解决增加和减法等量

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It’s Elemental
::它是元素

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The periodic table is a visual display of all the known elements. The elements are the many types of atoms that make up everything in the universe. Each element has specific properties that determine whether it is a metal, explosive, heavy, a gas, etc., but nearly all of these properties can be explained using mathematical reasoning based on the number of protons, neutrons, and electrons the atom has. The protons and neutrons make up nearly all of the mass of the atom. By looking at an element’s card in the periodic table,  you can determine the mass, the number of protons, and the number of neutrons that the average atom of that element will have.
::周期表是所有已知元素的视觉显示。 元素是构成宇宙万物的多种原子类型。 每个元素都有具体属性, 确定它是金属、 炸药、 重物、 气体等, 但几乎所有这些属性都可以根据质子、 中子和原子拥有的电子数量进行数学推理解释。 质子和中子几乎构成原子的所有质量。 通过在周期表中查看元素的卡片, 您可以确定元素的平均原子数量、质子数量和中子数量。

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The atomic number represents the number of protons, and the mass number represents the total number of protons and neutrons in the typical gold atom. 
::原子数代表质子数,质子数代表典型金原子质子和中子总数。

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Discussion Question
::讨论问题

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How many neutrons does the atom in the picture have?
::照片中的原子有多少个中子?

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Understanding Addition Equations
::" 理解增加等同 " 组织

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To  answer the question above, you will need some understanding of what an addition equation is and how it operates. A smaller element, lithium, is displayed below.
::为回答上述问题,您需要了解添加方程式是什么及其运作方式。下文将显示一个较小的元素,即锂。

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The typical l ithium element has 3 protons and 7 total protons and neutrons.  You can represent this relationship using an equation:
::典型的锂元素有3个质子和7个总质子和中子。您可以用一个方程式来表示这种关系:

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$$\begin{align*}\text{Protons } + \text{ Neutrons } & = \text{ Mass Number}\\ \large{P ~~~ + ~~~~ N~~~~~}& ~ \large{ = ~~~~~~M}\end{align*}$$
::质子+中子=质量数P+N=M

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S ubstitute your known values to produce the following:
::以您已知的数值替代以下数值:

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$$\begin{align*}\large{3 + N = 7}\end{align*}$$
::3+N=7

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In the interactive, solve for the number of neutrons in this equation by finding which numbers will keep the equation balanced.
::在互动中,通过找到哪些数字能保持方程平衡,解决中子数在这个方程中的问题。

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It’s Elemental Continued
::它的元素延续

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The idea of balance is important when solving equations because an equation is a statement of equality. Whatever you do to one side of the equation, you must do to the other side to keep the equation equal. Adding 5 to one side of the equation but not the other will result in two different values, one of which will always be 5 more than the other.
::平衡的理念在解答方程式时很重要, 因为方程式是平等声明。 无论您对方程式的一边做什么, 您都必须对另一方做什么才能保持等式等式的等式等式。 在方程式的一边加上 5 而不是 另一方将导致两个不同的值, 其中之一总是比另一边多 5 。

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You can display this idea visually by showing the operation performed on both sides of an equation. U se this to answer the question  from the opening activity.
::您可以通过显示方程式两侧的操作来直观地显示这个想法。使用它来回答从开始活动中提出的问题。

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Example
::示例示例示例示例

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A typical gold atom has 79 protons and 197 total protons and neutrons. How many neutrons does the atom have?
::典型的金原子有79个质子和197个质子和中子。原子有多少个中子?

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You  can model this with the equation:
::您可以用方程式模拟这个模式 :

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$$\begin{align*}x + 79 = 197\end{align*}$$
::x+79=197

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Take the 79 away from both sides to isolate the variable .
::将79人从两边带走 隔离变量

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$$\begin{align*}x + 79 &= 197 \\ -79 &\:\:\: - \! 79 \\ \hline x &= 118\end{align*}$$
::x+79=197-79-79x=118

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Answer: The typical gold atom has 118 neutrons.
::答复:典型的金原子有118个中子。

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This number of neutrons is considered to be a relatively large amount and explains why gold is one of the heaviest elements. One bar of gold weighs about 27 pounds!
::这种中子的数量被认为是一个相对较大的数量,这解释了为什么金子是最重的元素之一。 有一块金子的重量约为27磅! !

