Course: 3.1 类似术语的合并-interactive

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将类似术语合并

In This Lesson
::在本课程中

The language of Algebra is pretty specific. It is important to understand how each of the parts of a statement is described so you can clearly explain a situation vocabulary in a way that others can follow. The words e quation, expression , term , variable , coefficient , and constant each have specific meanings and are related in specific ways. The diagram below helps explain the relationships.
::代数的语言非常具体。重要的是要理解对语句中每个部分的描述方式, 以便您能够以其他人可以遵循的方式明确解释一个情况词汇。等式、表达式、任期、可变、系数和恒定等字都有具体的含义, 并以具体的方式相关。下面的图表有助于解释各种关系。

Algebra terms: equation, expression, term, variable, coefficient, and constant.

$\begin{aligned} - 5 r + 23 \end{aligned}$ is an expression with variable $\begin{aligned} r, \end{aligned}$ coefficient of -5, and a constant of 23.
::-5r+23是变量r的表达式,系数为5,常数为23。

$\begin{aligned} 3 x - 5 = 10 \end{aligned}$ is an example of an equation .
::3x-5=10 是方程式的一个例子。

Quick Sort!
::快速排序 !

In this interactive, you will sort the equations, expressions, variables, and constants in the box into the correct columns.
::在此互动中,您将把框中的方程式、表达式、变量和常数排序到正确的列中。

INTERACTIVE

Sort It Out

Move and sort the texts into the correct boxes.
::将文字移到正确的框中。

Here you discovered that variables can be added to each other. It is very important to note that if the variables are different, they cannot be added . For example, $\begin{aligned} a + b \neq a b \end{aligned}$ because $\begin{aligned} a b = a \times b . \end{aligned}$ $\begin{aligned} a + b \end{aligned}$ cannot be simplified and should be left as is.
::在此您发现变量可以相互添加。必须指出, 如果变量不同, 则不能添加变量。例如, a+bab 因为 ab=axb. a+b 不能简化, 并且应该保持原样。

Simplifying Variable Expressions
::简化变量表达式

When adding expressions with variables, you can combine like terms . Each of the rectangles has one side length as $\begin{aligned} x, \end{aligned}$ so their terms can be added or subtracted. The blue rectangle represents $\begin{aligned} 7 x . \end{aligned}$
::在用变量添加表达式时,可以将类似术语组合在一起。每个矩形的侧长为 x,这样它们的用词可以被添加或减去。蓝色矩形代表 7x。

INTERACTIVE

Simplifying Variable Expressions

Drag the tiles on the right into the gray square.
::将右侧的瓷砖拖到灰方。

Click on the tiles to change between addition and subtraction.
::单击牌可在加减之间更改。

Observe how all the like terms in the gray square can be simplified into the orange tile below.
::观察灰色广场上的所有类似术语如何简化为橙色瓷砖

Discussion Question
::讨论问题

Sometimes variables can have exponents, like $\begin{aligned} x^{2} \end{aligned}$ . Do you think you could add $\begin{aligned} 7 x + x^{2} \end{aligned}$ to get $\begin{aligned} 8 x^{2} ? \end{aligned}$
::有时变量可以有指数, 如 x2 。您认为您可以添加 7x+x2 来获得 8x2 吗 ?

Remember that you cannot add together two different variables, nor two variables that are the same but have different exponents.
::记住,您不能将两个不同的变量加在一起,也不能将两个相同但有不同指数的变量加在一起。

Math Burgers
::数学汉堡

Your family really wants to try out the new burger place in town, Math Burger. They do things a little differently there. Check the menu:
::你的家人真的想试试镇上的新汉堡店,马特汉堡店。他们做的有点不同。看看菜单:

Food Item	Small	Medium	Large
Cheeseburger	$\begin{aligned} 1 / 2 c \end{aligned}$ (kid's burger)	$\begin{aligned} c \end{aligned}$	N/A
Fries	$\begin{aligned} f \end{aligned}$	$\begin{aligned} f^{2} \end{aligned}$	$\begin{aligned} f^{3} \end{aligned}$
Drink	$\begin{aligned} d \end{aligned}$	$\begin{aligned} d^{2} \end{aligned}$	$\begin{aligned} d^{3} \end{aligned}$

Your family's order is below:
::你们家的秩序如下:

Dad: $\begin{aligned} 2 c, \end{aligned}$ $\begin{aligned} d^{2}, \end{aligned}$ and $\begin{aligned} f^{3} \end{aligned}$
::父亲: 2c, d2, f3

Mom: $\begin{aligned} c, \end{aligned}$ $\begin{aligned} d, \end{aligned}$ and $\begin{aligned} f^{2} \end{aligned}$
::母亲:c、d和f2

Billy (brother): $\begin{aligned} c, \end{aligned}$ $\begin{aligned} \frac{1}{2} c, \end{aligned}$ $\begin{aligned} d^{3}, \end{aligned}$ and $\begin{aligned} f^{3} \end{aligned}$
::比利(兄弟):c、12c、d3和f3

Sally (little sister): $\begin{aligned} \frac{1}{2} c, \end{aligned}$ $\begin{aligned} d, \end{aligned}$ and $\begin{aligned} f \end{aligned}$
::萨利(小妹妹):12c、d和f

You: $\begin{aligned} c, \end{aligned}$ $\begin{aligned} d^{2}, \end{aligned}$ and $\begin{aligned} f \end{aligned}$
::你: c, d2, f

H ow many of each item does your family order all together?
::你们家的每件东西一共有多少件?

In the interactive below, sort the burgers, drinks, and fries in the spaces below. Within each space, sort the drinks and fries further, such that you know how many of each type there are.
::在下面的交互中, 排序汉堡、饮料和薯条在下面的空间。在每一个空间里, 进一步排序饮料和薯条, 以便您知道每种类型中有多少。

What's a half burger plus a half burger? Keep that in mind as you sort.
::半个汉堡加半个汉堡是什么?

INTERACTIVE

Math Burgers

Move the food to the appropriate region.
::将食物转移到适当的地区。

Discussion Question
::讨论问题

How would you use what you learned to simplify $\begin{aligned} \frac{5}{4} r - \frac{1}{2} + 2 r + 4 ? \end{aligned}$
::您将如何使用您所学的知识来简化 54r - 12+2r+4 ?

Summary
::摘要

A constant is a number within an expression.
::常数是一个表达式中的数。

A variable is a letter used to represent an unknown value.
::变量是指用于表示未知值的字母。

An expression is any combination of constants, variables and operators. Sometimes variables have coefficients or numbers in front of it.
::表达式是指常数、变量和运算符的任何组合。有时变量前面有系数或数字。

An equation is two expressions with an equal sign between them.
::等式是两个表达式,它们之间的符号相同。

When combining like terms, group together the constants and variables with the same letter. To add or subtract like terms, variables must have the same exponent and letter.
::当合并类似条件时, 将常数和变量组合在一起, 并用相同字母。要增减类似条件, 变量必须具有相同的指数和字母。

Section outline

General

将类似术语合并

In This Lesson ::在本课程中

Quick Sort! ::快速排序 !

Simplifying Variable Expressions ::简化变量表达式

Math Burgers ::数学汉堡

Summary ::摘要

In This Lesson
::在本课程中

Quick Sort!
::快速排序 !

Simplifying Variable Expressions
::简化变量表达式

Math Burgers
::数学汉堡

Summary
::摘要