Course: 1.15描述模式的词汇

Section outline

Select section General

Collapse Expand
General

Collapse all Expand all
- Select activity 新闻通告
  
  新闻通告 Forum
Select section 描述模式的词汇

Collapse Expand
描述模式的词汇
Wyatt was hanging out at the mall when a woman walking by dropped her purse, scattering coins all over the ground. Wyatt rushed over to help. He picked up 30 pennies, 15 nickels, 10 dimes, and 13 quarters and returned them to the grateful woman. In order to tell his parents the story at dinner, Wyatt wants to figure out exactly how much money he helped the woman collect. He could go through and add all the coin values together, but is there an easier way for Wyatt to figure out the total value of the coins?
::怀亚特在商场闲逛时，一个路过的女人掉了钱包，硬币撒了一地。怀亚特冲过去帮忙。他捡起30枚1分硬币、15枚5分硬币、10枚10分硬币和13枚25美分硬币，把它们还给了那位感激涕零的女士。为了在晚餐时告诉他的父母这个故事，怀亚特想弄清楚他到底帮那个女人筹集了多少钱。他可以把所有硬币的价值加起来，但对于怀亚特来说，有没有更简单的方法来算出硬币的总价值呢？

In this concept, you will learn how to use expressions to solve real-world problems.
::在这个概念中,你将学会如何使用表达方式来解决现实世界的问题。

Describing Patterns
::描述模式

Sometimes you will need to create your own variable expressions in order to solve problems. Consider this real-world problem that can be written as a variable expression :
::有时您需要创建您自己的变量表达式来解决问题。将这个可以写成变量表达式的真实世界问题 :

Joanne has a pile of nickels and a pile of dimes. She counts her money and discovers that she has 25 nickels and 36 dimes. How much money does Joanne have in total?
::Joanne有一堆硬币和一堆硬币。她数了自己的钱,发现她有25个硬币和36个硬币。乔安妮总共有多少钱?

First, underline all of the important information in the problem.
::首先,强调这一问题的所有重要信息。

Joanne has a pile of nickels and a pile of dimes. She counts her money and discovers that she has 25 nickels and 36 dimes. How much money does Joanne have in total?
::Joanne有一堆硬币和一堆硬币。她数了自己的钱,发现她有25个硬币和36个硬币。乔安妮总共有多少钱?

A nickel is 5 cents; use decimal .05 to show that amount in dollars.
::镍为5美分;小数点为0.05,以美元表示这一数额。

A dime is 10 cents; use decimal .10 to show that amount in dollars.
::一分钱为10美分;用小数点10表示美元。

Next, write an expression with variables.
::下一步,用变量写一个表达式。

$\begin{aligned} .05 x + .10 y \end{aligned}$

The $\begin{aligned} x \end{aligned}$ represents the number of nickels, and the $\begin{aligned} y \end{aligned}$ represents the number of dimes. The expression $\begin{aligned} .05 x + .10 y \end{aligned}$ represents the total amount of money, in dollars, there would be with $\begin{aligned} x \end{aligned}$ nickels and $\begin{aligned} y \end{aligned}$ dimes.
::x 表示镍的数量,y 表示硬币的数量。 0. 05 x + 10 y 表示货币总额, 以美元计, 将使用x 镍和 y 美分。

In this case, you have been given the number of dimes and nickels. Substitute those values into your expression for $\begin{aligned} x \end{aligned}$ and $\begin{aligned} y \end{aligned}$ .
::在此情况下, 您已经得到了硬币和硬币的数量。将这些值替换为 x 和 y 的表达式。

$\begin{aligned} .05 (25) + .10 (36) \end{aligned}$

Next, evaluate the expression.
::接下来,评价表达式。

$\begin{aligned} 1.25 + 3.60 = 4.50 \end{aligned}$

The answer is $4.50.
::答案是4.50美元。

By changing the format of the coin value to decimal values of a dollar, the answer can be seen in dollars. It is much easier to think about the answer as $4.50, than 450 cents!
::通过将硬币值格式改变为美元十进制值,答案可以用美元表示。将答案想象成4.50美元比450美分容易得多!

