Course: 4.12整数除法 | The Way To Learn

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整数除法
The company that Sam works for is doing a weight loss challenge in 2015. The three different departments in the company are competing against each other. Whichever department has the most negative average change in weight will win.
::萨姆所领导的公司在2015年面临减重的挑战。公司的三个不同部门正在相互竞争。哪个部门的平均重量变化最负,哪个部门都会赢。

Department A has 12 employees and its current overall change in weight is -36 pounds.
::A部有12名雇员,目前其体重的总体变化为-36磅。

Department B has 9 employees and its current overall change in weight is -45 pounds.
::B部有9名雇员,目前其体重的总体变化为-45磅。

Department C has 35 employees and its current overall change in weight is -70 pounds.
::C部有35名雇员,目前其体重的总体变化为-70磅。

How could Sam determine which department is currently winning the weight loss challenge?
::Sam如何确定哪个部门目前正在赢得减重的挑战?

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

Integers are the set of whole numbers and their opposites.
::整组是整组数字和反面数字的组合。

When you divide integers, your answer after dividing is called a quotient .
::当将整数除以时,除以后的回答被称为商数。

Here is an example.
::举一个例子。

$\begin{aligned} 15 \div 3 = 5 \end{aligned}$

In this example, 5 is the quotient.
::在这个例子中,5是商数。

Dividing integers is very similar to dividing whole numbers. The only difference is you will have to decide if your quotient is negative or positive . The rules for deciding if your quotient is positive/negative are very similar to the rules you used with .
::dividing 整数与整数的除法非常相似。唯一的区别在于您必须决定您的商数是负数还是正数。决定您的商数是正数还是负数的规则与您使用的规则非常相似。

To divide two integers:
::要除以两个整数:

First, divide the absolute value of the integers.
::首先,将整数的绝对值除以。

Next, determine the sign of your quotient according to the following rules:

A positive number divided by a positive number equals a positive number.
::一个正数除以正数等于正数。

A positive number divided by a negative number equals a negative number.
::一个正数除以负数等于负数。

A negative number divided by a negative number equals a positive number.
::负数除以负数等于正数。

A negative number divided by a positive number equals a negative number.
::负数除以正数等于负数。

Any integer divided by zero is undefined.
::任何整数除以零均未定义。

Zero divided by any integer except zero equals zero.
::除零等于零外,零除以任何整数。

::接下来,按照以下规则确定您的商数的符号:正数除以正数等于正数。正数除以正数等于正数。正数除以负数等于负数。负数除以负数等于正数。负数除以正数等于负数等于负数。任何整数除以零均不定义。除零外,零除以任何整数。

Your quotient will be your result from step 1 with the sign from step 2.
::您的商数将来自步骤1 与标志从步骤2产生的结果。

It might help to remember that if your original two integers have the same sign, then their quotient will be positive. If your original two integers have different signs, then their quotient will be negative. This is the same as it was for integer multiplication!
::这或许有助于记住,如果原来的两个整数有相同的符号,那么它们的商数将是正数。如果原来的两个整数有不同的符号,那么它们的商数将是负数。这与整数乘法相同。

Let's look at an example.
::让我们举个例子。

Divide $\begin{aligned} (- 33) \div (- 3) \end{aligned}$
::差数 (- 33) (- 3)

The first step is to divide the absolute value of the factors .
::第一步是将各种因素的绝对价值分开。

$\begin{aligned} 33 \div 3 = 11 \end{aligned}$

The next step is to decide on the sign of your answer. Both integers were negative and a negative divided by a negative equals a positive. This means your quotient is positive.
::下一步是决定您回答的符号。整数都是负数, 负数除以负数等于正数。这意味着您的商数是正数。

$\begin{aligned} (- 33) \div (- 3) = 11 \end{aligned}$

The answer is 11.
::答案是11个

Here's another example.
::下面是另一个例子。

Divide $\begin{aligned} \frac{- 20}{5} \end{aligned}$ .
::分数 - 20 5 。

Remember that the fraction bar is the same as division. This problem is the same as
::记住分数栏与除法相同。这个问题与

$\begin{aligned} - 20 \div 5 \end{aligned}$

Again, the first step is to divide the absolute value of the factors.
::同样,第一步是将各种因素的绝对价值分开。

$\begin{aligned} 20 \div 5 = 4 \end{aligned}$

The next step is to decide on the sign of your answer. The two factors had different signs. A negative divided by a positive is a negative. This means your quotient is negative.
::下一步是决定您答案的符号。这两个因素有不同的迹象。负除以正数是负数。这意味着您的商数是负数。

$\begin{aligned} \frac{- 20}{5} = - 20 \div 5 = - 4 \end{aligned}$

The answer is -4.
::答案是 -4

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Sam and his weight loss challenge at work.
::早些时候,你被问及山姆和他在工作时的减肥挑战。

He wants to find out which department is currently winning the competition. In order for a department to be in the lead, it needs to have the most negative average change in weight.
::他想知道哪个部门目前正在赢得竞争。要使一个部门领先,它需要负平均重量变化最多。

Department A with 12 employees has a current overall change in weight of -36 pounds. To find the average change in weight for the department, you need to divide the change in weight by the number of employees.
::A部有12名雇员,目前总重量变化为-36磅,要发现该部门平均重量变化,需要将重量变化除以雇员人数。

$\begin{aligned} - 36 \div 12 = ? \end{aligned}$

You know that $\begin{aligned} 36 \div 12 = 3 \end{aligned}$ . You also know that a negative divided by a positive equals a negative. This means the answer is negative.
::您知道, 36 12 = 3。您也知道, 负除以正数等于负数。这意味着答案为负数。

$\begin{aligned} - 36 \div 12 = - 3 \end{aligned}$

Department A has an average change in weight of -3 pounds.
::A部体重平均变化为3磅。

Department B with 9 employees has a current overall change in weight of -45 pounds. Divide to find its current average change in weight:
::B部门有9名雇员,目前总重量变化为-45磅。

$\begin{aligned} - 45 \div 9 = ? \end{aligned}$

You know that $\begin{aligned} 45 \div 9 = 5 \end{aligned}$ and a negative divided by a positive equals a negative.
::你知道45=9=5 负除以正数等于负数

$\begin{aligned} - 45 \div 9 = - 5 \end{aligned}$ .

