Section outline

  • How many equivalent fractions are there on this number line?
    ::这个数字线上有多少等效分数?

    You can create by multiplying the numerator and denominator of a fraction by the same number. You can simplify a fraction by dividing the numerator and denominator by the same number. 
    ::您可以将一个分数的分子和分母乘以同一数字来创建。您可以通过将分子和分母除以相同数字来简化一个分数。

    Use the interactive below to see how some fractions can be equivalent to whole numbers . Later in this lesson, you will see how different fractions can actually be equivalent to each other. 
    ::使用下面的交互效果来查看某些分数如何与整数等同。 在此课后, 您将看到不同的分数实际上可以相互等等。

     

    INTERACTIVE
    Equivalent Fractions: Number Line
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    Joel's teacher has given the class a box of fractions. He asks them to arrange them on a number line.
    ::乔尔的老师给了班级一箱分数,他要求他们按数字线排列。

    • Arrange the fractions on the number line according to their value.
      ::根据其值排列数字行的分数 。
    • Move each fraction using the red point below it.
      ::使用下面的红点移动每个分数 。
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    1.

    The interactive shows that @$\begin{align*}\tfrac{6}{2}\end{align*}@$ is equivalent to @$\begin{align*}3.\end{align*}@$  This is because @$\begin{align*}2\end{align*}@$  goes into @$\begin{align*}6\end{align*}@$  three times. You can also think of it as @$\begin{align*}6\end{align*}@$  divided by @$\begin{align*}2\end{align*}@$  is equal to @$\begin{align*}3.\end{align*}@$  
    ::互动显示 @ $\ begin{ align} tfrac{ 6\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\@\@\@\@\@\\@\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

     

    Choose other fractions that are equivalent to @$\begin{align*}3.\end{align*}@$  
    ::选择等效于 @ $\ begin{ align\\\ 3.\ end{ align\ $ 的其他分数@ $\ begin{ align\\ 3.\ end{ align\ $ @ label

    Select all that apply
    a

    @$\begin{align*}\frac{16}{4}\end{align*}@$
    ::@ $\ begin{ align}\ frac{ 16}\\\\\ 4}\ end{ 调整} $

    b

    @$\begin{align*}\frac{30}{10}\end{align*}@$
    ::@ $\ begin{ align}\ frac{ 30\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ end{ 调整\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

    c

    @$\begin{align*}\frac{21}{7}\end{align*}@$
    ::@ $\ begin{ align}\ frac{ 21\\\\\\\\\\\\\\\\\\\\\\\\\end{ 调整\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

    d

    @$\begin{align*}\frac{36}{12}\end{align*}@$
    ::@ $\ begin{ align}\\ frac{ 36\\\\\\\\\\\\\\\\\\\\\\end{ 调整} $

     

     

    How many manicures can you give?
    ::你能给多少指甲修指甲?

    lesson content

    Anna wants to start a business offering manicures for her friends.  To make sure she charges enough per manicure to earn a profit, she wants to know how many mL of nail polish are in a bottle and how many mL of nail polish per coat of paint.
    ::Anna想为朋友提供修指甲。为了保证她每次修甲都要花足够的钱赚钱,她想知道瓶子里有多少指甲油的毫升,每件涂料有多少指甲油的毫升。

    In this interactive, find how many manicures Anna can make by dividing the whole number amount of polish she has in her bottles with how much polish is used for each manicure.
    ::在互动中, 找出安娜能做多少指甲, 将瓶子里的整批抛光量 与每张指甲用多少油分开。

     

    INTERACTIVE
    Nail Polish
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    • Anna's nail polish bottles hold 15 mL each.
      ::安娜的指甲油瓶每瓶15毫升。
    • Drag the brush over the nails to color them.
      ::拖着指甲上的刷子来涂色
    • Coloring all ten will show how much polish she used for both hand.
      ::全部十色的颜色将显示她对两只手使用的抛光量 。
    • Answer the questions (answer with fractions).
      ::回答问题(分数回答)。
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    CK-12 PLIX Interactive
    ::CK-12 PLIX 交互式互动

    Use the interactive to divide a mixed number by a whole number in a series of step-by-step questions.
    ::在一系列分步骤问题中,使用交互方式将混合数字除以整数。

     

     

     

    How long does each singer sing?
    ::每个歌手唱多久?

    lesson content

     

    Create a short  tune that lasts  3 3 5  seconds in the interactive below.  Each singer sings for an equal amount of time.  
    ::创建一个短曲, 在下面的互动中持续335秒。 每个歌手在相同时间里唱歌 。

    In the following interactive, pick the number of singers and figure out how long each sings for. Divide the number of seconds by how many singers you have to find out the length of each part.
    ::在接下来的互动中, 请选择歌手的数量, 并找出每个歌唱的时间长度 。 除秒数之外, 您需要找到多少个歌手才能知道每个部分的长度 。

     

    INTERACTIVE
    Making Music
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    • Use the dropdown menu to pick how many singers you want to have in your melody.
      ::使用下拉菜单来选择 您的旋律中要有多少歌手 。
    • Drag the boxes up and down to pick which notes they sing.
      ::将盒子上下拖动以拾取他们唱的音符。
    • Press the "Play" button to hear your song.
      ::按下“播放”按钮来听到你的歌声。
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    How does shutter speed work on a camera?
    ::百叶窗的速度如何对摄像头起作用?

    lesson content

    Professional photographers use a setting on their cameras called shutter speed.  The shutter speed is the fraction of a second that  a digital camera spends taking a photo.  Different types of photos turn out best using different lengths of shutter speed.  If something is moving  quickly,   then shutter speed fraction has to be very small to make  sure that photo does not turn out blurry .
    ::专业摄影师在相机上设置了一个名为“百叶窗速度”的摄像头。 百叶窗速度是数码相机拍摄照片所花时间的一秒钟的分数。 不同种类的照片使用不同长度的百叶窗速度来显示最佳效果。 如果有东西在快速移动, 那么百叶窗速度分数必须非常小才能确保照片不会变得模糊。

    Use the interactive to take two different photos and set the shutter speed for each. In the questions that follow, you will calculate how much faster one setting is compared to another by dividing the fractions that represent those settings.
    ::使用交互效果来拍摄两张不同的照片, 并设定每张的百叶窗速度 。 在接下来的问题中, 您将计算一个设置与另一个设置的比对速度, 以分隔代表这些设置的分数 。

     

    INTERACTIVE
    Shutter Speeds
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    • Click the boxes to choose two photos.
      ::单击框选择两张照片。
    • Once you have your photos, choose different shutter speeds.
      ::一旦你有了照片, 选择不同的百叶窗速度。
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      Summary
    • When dividing a number by a fraction, flip the second fraction and multiply.  For example:  2 ÷ 1 3 → 2 × 3  
      ::当将数字除以分数时, 翻转第二个分数和乘数。 例如 : 2\\ 13\ 2x3