4.16小数除小数

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  小数除小数

  

  [Figure 1]

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  Liam is almost done building a bookcase. He just needs to add the shelves. Each shelf must be 26.5 inches long. He has a piece of wood that is 90.1 inches long. How any shelves can he make from that piece of wood?
  ::利亚姆几乎要建书架了,他只需要加架子。每一架架架子必须长26.5英寸。他有一块90.1英寸长的木头。他能用那块木头做多少架子?

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  In this concept, you will learn how to  divide  a decimal by a decimal.
  ::在此概念中,您将学会如何将小数点除以小数点。

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  Dividing Decimals by Decimals
  ::以十进制区分的十进制

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  You can divide a decimal number by another decimal number, but placing the decimal back into the  quotient  can become tricky.  Simplify  the process by change the  divisor  to a whole number.
  ::您可以将小数点数除以另一个小数点数,但将小数点放回商数会变得棘手。通过将小数点修改为整数来简化进程。

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  Here is a division problem.
  ::这是一个分裂问题。

  $$\begin{array}{r}10.4÷2.6=\underset{\_}{}\end{array}$$

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  The  divisor  is 2.6. To change a decimal number to a whole number, multiply the decimal number by a power of ten to move the  decimal point . Multiply 2.6 by 10 to move the decimal point one space to the right.
  ::divisor 是 2. 6。 要将小数点数改为整数, 将小数点数乘以十乘以十, 以移动小数点。 乘以 2. 6 乘以 10 将小数点一空格向右移动 。

  $$\begin{array}{r}2.6\times 10=26\end{array}$$

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  Dividing by 26 is easier than  .6. However, dividing 10.4 by 26 is not the same as dividing 10.4 by 2.6. If you change the divisor, you must also change the  dividend .
  ::然而,将10.4除以26并不等于将10.4除以2.6。 如果改变分配,你还必须改变红利。

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  Remember that a division problem can also be written as a fraction. The dividend is placed in the  numerator  and the divisor is placed in the  denominator . In this problem, 10.4 is the dividend and is placed in the numerator. 2.6 is the divisor and is placed in the denominator.
  ::记住分裂问题也可以作为一个分数来写。 红利放在分子中, 分数放在分母中。 在这个问题中, 10.4 是红利, 放在分子中。 2. 6 是分数, 放在分数中 。

  $$\begin{array}{r}10.4÷2.6=\frac{10.4}{2.6}\end{array}$$

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  If you change the denominator, you must also change the numerator the same way in  order  for the fraction to have the same value. Multiply the numerator and denominator by 10.
  ::如果您更改分母, 您也必须以同样的方式更改分子数, 以使分数的值相同。 乘以分子数和分母乘以 10 。

  $$\begin{array}{r}10.4÷2.6=\frac{10.4\times 10}{2.6\times 10}=\frac{104}{26}\end{array}$$

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  Now write the new fraction as a division problem and divide to find the quotient.
  ::现在将新分数写成分裂问题, 并进行分割以找到商数 。

  $$\begin{array}{r}104÷26\text{ or }\stackrel{}{26\overline{)104}}\end{array}$$

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{4}{26\stackrel{¯}{)104}}\\ & & \underset{\_}{-104}\\ & & 0\end{array}\end{array}$$

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  $\begin{array}{r}10.4÷2.6\end{array}$  is the same as  $\begin{array}{r}104÷26\end{array}$ . The quotient of 10.4 divided by 2.6 is 4.
  ::10.4 10.4除以2.6除以4的商数为4。

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  Here is another division problem. This time the divisor has two decimal places.
  ::还有一个分裂问题。 这次, divisor 有两个小数点位数 。

  $$\begin{array}{r}\stackrel{}{0.45\overline{)1.44}}\end{array}$$

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  First, change the divisor to a whole number by multiplying it by a power of ten. Multiply 0.45 by 100. Then, do the same thing to the dividend.
  ::首先,通过乘以10的功率,将二位数改变为整位数。乘以0.45乘以100,然后,对红利也做同样的事情。

  $$\begin{array}{r}\begin{array}{rcl}0.45\times 100& =& 45\\ 1.44\times 100& =& 144\end{array}\end{array}$$

