Section: 基本运算的数值表达式求值 | 1.10基本运算的数值表达式求值

Section outline

Margot volunteers at a local bird sanctuary. She just spent two weeks on vacation, so on her first day back she is talking to her supervisor about what she has missed. When Margot left, there were 256 birds. In her absence, 3 birds have each given birth to 5 baby birds, 2 birds were released into the wild and 3 new injured birds were brought in. How can Margot write an expression to figure out the new sanctuary population?
::Margot自愿者在本地的鸟类保护区。她刚渡假两周, 所以在她刚回来的第一天, 她和她的上司谈论她错过了什么。当Margot离开时, 有256只鸟。在她离开时, 3只鸟每个生了5只小鸟, 2只鸟被放进野生, 3只新受伤的鸟被带进来。 Margot 如何写出一个表达来了解新的保护区人口?

In this concept, you will learn how to evaluate numerical expressions using the four operations .
::在此概念中,您将学习如何使用四个操作来评价数字表达式。

Order of Operations
::行动命令令

An equation is a number sentence that describes two values that are equal to each other. The values are separated by the "equals" sign, e.g. 3 + 4 = 7. In this case, 3 + 4 and 7 are equal entities. Sometimes you will be given an incomplete equation, which you have to "solve" in order to make both sides equal.
::等式是一个数字句, 描述两个对等的值。数值由“ 等值” 符号分隔, 例如 3+ 4 = 7 。在此情况下, 3+ 4 和 7 是等式实体。有时您将得到一个不完整的等式, 您必须“ 解决 ” 才能使两边平等。

An expression is a number sentence without an equals sign. It can be simplified and/or evaluated, but it cannot be "solved".
::表达式是一个没有等号的数句。它可以简化和/ 或评估, 但不能“ 解决 ” 。

Expressions can involve more than one operation , so it is important to know which operation to do first. The tells you the correct order for completing operations within an expression.
::表达式可能涉及不止一个操作, 因此必须先知道要做什么操作。表达式会告诉你在表达式内完成操作的正确顺序。

Order of Operations
::行动命令令

P - " data-term="Parentheses" role="term" tabindex="0"> parentheses
::P - 括号括号

E - exponents
::E. 推举

MD - multiplication or division , in order from left to right
::MD - 乘数或除法,按从左到右顺序排列

AS - addition or subtraction , in order from left to right
::AS - 增加或减减,按从左到右顺序排列

Let's look at an example.
::让我们举个例子。

$\begin{aligned} 4 + 3 \times 5 \end{aligned}$

This is an expression with both addition and multiplication. The order of operations tells you that multiplication comes before addition. So, first multiply and then add.
::这是添加和乘法的表达式。操作的顺序告诉您, 乘法在添加之前就会出现。所以, 首先乘法然后添加。

$\begin{aligned} 4 + 3 \times 5 \\ 4 + 15 \\ 19 \end{aligned}$

When you evaluate this expression correctly, using order of operations, the answer is 19.
::当您正确评价此表达式时, 使用操作顺序, 答案是 19 。

If you had NOT followed the order of operations, and instead evaluated from left to right, it would look like this.
::如果你没有遵循操作顺序, 而是从左到右评估, 它会看起来像这样。

$\begin{aligned} 4 + 3 \times 5 \\ 7 \times 5 \\ 35 \end{aligned}$

You would have gotten an incorrect answer. That is why it is important to always follow the order of operations.
::你会得到一个错误的答案,这就是为什么必须始终按照行动顺序行事。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Margot and her bountiful birds.
::之前,你得到一个问题关于玛戈特和她的丰盛鸟。

Margot needs to write and evaluate an expression to see how the original population of 256 has changed since 3 birds each gave birth to 5 baby birds, 2 birds were released, and 3 injured birds were brought in.
::Margot需要写作和评估表达方式, 看看256人的原人口是如何变化的, 因为每只鸟有3只鸟生了5只小鸟, 2只鸟被释放, 3只受伤的鸟被带进来。

First, identify the important information in the problem.
::首先,查明问题的重要信息。

256 birds to start
::256只鸟开始

3 birds have 5 babies each
::3只鸟,3只鸟,每只有5个婴儿

2 birds released
::释放了2只鸟

3 birds added
::新增3只鸟

Next, write this as an expression.
::下一个,写成表达式。

$\begin{aligned} 256 + 3 \times 5 - 2 + 3 \end{aligned}$

Then, use order of operations to evaluate the expression.
::然后,使用操作顺序来评价表达式。

$\begin{aligned} 256 + 3 \times 5 - 2 + 3 & Multiply 3 \times 5 \\ 256 + 15 - 2 + 3 & Add 256 + 15 \\ 271 - 2 + 3 & Subtract 271 - 2 \\ 269 + 3 & Add 269 + 3 \\ 272 \end{aligned}$