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In the next interactive, use subtraction on both sides of the equation to solve for the number of neutrons in each element.
::在下一次互动中,在方程两侧使用减法解决每个元素的中子数。

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Subtraction Equations
::减减法等量

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Another type of one-step equation involves subtraction. While the operation looks different, the relationship between addition and subtraction uses the same strategy. To remove a number from one side of an equation, use the additive inverse . The additive inverse  is the number that when added to the original number will produce zero. Additive inverse is another word for opposite. 
::另一类单步方程则涉及减法。 虽然操作看起来不同, 增减之间的关系使用相同的策略。 要从方程的一边删除数字, 请使用添加反转。 添加反比是加入原数后产生的数字为零。 增减反比是另一个相反的单词 。

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This interactive will help you visualize the additive inverse of integers .
::此互动会帮助您将添加值反向整数图像化 。

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An operation used to cancel a number is called an inverse operation . Inverse operations are operations that undo each other. Inverse operations will be an important concept as  you move forward in equations.  
::用于取消一个数字的操作被称为反向操作。反向操作是相互折叠的操作。反向操作将是一个重要的概念,因为您在方程式中向前移动。

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When  you use the additive inverse to cancel a number on one side of the equation,  you need to do it to the other side to keep the equation equal. In the following interactive, use inverse operations to balance and solve the subtraction equations.
::当您使用复数反转来取消方程式一面的编号时,您需要将其切换到另一侧才能保持方程式相等。在接下来的互动中,使用反向操作来平衡和解析减法方程式。

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Discussion Question
::讨论问题

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Why do the inverse operations of addition and subtraction undo each other?
::为什么增加和减法的逆向操作会相互抵消呢?

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Example
::示例示例示例示例

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In business, the equation  $\begin{align*}Revenue \:– \:Expenses = Profit\end{align*}$  is used to calculate profit. However, given any two of these three values,  you can figure out the missing value.
::在商业中,收入 - 支出=利润的等式被用来计算利润。 但是,考虑到这三点中的任何一个值,你可以找出缺失的价值。

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A company will have $280,000 in expenses this year and hopes to earn $250,000 in profit. How much revenue will they need to earn to achieve their goal?
::一家公司今年将有280,000美元的开支,并希望赚取250,000美元的利润。 他们需要赚取多少收入来实现其目标?

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S ubstitute the known values into the equation above :
::在上述方程中替换已知值:

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  •  Revenue:  $\begin{align*}x\end{align*}$
::• 收入:x

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  •   Expenses: 280,000
::• 支出:280 000美元

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  •   Profit: 250,000
::• 利润:250 000美元

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$$\begin{align*}x - 280,000 = 250,000\end{align*}$$
::x-280,000=250,000

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In the equation, 280,000 is being subtracted from the variable . To isolate the variable,  you will need to do the opposite of subtracting 280,000, which is adding 280,000. T o keep the equation balanced,  you must add 280,000 to both sides.
::在方程中, 280,000 正在从变量中减去 280,000 。 要分离变量, 您需要做减去280,000 的相反操作, 即增加280,000 。 要保持方程平衡, 您必须在两边加上280,000 。

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$$\begin{align*}x - 280,000 &= 250,000 \\ + 280,000 &\:+ 280,000 \\ \hline x &= 530,000\end{align*}$$
::x-280,000=250,000+280,000+280,000x=530,000

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Answer: The company must earn $530,000 in revenue to have a profit of $250,000.
::答复:公司必须赚取530 000美元的收入,才能获利250 000美元。