Department B has an average change in weight of -5 pounds.
::B部体重平均变化为5磅。

Department C with 35 employees has a current overall change in weight of -70 pounds. Divide to find its current average change in weight:
::C部门有35名雇员,目前总重量变化为-70磅。

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

You know that $\begin{aligned} 70 \div 35 = 2 \end{aligned}$ and a negative divided by a positive equals a negative.
::你知道70+35=2和负除以正数等于负数。

$\begin{aligned} - 70 \div 35 = - 2 \end{aligned}$ .

Department C has an average change in weight of -2 pounds.
::C部平均重量变化为 -2磅

Currently, Department B has the most negative average change in weight with -5 pounds.
::目前,B部体重平均负变化最大,为5磅。

The answer is that Department B is currently winning the weight loss challenge.
::答案是B部目前正在赢得减肥的挑战。

Example 2
::例2

On 3 consecutive plays, a football team lost a total of 30 yards. The team lost the same number of yards on each play. Represent the change in the number of yards on each play as a negative integer.
::在连续3场比赛中,一个足球队总共损失了30码,每场比赛损失的场数相同,代表每场比赛的场数变化为负整数。

First, represent the total number of yards lost as an integer.
::首先,表示以整数表示损失的场次总数。

Since the integer shows a loss of 30 yards, use a negative integer, -30.
::由于整数显示损失30码,使用负整数 -30

To represent the loss for each of the 3 plays, divide the integer representing the total number of yards lost by 3.
::要代表每场3场比赛的损失,将代表损失的场次总数整数除以3。

$\begin{aligned} - 30 \div 3 = ? \end{aligned}$

First, divide the absolute value of the factors.
::首先,将因素的绝对值分开。

$\begin{aligned} 30 \div 3 = 10 \end{aligned}$

Next, decide on the sign for your quotient. A negative divided by a positive equals a negative, so your quotient is a negative.
::接下来,决定你的商数。负除以正数等于负数,所以你的商数是负数。

$\begin{aligned} - 30 \div 3 = - 10 \end{aligned}$

The answer is -10.
::答案是 -10

The integer -10 represents the change in the number of yards on each play.
::整数 - 10 表示每场比赛的码数变化。

Example 3
::例3

Divide $\begin{aligned} - 12 \div - 3 \end{aligned}$ .
::分数 - 12 - 3 。

First, divide the absolute value of the factors.
::首先,将因素的绝对值分开。

$\begin{aligned} 12 \div 3 = 4 \end{aligned}$ .

Next, decide on the sign for your quotient. A negative divided by a negative equals a positive, so your quotient is a positive.
::接下来,决定你的商数。负除以负等于正,所以你的商数是正。

$\begin{aligned} - 12 \div - 3 = 4 \end{aligned}$

The answer is 4.
::答案是4。

Example 4
::例4

Divide $\begin{aligned} \frac{18}{- 3} \end{aligned}$ .
::除以18 - 3。

This is the same as $\begin{aligned} 18 \div - 3 \end{aligned}$ .
::这与18+-3相同。

First, divide the absolute value of the factors.
::首先,将因素的绝对值分开。

$\begin{aligned} 18 \div 3 = 6 \end{aligned}$ .

Next, decide on the sign for your quotient. A positive divided by a negative equals a negative, so your quotient is a negative.
::下一个,决定你的商数。正除以负等于负,所以你的商数是负。

$\begin{aligned} 18 \div - 3 = - 6 \end{aligned}$

The answer is -6.
::答案是 -6

Example 5
::例5

Divide $\begin{aligned} - 24 \div 8 \end{aligned}$ .
::分数 - 24 + 8 。

First, divide the absolute value of the factors.
::首先,将因素的绝对值分开。

$\begin{aligned} 24 \div 8 = 3 \end{aligned}$

Next, decide on the sign for your quotient. A negative divided by a positive equals a negative, so your quotient is a negative.
::接下来,决定你的商数。负除以正数等于负数,所以你的商数是负数。

$\begin{aligned} - 24 \div 8 = - 3 \end{aligned}$

The answer is -3.
::答案是 -3

Review
::回顾

Find each quotient.
::找到每个商数。

$\begin{aligned} - 18 \div 6 \end{aligned}$

$\begin{aligned} - 18 \div - 6 \end{aligned}$

$\begin{aligned} 48 \div 8 \end{aligned}$

$\begin{aligned} 64 \div (- 8) \end{aligned}$

$\begin{aligned} - 28 \div (- 4) \end{aligned}$

$\begin{aligned} - 35 \div 7 \end{aligned}$

$\begin{aligned} - 80 \div (- 4) \end{aligned}$

$\begin{aligned} - 50 \div 10 \end{aligned}$

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

$\begin{aligned} 42 \div - 6 \end{aligned}$

$\begin{aligned} - 72 \div 9 \end{aligned}$

$\begin{aligned} - 48 \div - 12 \end{aligned}$

$\begin{aligned} - 16 \div 4 \end{aligned}$

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

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

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

General

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