Section: 使用零占位符的十进制商 | 4.11使用零占位符的十进制商

Section outline

Jerry is hosting a barbeque for his friends. He buys 10.5 pounds of ground meat to make hamburgers. He wants to make 20 hamburger patties for the party. How much meat will be in each patty if he divides the meat evenly?
::Jerry为朋友办了烤肉会,他买了10.5磅的土肉做汉堡包。他想为派对做20块汉堡饼。如果他把肉平分的话,每块肉里会有多少肉?

In this concept, you will learn how to divide a decimal using zero place holders.
::在此概念中, 您将学习如何使用零位持有者来区分小数。

Zero Placeholder
::零占位符

Not all problems will divide exactly. In some cases, a division problem will have a remainder . A remainder is the amount left over when the dividend is not equally divided by the divisor . The remainder is written as “R” followed by a number.
::并非所有问题都会完全分开。在某些情况下,分裂问题还有剩余部分。其余部分是股息不是由股息平分时留下的剩余部分。其余部分写成“ R ” , 后面加一个数字。

Here is a division problem with a remainder.
::这是一个分裂问题,还有其余部分。

$\begin{aligned} \begin{array}{rcl} 2.9 R 4 \\ 5 14.9 \\ \underline{- 10} \\ 4 9 \\ \underline{- 4 5} \\ 4 \end{array} \end{aligned}$

The quotient of 14.9 divided by 5 is 2.9 with a remainder of 4. You can continue dividing the dividend to find a more accurate quotient. Place a zero as a placeholder at the end of the decimal number in the division box.
::14.9除以5的商数为14.9除以5的商数是2.9,其余为4.4。您可以继续分割红利,以找到更准确的商数。将零作为占位符放在除法框小数的末尾。

Here is the same division problem with a zero placeholder .
::与零占位符相同的分裂问题。

$\begin{aligned} \begin{array}{rcl} 2.98 \\ 5 14.9 0 \\ \underline{- 10} \\ 4 9 \\ \underline{- 4 5} \\ 40 \\ \underline{- 40} \\ 0 \end{array} \end{aligned}$

The quotient of 14.9 divided by 5 is 2.98. This means that 5 can go into 14.9 exactly 2.98 times.
::14.9除以5的商数是2.98。这意味着,5的商数可以乘以14.9,正好是2.98倍。

Adding zero placeholders at the end of a decimal does not change the value of the decimal.
::在小数点末尾添加零占位符不会改变小数点的值。

$\begin{aligned} 14.9 = 14.9000 \end{aligned}$

Zero placeholders can be used to continue dividing to get a more accurate quotient. You can also add as many zero placeholders as you need.
::零占位符可用于继续分隔,以获得更准确的商数。您也可以根据需要添加最多为零的占位符。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Jerry and the hamburgers.
::早些时候,你得到一个问题关于杰瑞和汉堡包。

Jerry wants to make 20 hamburger patties from 10.5 pounds of ground meat. Divide 10.5 by 20 to find the exact weight of each patty.
::杰瑞想从10.5磅的地肉做20块汉堡饼将10.5除以20

First, start dividing 10.5 by 20.
::首先,开始将10.5除以20。

$\begin{aligned} \begin{array}{rcl} .5 \\ 20 10.5 \\ \underline{- 10 0} \\ 5 \end{array} \end{aligned}$

Then, add zero placeholders and continue to divide.
::然后,加零占位符,继续分裂。

$\begin{aligned} \begin{array}{rcl} 525 \\ 20 10.5 00 \\ \underline{- 10 0} \\ 50 \\ \underline{- 40} \\ 100 \\ \underline{- 100} \\ 0 \end{array} \end{aligned}$

Next, add the decimal point to the quotient.
::下一步,在商数中添加小数点。

$\begin{aligned} 0.525 \\ 20 10.5 00 \end{aligned}$

Each patty will weigh exactly 0.525 pounds.
::每个帕蒂的重量将达到0.525磅

Example 2
::例2

Divide and use zero placeholders if needed.
::必要时分差使用零占位符。

$\begin{aligned} 3.1 \div 8 = \underline{} \end{aligned}$

First, start dividing 3.1 by 8. Remember that 3.1 is the dividend and 8 is the divisor.
::首先,将3.1除以8。记住,3.1是红利,8是红利。

$\begin{aligned} \begin{array}{rcl} 3 \\ 8 3.1 \\ \underline{- 24} \\ 7 \end{array} \end{aligned}$

Then, add zero placeholders and continue to divide.
::然后,加零占位符,继续分裂。

$\begin{aligned} \begin{array}{rcl} 3875 \\ 8 3.1 000 \\ \underline{- 24} \\ 70 \\ \underline{- 64} \\ 60 \\ \underline{- 56} \\ 40 \\ \underline{- 40} \\ 0 \end{array} \end{aligned}$

