Course: 7.7 乘法和除法用语作为等同

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乘数和除法用词法作为等同

There is a bunny population behind Ishmael’s house. Ishmael is helping the local park ranger track the population numbers. At the start of July there are 127 females. By the end of the month, Ishmael and the ranger count 415 new bunnies. What is the average number of bunnies that each female had during that time? How can Ishmael write an equation that shows this situation?
::Ishmael正在帮助当地的公园护林员追踪人口数量。 7月初,有127名女性。到月底,Ishmael和护林员数了415个新兔子。在此期间,每个女性的平均兔子数量是多少? Ishmael如何写出一个反映这种情况的方程式?

In this concept, you will learn how to write multiplication and division phrases as single variable equations.
::在此概念中,您将学习如何将乘数和除法短语写成单变量方程式。

Writing Multiplication and Division Phrases as Equations
::乘法和除法用词法作为等式

Just as you can write addition and subtraction expressions from words or phrases, you can also write multiplication and division expressions. You can use key words to help you with this. The more familiar you become with the key words that identify a multiplication or division expression , the better you will become at writing expressions.
::正如您可以从文字或短语中写入添加和减减表达式,您也可以写出乘法和除法表达式。您可以使用关键词来帮助您。您越熟悉识别乘法或除法表达式的关键词,写法表达式时您就会越好。

Here are some phrases that can be translated into multiplication or division expressions.
::这里有些短语可以翻译成乘数或除法表达式。

Multiplication Phrases		Division Phrases
9 times $\begin{aligned} k \end{aligned}$	$\begin{aligned} 9 \times k \end{aligned}$ or $\begin{aligned} 9 k \end{aligned}$	8 divided into $\begin{aligned} n \end{aligned}$ groups	$\begin{aligned} 8 \div n \end{aligned}$ or $\begin{aligned} \frac{8}{n} \end{aligned}$
twice as much as $\begin{aligned} m \end{aligned}$	$\begin{aligned} 2 \times m \end{aligned}$ or $\begin{aligned} 2 m \end{aligned}$	$\begin{aligned} q \end{aligned}$ shared equally by 3 people	$\begin{aligned} q \div 3 \end{aligned}$ or $\begin{aligned} \frac{q}{3} \end{aligned}$
		half of $\begin{aligned} r \end{aligned}$	$\begin{aligned} r \div 2 \end{aligned}$ or $\begin{aligned} \frac{r}{2} \end{aligned}$
		one-third of $\begin{aligned} p \end{aligned}$	$\begin{aligned} p \div 3 \end{aligned}$ or $\begin{aligned} \frac{p}{3} \end{aligned}$

Remember, these words are only a helpful guide. You should always think about which operation makes sense for a particular situation.
::记住,这些文字只是个有用的指南。你应该总是想一想哪一种操作对特定情况有意义。

Let’s look at an example.
::让我们举个例子。

Write an algebraic expression to represent the phrase “three times a number, $\begin{aligned} t \end{aligned}$ .”
::写一个代数表达式,以表示“3乘以数字, t”。

Use a number, an operation sign, or a variable to represent each part of the phrase.
::使用数字、操作符号或变量代表短语的每个部分。

First, consider the phrase and look for key terms .
::首先,考虑这一短语并寻找关键术语。

three times a number, $\begin{aligned} t \end{aligned}$
::3乘以3个数字, t

Next, rewrite the phrase using numbers and operations .
::接下来,用数字和操作重写该短语。

$\begin{aligned} 3 \times t \end{aligned}$
::3x吨

Then, simplify the expression.
::然后,简化表达方式。

$\begin{aligned} 3 t \end{aligned}$
::3吨

The phrase is represented by the expression $\begin{aligned} 3 t \end{aligned}$ .
::该短语由3t表达式表示。

Here is another example.
::下面是另一个例子。

Mr. Warren separated 30 students into $\begin{aligned} n \end{aligned}$ equal groups. Write an algebraic expression to represent the number of students in each group.
::Warren先生将30名学生隔离为n等分组,写代数表示表示每个组的学生人数。

First, consider the phrase and look for key terms.
::首先,考虑这一短语并寻找关键术语。

30 students into $\begin{aligned} n \end{aligned}$ equal groups
::30名学生进入n平等群体

Separating 30 students into $\begin{aligned} n \end{aligned}$ equal groups means dividing 30 students into $\begin{aligned} n \end{aligned}$ equal groups.
::将30名学生分为n等组,意味着将30名学生分为n等组。

Next, write a division expression.
::下一位,写一个分隔表达式。

$\begin{aligned} \frac{30}{n} \end{aligned}$
::30n 30n

The phrase is represented by the expression $\begin{aligned} \frac{30}{n} \end{aligned}$ .
::该短语用30n表示。

When an expression equals something it is an equation. If the number of students in each group needed to be five, for instance, you could write the following equation.
::当表达式等于某物时,这是一个等式。例如,如果每个组的学生人数需要为5人,您可以写下一个等式。

