

      ::移动红色点以改变车速速度 。
    • Tap the points to see the coordinates.
      • The x − value is the hours and the y − value is the miles.
        ::x - 值是小时,y - 值是英里。
      • (Numbers are rounded to the nearest hundredth.)
        :伤心数字四舍五入到最接近的第一百位。 )

      ::x - 值是小时, y - 值是英里。 (数字四舍五入到最接近的百分百。 )


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    Discussion Question
    ::讨论问题

    Why is 50 miles per hour a unit rate, and 150 miles per 3 hours is not?
    ::为什么每小时50英里的单位费率是每小时50英里,每3小时150英里不是?

       Summary
    ::摘要

    • A rate is a ratio that compares two units.
      ::A比率是两个单位比较的比率。
    • A unit rate is a rate per 1.
      ::A单位费率为每1个单位的费率。
    • To find the unit rate, multiply or divide the rate to get a rate per 1.
      ::要找到单位率,乘或除以单位率,以获得每1的费率。