课程： 11.13整数除法 | The Way To Learn

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整数除法
Cat wants to do the 24 hour comics challenge, but she is a little overwhelmed at the idea of drawing 24 pages from scratch in one day. She has a story idea so she tries to break it into manageable pieces. Of the 24 pages, she knows that she wants one full page for the title page, and she wants one full page splash at the climax. She also knows that she wants the first story page to be three panels of establishing shots. When she does a very rough story-board, she figures out that she needs 147 distinct panels to tell her story. So how many panels will she need to average per page?
::猫想完成24小时的漫画挑战, 但她对一天从头开始画24页的想法有点不知所措。她有一个故事想法, 所以她试图把它拆成可操作的片段。在24页中, 她知道她想要一整页的标题页, 她想要在顶点上洒一整页。她还知道, 她想要第一个故事页成为三个制作镜头的面板。当她做一个非常粗糙的故事板时, 她发现她需要147个不同的面板来讲述她的故事。所以她需要多少个面板来平均每页?

In this concept, you will learn how to divide integers.
::在这个概念中,你会学会如何分割整数。

Dividing Integers
::Divide 整数器

An integer is the set of whole numbers and their opposites.
::整数是整数及其反面的一组。

A quotient is the answer in a division problem. Division is the number of times one number goes into another number.
::“商数”是各司问题的答案。“司”是指一个数字乘以另一个数字的次数。

The divisor is the number divided into the other number.
::divisor 是数字, 分为其他数字。

Here are the sign rules for division:
::以下是"组织"的标志性规则:

Positive $\begin{aligned} \div \end{aligned}$ positive = positive

Negative $\begin{aligned} \div \end{aligned}$ positive, or vice versa=negative

Negative $\begin{aligned} \div \end{aligned}$ negative = positive

Another way to think of it is if there are an odd number of negatives in the problem, the answer is negative. If there are an even number, the answer is positive. These rules are the same as for multiplication.
::另一种思考方式是,如果问题有奇数的负数,答案是否定的。如果数字是偶数,答案是肯定的。这些规则与乘法相同。

Here is an example.
::举一个例子。

10 $\begin{aligned} \div \end{aligned}$ 2 =

In this example, ten is being divided into increments of two. So first, break 10 into increments of 2.
::在这个例子中,10个被分为2个加量。首先,10个被分为2个加量。首先,10个被分为2个加量。

2 + 2 = 4

2 + 2 + 2 = 6

2 + 2 + 2 + 2 = 8

2 + 2 + 2 + 2 + 2 = 10

Next, count how many increments of the divisor added up to the other number.
::接下来,请计算下插图插图的加插数与其它数字相加。

In this case, there were five 2s.
::在本案中,有5 2。

The answer is 5.
::答案是5。

Here is another example.
::下面是另一个例子。

$\begin{aligned} 30 \div - 5 \end{aligned}$ = ____

First, break 30 into increments of 5, ignoring the sign.
::首先,将30分分成5分, 忽略标志。

5 + 5 + 5 + 5 + 5 + 5 = 30

Next, count the number of increments.
::接下来,计数加薪次数。

In this case, there are six 5s. If you know the multiplication table, you can simplify the process without converting to addition every time. Then, you just need to worry about the signs.
::在此情况下, 有 6 个 5 个。如果您知道乘法表, 您可以简化程序, 而不是每次转换为加法。然后, 您只需要担心符号。

Then, take into account the sign.
::那么,考虑一下这个标志。

The original divisor was negative. In order to divide a negative number into a positive number, the answer must also be negative.
::最初的差幅是负的。要将负数分成正数,答案必须是负数。

The answer is -6.
::答案是 -6

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Cat and her comic book.
::早些时候,你被问及Cat和她的漫画书

She wants to figure out how many panels she needs to draw per page. She knows she needs 147 panels to tell her story. Her comic book is 24 pages. But of those, the first is a title page, the second is a page of establishing shots, and her climax page only has one panel. So she only really has 21 pages to work with.
::她想弄清楚她每页要画多少个面板。她知道她需要147个面板来讲述她的故事。她的漫画书有24页。但其中第一页是标题页,第二页是建立镜头的页面,而她的高潮页面只有一个面板。因此她只有21页要工作。

In order to decide how many panels to draw on each page, she sets up a division problem.
::为了决定每一页要使用多少个小组,她提出了一个分部问题。

$\begin{aligned} 147 \div 21 \end{aligned}$

Next, she divides the number of panels my the number of pages.
::其次,她将我页数的面板数分开。

She finds that she needs to plan to have an average of 7 panels per page to tell her story.
::她认为,她需要计划平均每页有7个面板来讲述她的故事。