Then, add the decimal point to the quotient.
::然后,在商数中加入小数点。

$\begin{aligned} 0.3875 \\ 8 3.1 000 \end{aligned}$

The final answer for 3.1 divided by 8 is 0.3875.
::3.1除以8的最后答案是0.3875。

Divide the following problems and use zero placeholders if needed.
::将以下问题分开,必要时使用零占位符。

Example 3
::例3

$\begin{aligned} 13.95 \div 6 = \underline{} \end{aligned}$

First, start dividing 13.95 by 6.
::首先,开始将13.95除以6。

$\begin{aligned} \begin{array}{rcl} 2 32 \\ 6 13.95 \\ \underline{- 12} \\ 19 \\ \underline{- 18} \\ 15 \\ \underline{- 12} \\ 3 \end{array} \end{aligned}$

Then, add zero placeholders and continue to divide.
::然后,加零占位符,继续分裂。

$\begin{aligned} \begin{array}{rcl} 2 325 \\ 6 13.95 0 \\ \underline{- 12} \\ 19 \\ \underline{- 18} \\ 15 \\ \underline{- 12} \\ 30 \\ \underline{- 30} \\ 0 \end{array} \end{aligned}$

Next, add the decimal point to the quotient.
::下一步,在商数中添加小数点。

$\begin{aligned} 2.325 \\ 6 13.95 0 \end{aligned}$

The quotient of 13.95 divided by 6 is 2.325.
::13.95除以6的商数为2.325。

Example 4
::例4

$\begin{aligned} 2.5 \div 2 = \underline{} \end{aligned}$

First, start dividing 2.5 by 2.
::首先,开始将2.5除以2。

$\begin{aligned} \begin{array}{rcl} 1 2 \\ 2 2.5 \\ \underline{- 2} \\ 0 5 \\ \underline{- 4} \\ 1 \end{array} \end{aligned}$

Then, add zero placeholders and continue to divide.
::然后,加零占位符,继续分裂。

$\begin{aligned} \begin{array}{rcl} 1 25 \\ 2 2.5 0 \\ \underline{- 2} \\ 05 \\ \underline{- 4} \\ 10 \\ \underline{- 10} \\ 0 \end{array} \end{aligned}$

Next, add the decimal point to the quotient.
::下一步,在商数中添加小数点。

$\begin{aligned} 1.25 \\ 2 2.5 0 \end{aligned}$

The quotient of 2.5 divided by 2 is 1.25.
::2.5除以2除以2的商数为1.25。

Example 5
::例5

$\begin{aligned} 1.66 \div 4 = \underline{} \end{aligned}$

First, start dividing 1.66 by 4.
::首先,从1.66除以4开始。

$\begin{aligned} \begin{array}{rcl} 41 \\ 4 1.66 \\ \underline{- 16} \\ 06 \\ \underline{- 4} \\ 2 \end{array} \end{aligned}$

Then, add zero placeholders and continue to divide.
::然后,加零占位符,继续分裂。

$\begin{aligned} \begin{array}{rcl} 415 \\ 4 1.66 0 \\ \underline{- 16} \\ 06 \\ \underline{- 4} \\ 20 \\ \underline{- 20} \\ 0 \end{array} \end{aligned}$

Next, add the decimal point to the quotient.
::下一步,在商数中添加小数点。

$\begin{aligned} 0.415 \\ 4 1.66 0 \end{aligned}$

The quotient of 1.66 divided by 4 is 0.415.
::1.66除以4的商数为0.415。

Review
::回顾

Divide the following problems and use zero placeholders if needed.
::将以下问题分开,必要时使用零占位符。

$\begin{aligned} 5 17.6 \end{aligned}$

$\begin{aligned} 4 12.3 \end{aligned}$

$\begin{aligned} 4 14.4 \end{aligned}$

$\begin{aligned} 5 27.51 \end{aligned}$

$\begin{aligned} 6 13.6 \end{aligned}$

$\begin{aligned} 6 54.9 \end{aligned}$

$\begin{aligned} 8 4.18 \end{aligned}$

$\begin{aligned} 8 94.1 \end{aligned}$

$\begin{aligned} 8 10.04 \end{aligned}$

$\begin{aligned} 4 24.89 \end{aligned}$

$\begin{aligned} 12 27.9 \end{aligned}$

Review (Answers)
::回顾(答复)

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。

Resources
::资源

Section outline

Zero Placeholder ::零占位符

Examples ::实例

Example 1 ::例1

Example 2 ::例2

Example 3 ::例3

Example 4 ::例4

Example 5 ::例5

Review ::回顾

Review (Answers) ::回顾(答复)

Resources ::资源

Zero Placeholder
::零占位符

Examples
::实例

Example 1
::例1

Example 2
::例2

Example 3
::例3

Example 4
::例4

Example 5
::例5

Review
::回顾

Review (Answers)
::回顾(答复)

Resources
::资源