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  Here is the new division problem. Divide to find the quotient.
  ::这就是新的分裂问题。为了找到商数而分裂。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{3}{45\stackrel{¯}{)144}}\\ & & \underset{\_}{-135}\\ & & 9\end{array}\end{array}$$

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  Use  zero  placeholders  to continue dividing.
  ::使用零占位符继续分隔 。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{3.2}{45\overline{)144.0}}\\ & & \underset{\_}{-135}\\ & & 90\\ & & \underset{\_}{-90}\\ & & 0\end{array}\end{array}$$

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  The quotient of 1.44 divided by 0.45 is 3.2.
  ::1.44除以0.45的商数为3.2。

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  Notice the pattern. You move the decimal the same number of spaces in the dividend as you do in the divisor.
  ::注意图案。 您移动小数点时, 小数点在股息中的空格数与您在 divisor 中的空格数相同 。

  $$\begin{array}{r}\begin{array}{rcl}2.6\to 2\underset{\to }{6}& & 0.45\to \underset{\to }{45}\\ 10.4\to 10\underset{\to }{4}& & 1.35\to 1\underset{\to }{35}\end{array}\end{array}$$

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  To multiply a decimal number by a decimal number, change the divisor to a whole number and move the decimal point the same number of spaces in the dividend. Then, divide to find the quotient.
  ::将小数数乘以小数数,将小数数修改为整数,然后将小数点移到股息中相同的空格数。然后,为找到商数进行分隔。

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Liam and his bookcase.
  ::早些时候,你得到一个问题 关于利亚姆和他的书架。

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  He wants to know how many 26.5 inch shelves he can make from a piece of wood that is 90.1 inches long. Divide to find the answer.
  ::他想知道他能从一块90.1英寸长的木头上 制成多少26.5英寸的架子

  $$\begin{array}{r}\stackrel{}{26.5\overline{)90.1}}\end{array}$$

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  First, change the divisor to a whole number.
  ::首先,把食堂改成整个数字。

  $$\begin{array}{r}26.5\to 26\underset{\to }{5}.\end{array}$$

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  Then, do the same thing to the dividend.
  ::然后,对红利也做同样的事情。

  $$\begin{array}{r}90.1\to 90\underset{\to }{1}.\end{array}$$

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  Next, write the new division problem and divide to find the quotient.
  ::接下来,写出新的分裂问题和分裂,以找到商数。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{3.4}{265\overline{)901.0}}\\ & & \underset{\_}{-795}\\ & & 1060\\ & & \underset{\_}{-1060}\\ & & 0\end{array}\end{array}$$

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  Liam can make at least 3 shelves from the piece of wood.
  ::利亚姆能从木头上 做至少3个架子

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  Example 2
  ::例2

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  Divide the decimals.
  ::除以小数。

  $$\begin{array}{r}\stackrel{}{3.45\overline{)7.245}}\end{array}$$

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  First, change 3.45 to a whole number by multiplying it by a power of ten. Multiply 3.45 by 100 or simply move the decimal point two spaces to the right.
  ::首先,通过乘以10的功率,将3.45乘以整个数字。乘以3.45乘以100,或者简单地将小数点的两个空格移到右边。

  $$\begin{array}{r}3.45\times 100=345\text{ or }3\underset{\to }{45}.\end{array}$$

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  Then, do the same thing to the dividend. Multiply 7.245 by 100 or move the decimal point two spaces to the right.
  ::然后对红利做同样的事情。 乘以 7245 乘以 100 或将小数点 2 空格移到右边 。

  $$\begin{array}{r}7.245\times 100=724.5\text{ or }7\underset{\to }{24}.5\end{array}$$

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  Next, write the new division problem and divide to find the quotient.
  ::接下来,写出新的分裂问题和分裂,以找到商数。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{2.1}{345\overline{)724.5}}\\ & & \underset{\_}{-690}\\ & & 345\\ & & \underset{\_}{-345}\\ & & 0\end{array}\end{array}$$

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  The quotient of 7.245 divided by 3.45 is 2.1.
  ::7.245除以3.45的商数为2.1。

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  Divide the decimals. Use zero placeholders if needed.
  ::除以小数。如果需要,使用零占位符。

