Section outline

  • Multiplying Rational Numbers
    ::乘数合理数字

    This lesson introduces multiplying integers and .You have probably seen multiplying fractions and decimals, but multiplying positive and negative numbers may be new. Look for patterns. The only thing that is different is the sign of the answer may change.  Multiplication itself is still the same as it always has been. For any two numbers a and b ,  a × b  is the same as saying a groups of b . So, 4 × 3  is the same as saying 4 groups of 3 or  3 + 3 + 3 + 3.
    ::此课引入了乘数整数和. 您可能已经看到过乘数分数和小数数, 但乘数正数和负数可能是新的。 寻找模式。 唯一不同的是答案的标志可能改变。 乘数本身仍然和以往一样。 对于任何两个数字a和b, axb 与表示 b 组相同。 所以, 4x3 与表示 4 组 3 或 3+3+3+3 +3 相同 。

    In addition, this text will use several different ways to represent multiplication. You have seen  a × b ,  but other ways to write this are  a ⋅ b  and  ( a ) ( b ) .  Remember, a and b are called factors , and their answer is the product of a multiplication problem. 
    ::此外,此文本将使用几种不同的方式来表示乘法。 您已经看到 axb, 但其他写法是 ab 和 (a) (b) 。 记住, a 和 b 被称为因素, 他们的回答是乘法问题的结果 。

     

    Annie's Debt
    ::安妮的债务

    Annie owes $6 to 3 friends : Lou, Sue, and Hugh. How much money does she owe in total? 
    ::安妮欠三个朋友6美元 卢,苏和休 她欠了多少钱?

    Use the interactive to drag the dollar bills from Annie's wallet into Lou, Sue, and Hugh's wallets. Remember that owing money means you have a  negative amount .
    ::使用互动将美元钞票从安妮的钱包中拖到卢、苏和休的钱包中。记住,欠债意味着你的负值。

     

    INTERACTIVE
    Annie's Debt
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    • Move the dollar bills from Annie's wallet to her friends' wallets to see how much money she owes her friends.
      ::把钱从安妮的钱包里 挪到她朋友的钱包里 看看她欠她朋友多少钱
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    You have just learned that when two numbers are being multiplied together, the answer can be positive or negative. If the factors are the same sign, the product will be positive, if they are different signs, the product will be negative.
    ::您刚刚了解到,当两个数字相乘时,答案可以是正的,也可以是负的。 如果因素是相同的信号,产品将是正的,如果是不同的信号,产品将是负的。

    Recall that any number multiplied by 0  will always be 0  and any number multiplied by 1 will be  itself.
    ::回顾任何数字乘以0将始终为0,任何数字乘以1将自有。

     

    TV Show Skip Back
    ::向后跳过电视放映

     

    INTERACTIVE
    TV Show Skip Back
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    Steffan wants to skip back to the beginning of a TV show he's been watching. When he presses the skip back button on his remote, it takes him back 2 minutes.
    ::Steffan想跳回他一直在看的电视节目的开头。当他按着遥控器上的跳回按钮时,他需要2分钟。

    • Press the "Skip back' button to rewind the show all the way and try to figure out how many times Steffan has to press the rewind button.
      ::按下“ 后退” 按钮来倒回播放, 并尝试弄清楚 Steffan 要按多少次后退按钮 。
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    Are you -8?
    ::你 -8吗?

    Which of the expressions below equal -8? Sort the expressions into the correct columns.
    ::下面哪个表达式等于 - 8? 将表达式排序到正确的列中。

     

    INTERACTIVE
    Are You -8?
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    • Select the box to the left of each expression that equals -8.

      ::选择每个表达式左侧等于 - 8 的框。
    • Check your answers with the "Check" button.
      ::用“ 检查” 按钮检查您的答案 。
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       Summary
    ::摘要

    • When multiplying, i f the signs of the factors are the same, the product is positive.
      ::当乘以时,如果因素的迹象相同,产品是正数。
    • When multiplying, if the signs of the factors are different, the product is negative. 
      ::当乘以时,如果因素的迹象不同,产品是负的。
    • When multiplying fractions, change any mixed numbers to improper fractions, and then multiply across; multiply the numerators, multiply the denominators. 
      ::当乘以分数时,将任何混合数改为不适当的分数,然后再乘以;乘以数字,乘以分数。
    • When multiplying decimals, multiply like whole numbers and at the end, move the decimal place the according to how many decimal places are in the problem (add the decimal places of the factors together).
      ::当乘以小数点时,像整数一样乘以整数,在结尾处,移动小数点后,根据问题中小数点位数的大小位数(同时加上因素的小数点位数)移动小数点位数。