The answer is 7.
::答案是7个

Example 2
::例2

Carry out the division problem.
::解决分裂问题

$\begin{aligned} 18 \div - 2 \div 3 \end{aligned}$

First, carry out the division of the first two integers ignoring the third integer and the signs
::首先,执行前两个整数的分割,忽略第三个整数和符号

$\begin{aligned} 18 \div 2 \end{aligned}$ = 9

Next, carry out the division with that answer and the 3. (Remember: the number on the right always goes into the number on the left.)
::接下来,用回答和3来进行分割。 (记住:右侧的号码总是在左侧的号码中。 )

$\begin{aligned} 9 \div 3 = 3 \end{aligned}$

Then, count the number of negatives.
::然后,计数负数。

In this case, there is one negative in the original problem. One is odd, so the final answer is negative.
::在这种情况下,在最初的问题中有一个是否定的。一个是奇怪的,所以最后答案是否定的。

The answer is -3.
::答案是 -3

Example 3
::例3

Carry out the division problem.
::解决分裂问题

-16 $\begin{aligned} \div \end{aligned}$ -2 = ____

First, divide the second number into the first, ignoring signs.
::首先,将第二个数字分为第一个数字,忽略符号。

$\begin{aligned} 16 \div 2 = 8 \end{aligned}$

Then, count the number of negatives in the original problem.
::然后,计算原始问题中的负数。

In this case, there are two. Two is even, so the final answer is positive.
::在这种情况下,有两个。两个是偶数,所以最后答案是肯定的。

The answer is 8.
::答案是8岁

Example 4
::例4

Carry out the division problem.
::解决分裂问题

-24 $\begin{aligned} \div \end{aligned}$ -12 =____

First, divide the second number into the first, ignoring signs.
::首先,将第二个数字分为第一个数字,忽略符号。

$\begin{aligned} 24 \div 12 = 2 \end{aligned}$

Next, count the number of negatives in the original problem.
::接下来,在原始问题中计数负数。

In this case, there are two. Two is even, so the final answer is positive.
::在这种情况下,有两个。两个是偶数,所以最后答案是肯定的。

The answer is 2.
::答案是2。

Example 5
::例5

Carry out the division problem.
::解决分裂问题

-64 $\begin{aligned} \div \end{aligned}$ 2 = ____

First, divide the second number into the first, ignoring signs.
::首先,将第二个数字分为第一个数字,忽略符号。

$\begin{aligned} 64 \div 2 = 32 \end{aligned}$

Next, count the number of negatives in the original problem.
::接下来,在原始问题中计数负数。

In this case, there is one. One is odd, so the final answer is negative.
::在这种情况下,就有一个。一个是奇怪的,所以最后答案是否定的。

The answer is -32.

::答案是 -32

Review
::回顾

Find the quotient of each integer pair.
::查找每对整对数的商数。

-18 $\begin{aligned} \div \end{aligned}$ 9 = ____

-22 $\begin{aligned} \div \end{aligned}$ -11 = ____

-32 $\begin{aligned} \div \end{aligned}$ 8 = ____

32 $\begin{aligned} \div \end{aligned}$ 8 = ____

-21 $\begin{aligned} \div \end{aligned}$ 7 = ____

-72 $\begin{aligned} \div \end{aligned}$ 12 = ____

-80 $\begin{aligned} \div \end{aligned}$ -10 = ____

56 $\begin{aligned} \div \end{aligned}$ -7 = ____

63 $\begin{aligned} \div \end{aligned}$ -9 = ____

-121 $\begin{aligned} \div \end{aligned}$ -11 = ____

144 $\begin{aligned} \div \end{aligned}$ -12 = ____

200 $\begin{aligned} \div \end{aligned}$ -4 = ____

-50 $\begin{aligned} \div \end{aligned}$ -2 = ____

28 $\begin{aligned} \div \end{aligned}$ -2 = ____

66 $\begin{aligned} \div \end{aligned}$ 3 = ____

150 $\begin{aligned} \div \end{aligned}$ -3 = ____

180 $\begin{aligned} \div \end{aligned}$ -90 = ____

70 $\begin{aligned} \div \end{aligned}$ -35 = ____

-44 $\begin{aligned} \div \end{aligned}$ -22 = ____

75 $\begin{aligned} \div \end{aligned}$ 3 = ____

Evaluate each numerical expression.
::评估每个数字表达式。

$\begin{aligned} \frac{- 9 + - 3}{6} \end{aligned}$

$\begin{aligned} \frac{- 9 (- 6)}{2} \end{aligned}$

$\begin{aligned} \frac{(15) (3)}{- 5} \end{aligned}$

$\begin{aligned} \frac{- 18 (4)}{9} \end{aligned}$

$\begin{aligned} \frac{- 3 - 12}{- 5} \end{aligned}$

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

章节大纲

常规

整数除法

Dividing Integers ::Divide 整数器

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

Dividing Integers
::Divide 整数器

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