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  Example 3
  ::例3

  $$\begin{array}{r}\stackrel{}{1.2\overline{)4.8}}\end{array}$$

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  First, change the divisor to a whole number.
  ::首先,把食堂改成整个数字。

  $$\begin{array}{r}1.2\times 10=12\text{ or }1\underset{\to }{2}.\end{array}$$

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  Then, do the same thing to the dividend.
  ::然后,对红利也做同样的事情。

  $$\begin{array}{r}4.8\times 10=48\text{ or }4\underset{\to }{8}.\end{array}$$

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  Next, write the new division problem and divide to find the quotient.
  ::接下来,写出新的分裂问题和分裂,以找到商数。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{4}{12\stackrel{¯}{)48}}\\ & & \underset{\_}{-48}\\ & & 0\end{array}\end{array}$$

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  The quotient of 4.8 divided by 1.2 is 4.
  ::4.8除以1.2的商数为4。

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  Example 4
  ::例4

  $$\begin{array}{r}\stackrel{}{5.6\overline{)14.28}}\end{array}$$

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  First, change the divisor to a whole number.
  ::首先,把食堂改成整个数字。

  $$\begin{array}{r}5.6\times 10=56\text{ or }5\underset{\to }{6}.\end{array}$$

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  Then, do the same thing to the dividend.
  ::然后,对红利也做同样的事情。

  $$\begin{array}{r}14.28\times 10=142.8\text{ or }14\underset{\to }{2}.8\end{array}$$

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  Next, write the new division problem and divide to find the quotient.
  ::接下来,写出新的分裂问题和分裂,以找到商数。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{2.55}{56\overline{)142.80}}\\ & & \underset{\_}{-112}\\ & & 308\\ & & \underset{\_}{-280}\\ & & 280\\ & & \underset{\_}{-280}\\ & & 0\end{array}\end{array}$$

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  The quotient of 14.28 divided by 5.6 is 2.55.
  ::14.28除以5.6的商数为2.55。

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  Example 5
  ::例5

  $$\begin{array}{r}\stackrel{}{6.98\overline{)13.96}}\end{array}$$

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  First, change the divisor to a whole number.
  ::首先,把食堂改成整个数字。

  $$\begin{array}{r}6.98\times 100=698\text{ or }6\underset{\to }{98}.\end{array}$$

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  Then, do the same thing to the dividend.
  ::然后,对红利也做同样的事情。

  $$\begin{array}{r}13.96\times 100=1,396\text{ or }13\underset{\to }{96}.\end{array}$$

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  Next, write the new division problem and divide to find the quotient.
  ::接下来,写出新的分裂问题和分裂,以找到商数。

  $$\begin{array}{r}\begin{array}{rcl}& & \stackrel{2}{698\stackrel{¯}{)1,396}}\\ & & \underset{\_}{-1,396}\\ & & 0\end{array}\end{array}$$

  The quotient of 13.96 divided by 6.98 is 2.

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  Review
  ::回顾

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  Divide the following decimals. Use zero place holders if needed.
  ::除以以下小数。如果需要,使用零占位符。

  1. $\begin{array}{r}\stackrel{}{1.2\overline{)4.08}}\end{array}$
  2. $\begin{array}{r}\stackrel{}{3.5\overline{)12.6}}\end{array}$
  3. $\begin{array}{r}\stackrel{}{14.5\overline{)29}}\end{array}$
  4. $\begin{array}{r}\stackrel{}{8.9\overline{)11.57}}\end{array}$
  5. $\begin{array}{r}\stackrel{}{0.32\overline{)0.08}}\end{array}$
  6. $\begin{array}{r}\stackrel{}{1.2\overline{)7.8}}\end{array}$
  7. $\begin{array}{r}\stackrel{}{9.6\overline{)11.52}}\end{array}$  
  8. $\begin{array}{r}\stackrel{}{14.5\overline{)33.35}}\end{array}$
  9. $\begin{array}{r}\stackrel{}{12.5\overline{)7.5}}\end{array}$
  10. $\begin{array}{r}\stackrel{}{2.5\overline{)13.29}}\end{array}$
  11. $\begin{array}{r}\stackrel{}{1.2\overline{)7.2}}\end{array}$  
  12. $\begin{array}{r}\stackrel{}{0.8\overline{)1.8}}\end{array}$  
  13. $\begin{array}{r}\stackrel{}{4.6\overline{)10.58}}\end{array}$
  14. $\begin{array}{r}\stackrel{}{1.6\overline{)0.3}}\end{array}$

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  Review (Answers) 
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源