The answer is 272.
::答案是272号

Margot’s sanctuary now has 272 birds.
::Margot的避难所现在有272只鸟。

Example 2
::例2

Evaluate the expression using order of operations.
::使用操作顺序对表达方式进行评估。

$\begin{aligned} 6 + 8 \times 4 - 11 + 6 = \underline{} \end{aligned}$

First, complete the multiplication from left to right.
::首先,完成从左向右的乘法。

$\begin{aligned} 6 + 32 - 11 + 6 \end{aligned}$

Then, complete the addition and subtraction from left to right.
::然后,完成加法和减法,然后从左向右减法。

$\begin{aligned} 6 + 32 - 11 + 6 \\ 38 - 11 + 6 \\ 27 + 6 \\ 33 \end{aligned}$

The answer is 33.
::答案是33岁

Example 3
::例3

Evaluate the following expression.
::评估以下表述。

$\begin{aligned} 8 - 1 \times 4 + 3 = \underline{} \end{aligned}$

First, perform the multiplication:
::首先,执行乘法:

$\begin{aligned} 8 - 1 \times 4 + 3 & Multiply 1 \times 4 = 4 \\ 8 - 4 + 3 \end{aligned}$

Next, add and subtract from left to right:
::下一步,从左向右增减:

$\begin{aligned} 8 - 4 + 3 & Subtract 8 - 4 = 4 \\ 4 + 3 & Add 4 + 3 = 7 \\ 7 \end{aligned}$

The solution is 7.
::解决办法是7。

Example 4
::例4

Evaluate the following expression.
::评估以下表述。

$\begin{aligned} 5 + 9 \times 3 - 6 + 2 = \underline{} \end{aligned}$

First, perform multiplication and division from left to right:
::首先,从左向右进行乘法和分法:

$\begin{aligned} 2 \times 6 + 8 \div 2 & Multiply 2 \times 6 \\ 12 + 8 \div 2 & Divide 8 \div 2 \\ 12 + 4 \end{aligned}$

Next, add:
::下加:

$\begin{aligned} 12 + 4 & Add 12 + 4 \\ 16 \end{aligned}$

The answer is 16.
::答案是16岁

Example 5
::例5

Evaluate the following expression.
::评估以下表述。

$\begin{aligned} 5 + 9 \times 3 - 6 + 2 = \underline{} \end{aligned}$

First, perform multiplication and division from left to right:
::首先,从左向右进行乘法和分法:

$\begin{aligned} 5 + 9 \times 3 - 6 + 2 & Multiply 9 \times 3 \\ 5 + 27 - 6 + 2 \end{aligned}$

Next, add and subtract from left to right:
::下一步,从左向右增减:

$\begin{aligned} 5 + 27 - 6 + 2 & Add 5 + 27 \\ 32 - 6 + 2 & Subtract 32 - 6 \\ 26 + 2 & Add 26 + 2 \\ 28 \end{aligned}$

The answer is 28.
::答案是28岁

Review
::回顾

Evaluate each expression according to the correct order of operations.
::按照正确的操作顺序对每种表达方式进行评估。

$\begin{aligned} 2 + 3 \times 4 + 7 = \underline{} \end{aligned}$

$\begin{aligned} 4 + 5 \times 2 + 9 - 1 = \underline{} \end{aligned}$

$\begin{aligned} 6 \times 7 + 2 \times 3 = \underline{} \end{aligned}$

$\begin{aligned} 4 \times 5 + 3 \times 1 - 9 = \underline{} \end{aligned}$

$\begin{aligned} 5 \times 3 \times 2 + 5 - 1 = \underline{} \end{aligned}$

$\begin{aligned} 4 + 7 \times 3 + 8 \times 2 = \underline{} \end{aligned}$

$\begin{aligned} 9 - 3 \times 1 + 4 - 7 = \underline{} \end{aligned}$

$\begin{aligned} 10 + 3 \times 4 + 2 - 8 = \underline{} \end{aligned}$

$\begin{aligned} 11 \times 3 + 2 \times 4 - 3 = \underline{} \end{aligned}$

$\begin{aligned} 6 + 7 \times 8 - 9 \times 2 \end{aligned}$

$\begin{aligned} 3 + 4^{2} - 5 \times 2 + 9 = \underline{} \end{aligned}$

$\begin{aligned} 2^{2} + 5 \times 2 + 6^{2} - 11 = \underline{} \end{aligned}$

$\begin{aligned} 3^{2} \times 2 + 4 - 9 = \underline{} \end{aligned}$

$\begin{aligned} 6 + 3 \times 2^{2} + 7 - 1 = \underline{} \end{aligned}$

$\begin{aligned} 7 + 2 \times 4 + 3^{2} - 5 = \underline{} \end{aligned}$

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

Order of Operations ::行动命令令

Order of Operations ::行动命令令

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

Order of Operations
::行动命令令

Order of Operations
::行动命令令

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