章节大纲

  • How do you show fraction division with a rectangle?
    ::您如何用矩形显示分数分隔 ?

    Use the rectangle in the interactive below to model division with fractions. Consider how the resulting small blue square represents dividing the large blue square twice. Throughout this section you will use the areas and lengths of to find the widths.
    ::使用下面互动的矩形来用分数来模拟分数。 想想由此产生的小蓝色方块是如何将大蓝色方块分割两次的。 在本节中, 您将使用区域和长度来查找宽度 。

     

    INTERACTIVE
    Division of Fractions by Whole Numbers
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    • Move the red points to visualize a fraction of the square and to divide that fraction. 
      ::将红点移动到正方块的一小部分, 并分隔该部分 。
    • Move the blue point into the blue circle to see the mathematical expression.
      ::将蓝点移动到蓝圆,以看到数学表达式。
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    1.

    How many squares will there be, given the statement, @$\begin{align*}\frac{1}{7} ÷ 6\end{align*}@$  ?
    ::@$\ begin{align}frac}1\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

     

     

     

    How long is the dog park?
    ::狗公园还有多久?

    A golden retriever adult dog playing with a puppy
    Dogs playing

     

    A neighborhood put in a new rectangular, dog park. Shira sees a sign that says the length of the park is 3 4 mi  and the area of the park is  1 2 mi 2 . In this interactive, you are given the area and the length of the park. Using the division of fractions, how can you find the width of the park?
    ::位于一个新的长方形的狗公园。 Shira看到一个标志,上面写着公园的长度是34米,公园的面积是12米2。在这个互动中,您得到了公园的面积和长度。使用分数的划分,您如何找到公园的宽度?

     

    INTERACTIVE
    Dog Park Dimensions
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    • Firstly, drag the numbers into the boxes to set up the division problem. A button to continue will appear once correct.
      ::首先, 将数字拖放到框中以设置分裂问题。 要继续的按钮一旦正确将出现 。
    • Secondly, click on the numbers and operation to set up multiplying by the reciprocal. Another button to continue will appear once correct.
      ::其次,点击数字和操作来设置乘以对等的乘数。 继续的另一个按钮将出现一次正确 。
    • Finally, enter the simplified product into the boxes to find the width of the park.
      ::最后,将简化产品输入箱中,以找到公园宽度。
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    How tall is the fish tank?
    ::鱼缸有多高?

    lesson content
    Fish in a fishtank

    Allison looks at a big tank at the aquarium. She measures the  base of the tank   and finds that it is   3 5 m .   Allison  reads a sign that says the front of the tank has an area of  4 5 m 2 .  The height of the tank is taller than her meter stick so she decides to calculate it .
    ::Allison看水族馆的大型水箱。 她测量了水箱的底部,发现是35米。 Allison读到一个标志,上面写着坦克前部有45米的面积。 2 水箱的高度比她的表棍高,所以她决定计算。

    In the next interactive, find the quotient of fractions to determine the height of the aquarium.
    ::在下一次互动中,找到分数的商数,以确定水族馆的高度。

     

    INTERACTIVE
    Fish Tank Dimensions
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    • Drag the fish tank width and front area  fractions into the boxes to set up the division problem. A button to continue will appear once correct.

      ::将鱼缸宽度和前方区域分数拖到框中以设置分裂问题。要继续的按钮一旦正确将显示 。
    • Click on the numbers and operation to set up multiplying by the reciprocal. Another button to continue will appear once correct.
      ::点击数字和操作来设置乘以对等的乘数。 要继续的另一个按钮将出现一次正确 。
    • Enter the product of the fractions as a simplified improper fraction into the boxes.
      ::将分数的产物作为简化的不当分数输入框中。
    • Enter the equivalent mixed fraction into the boxes to find the height of the tank.
      ::在盒中输入相等的混合分数,以找到罐体的高度。
    • Use the check button to check your answers.
      ::使用复选按钮检查您的答案 。
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    Will the cardboard fit on the slide?
    ::纸板在幻灯片上合适吗?

    A slide made of concrete so you can ride downhill on a piece of cardboard.

     

    Grayson and his friends like to sit on cardboard while riding down the slide at the park to increase his speed.  His mother calls to say she has  a piece of cardboard that is  3 1 2 ft  in length with an area of  2 5 8 ft 2 .  How can Grayson find the width of the cardboard?
    ::格雷森和他的朋友们喜欢坐在纸板上,同时骑着滑板在公园里加快速度。他的母亲打电话说,她有一块312英尺长的纸板,面积为258英尺。 格雷森如何找到纸板的宽度?

    Use the interactive below to find the width of the cardboard by multiplying the area by the reciprocal of the divisor which is the length.
    ::使用下面的交互效果来查找纸板的宽度,将区域乘以长度的对等三角形。

    INTERACTIVE
    Cardboard Dimensions
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    • Firstly, drag the numbers into the boxes to set up the division problem. 
      ::首先, 将数字拖放到框中来设置分割问题 。
    • Then convert the mixed numbers to improper fractions by inputting them into the boxes. A button to continue will appear once correct.
      ::然后将混合数转换成不适当的分数, 将其输入框中 。 要继续的按钮一旦出现正确 。
    • Next, click on the numbers and operation to set up multiplying by the reciprocal. Another button to continue will appear once correct.
      ::下一步, 点击数字和操作来设置乘以对等的乘数。 继续的另一个按钮将出现一次正确 。
    • Finally, enter the simplified product into the boxes to find the width of the park.
      ::最后,将简化产品输入箱中,以找到公园宽度。
    • Use the check button to check your answers.
      ::使用复选按钮检查您的答案 。
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    Can you solve the missing area puzzles?
    ::您能解开缺失的区域拼图吗 ?

    In this interactive, calculate missing side lengths by dividing the area of a rectangle by the known length of that rectangle. Some of these puzzles are very tricky, so focus on what you know and what you don’t know in each!
    ::在此互动中, 通过将矩形区域除以已知矩形的长度来计算所缺的侧边长度 。 其中一些谜题非常棘手, 所以聚焦于您所知道的和您所不知道的 !

     

    INTERACTIVE
    Area Puzzles
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    • Enter the missing side length or area in the boxes.
      ::输入框中缺失的侧边长度或区域。
    • After, click the button to try the next puzzle.
      ::之后,单击按钮尝试下一个谜题。
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       Summary
    ::摘要

    When solving fractional area problems:
    ::当解决片段区域问题时 :

    • Divide the area by the length to get the width.
      ::将区域除以长度以获得宽度。
    • Change the division statement to a multiplication statement by multiplying by the reciprocal of the divisor. Then, you can multiply straight across as with other fraction multiplication problems.
      ::将除法语句改为乘法语句,乘以除法语句的对等。然后,您可以与其他分数乘法问题一样,直接相乘。

    For example,  1 2 ÷ 3 4 = 1 2 × 4 3  
    ::例如, 1234=12×43