$\begin{aligned} n = 5 \end{aligned}$
::n=5

Then, you could evaluate the expression $\begin{aligned} \frac{30}{n} \end{aligned}$ using the given variable 5.
::然后,您就可以使用给定变量5来评估表达式 30n。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Ishmael’s local bunnies.
::更早之前, 伊什梅尔在当地的兔子给您带来麻烦。

There are 127 females and 415 bunnies. Ishmael needs to write an equation that represents the average number of bunnies each female had.
::有127名女性和415名兔子,Ishmael需要写一个方程式,代表每个女性的兔子平均数量。

First, let $\begin{aligned} n \end{aligned}$ be the average number of bunnies per female.
::首先,不要成为每名女性的兔子平均数量。

$\begin{aligned} 127 n \end{aligned}$
::127n 127n

This is the total number of bunnies in the population.
::这就是人口中兔子的总数。

Then, because you know there are 415 bunnies, you can write an equation.
::然后,因为你知道有415只兔子, 你可以写一个方程。

$\begin{aligned} 127 n = 415 \end{aligned}$
::127n=415

Example 2
::例2

Write a single variable equation for the following phrase.
::为以下短语写入单个变量方程式。

Keith bought tickets to the movies. The tickets were $8.50 each. Keith spent a total of $34.00. How many tickets did Keith buy?
::Keith购买了电影票,每张票是8.50美元。Keith总共花了34美元。Keith买了几张票?

First, let $\begin{aligned} t \end{aligned}$ represent the number of tickets that Keith bought.
::首先,让我们来说明一下基思买的票数。

The cost of each ticket is $8.50. The total price of the tickets will be the number of tickets, represented by $\begin{aligned} t \end{aligned}$ , times the price of each ticket.
::每张票价为8.50美元,总价为每张票价乘以2乘以2的票价。

Next, write an expression that represents this.
::下一个,写一个表达式来代表这个。

$\begin{aligned} 8.5 t \end{aligned}$
::8.5t

Then, because you know the total cost of the tickets was $34.00, write an equation.
::然后,因为你知道总票价是34.00美元, 写一个方程。

$\begin{aligned} 8.5 t = 34.00 \end{aligned}$
::8.5t=34.00

Write a multiplication or division equation for the following phrases.
::下列短语的乘法或除法方程写成。

Example 3
::例3

Four times a number is eight.
::4乘以一个数字是8。

Let $\begin{aligned} x \end{aligned}$ be “a number.”
::让 x 成为“ 数字 ” 。

“Times” means multiplication and “is” means equals.
::“时间”是指乘法,“是”指等同。

The answer is $\begin{aligned} 4 x = 8 \end{aligned}$ .
::答案是4x=8

Example 4
::例4

Sixteen candles divided into a number of piles is two candles in each pile. Let $\begin{aligned} x \end{aligned}$ be the number of piles.
::16根蜡烛分成几堆,每堆有两根蜡烛。

“Divided into” means division but be careful about the order , and “is” means equals.
::“分而治之”意指分裂,但注意秩序,“是”意指平等。

The answer is $\begin{aligned} \frac{16}{2} = 2 \end{aligned}$ .
::答案是162=2

Example 5
::例5

The product of five and a number is fifteen.
::5和15的产物。

Let $\begin{aligned} x \end{aligned}$ be “a number.”
::让 x 成为“ 数字 ” 。

“Product” means you are multiplying, and “is” means equals.
::“生产”是指乘以,“是”指等量。

The answer is $\begin{aligned} 5 x = 15 \end{aligned}$ .
::答案是5x15=15

Review
::回顾

Write an equation for each phrase.
::每个词组写一个方程。

The product of four and a number is twelve.
::4个和1个数的产物是12个。

Six times a number is thirty.
::6倍一个数字是30。

Twelve times a number is forty-eight.
::12乘以一个数字是48

Fourteen times a number is twenty-eight.
::14乘以一个数字是28。

The product of five and a number is thirty.
::5和数是30的产物。

Eight times a number is sixty-four.
::数字的八倍是六十四

Twenty divided by a number is four.
::20除以一个数字是4。

Eighty divided by a number is four.
::80除以一个数字是4。

Nineteen times an unknown number is ninety-five.
::一个未知数字的19次是95次。

Thirteen times an unknown number is thirty-nine.
::13次未知数字是39次。

Twelve divided into groups is six.
::十二人分成六组

An unknown number divided by two is eight.
::未知数字除以2除以2是8。

An unknown number divided by seven is fourteen.
::未知数字除以7除以7是14。

An unknown number times five is thirty-five.
::未知数字乘以5是35。

An unknown number divided by twelve is twelve.
::未知数字除以12是12。

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。

Section outline

General

乘数和除法用词法作为等同

Writing Multiplication and Division Phrases as Equations ::乘法和除法用词法作为等式

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