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Wyatt and his good deed.
::早些时候,有人给了你一个问题关于Wyatt和他的善行。

Wyatt needs to figure out the total value of all the coins he collected: 30 pennies, 15 nickels, 10 dimes and 13 quarters.
::Wyatt需要弄清楚他收集的所有硬币的总价值: 30便士、15便士、10便士和13季度。

First, write an expression.
::首先,写一个表达方式。

$\begin{aligned} .01 a + .05 b + .10 c + .25 d \end{aligned}$

The coin values are written here as decimal values of a dollar: .01 is a penny, .05 is a nickel, .10 is a dime, and .25 is a quarter. This is important as it allows you to consider the different coins on the same scale. It will also means the final answer will be in dollars.
::硬币值在此以美元小数值写成 : . 01 是便士, 0. 05 是镍, 0. 10 是便士, 0. 25 是四分之一。这很重要, 因为它允许您考虑同一比例的不同硬币。这也意味着最终答案将以美元表示。

Next, substitute the given values for the variables.
::接下来,将给定值替换为变量。

$\begin{aligned} .01 (30) + .05 (15) + .10 (10) + .25 (13) \end{aligned}$

Then, follow to multiply and then add.
::然后,你顺其自然,然后,你应当增加,然后,你应当增加。

$\begin{aligned} .01 (30) + .05 (15) + .10 (10) + .25 (13) \\ .30 + .75 + 1.0 + 3.25 \\ 5.30 \end{aligned}$

The answer is $5.30.
::答案是5.30美元。

Wyatt can tell his parents that he helped the woman collect 5 dollars and 30 cents.
::Wyatt可以告诉他的父母他帮助那女人赚了5美元30美分

Example 2
::例2

Write an expression for this word problem and evaluate.
::为这个单词问题写一个表达式并进行评估。

Imagine that you have found a pile of money in a drawer. There are 10 nickels, 5 dimes and 15 quarters. What is the total sum of money you have found?
::想象一下,你在一个抽屉里发现了一大笔钱。有10分,5分,15分。你发现的钱总额是多少?

First, write an expression. Because you are working with money, it can be helpful to express all different coins as decimal values of a dollar. This means nickels are .05, dimes are .10 and quarters are .25. Write an expression using $\begin{aligned} n \end{aligned}$ to represent the number of nickels, $\begin{aligned} d \end{aligned}$ to represent the number of dimes , and $\begin{aligned} q \end{aligned}$ to represent the number of quarters .
::首先, 写一个表达式。因为您正在用金钱工作, 将所有不同的硬币以美元的小数值表示是有用的。这意味着镍值为 . 05, 硬币值为 10, 硬币值为 .25。写一个表达式, 用 n 表示镍的数量, d 表示硬币的数量, q 表示季度的数量。

$\begin{aligned} .05 n + .10 d + .25 q \end{aligned}$

Next, substitute the numbers of each coin for the variables. There are 10 nickels, 5 dimes and 15 quarters.
::接下来,用每个硬币的数来代替变量。有10个硬币,5个硬币,15个季度。

$\begin{aligned} .05 (10) + .10 (5) + .25 (15) \end{aligned}$

Then, follow order of operations to evaluate the expression.
::然后按照操作顺序来评价表达方式。

$\begin{aligned} .50 + .50 + 3.75 \end{aligned}$

The answer is 4.75. You found $4.75.
::答案是4.75美元你找到了4.75美元

Example 3
::例3

If you have 6 nickels and five dimes, what is the sum?
::如果你有6分5分,那多少钱?

First, write an expression using a variable, like $\begin{aligned} n \end{aligned}$ , to represent the number of nickels, and different variable, like $\begin{aligned} d \end{aligned}$ , to represent the number of dimes. Multiply the number of nickels by 0.05, and the number of dimes by 0.10.
::首先,写一个表达式,用一个变量,例如 n,来表示镍的数量,用不同的变量,例如 d,来表示硬币的数量。将镍的数量乘以 0.05, 硬币的数量乘以 0.10。

$\begin{aligned} .05 n + .10 d \end{aligned}$

Then, substitute the given number of each coin in place of the correct variable.
::然后,以每个硬币的给定数目代替正确的变量。

$\begin{aligned} .05 n + .10 d \\ .05 (6) + .10 (5) \end{aligned}$

Finally, simplify the expression using the correct order of operations by multiplying and then adding.
::最后,使用正确的操作顺序,通过乘法和加法简化表达式。

$\begin{aligned} .05 (6) + .10 (5) \\ .30 + .50 \\ .80 \end{aligned}$

The solution is $0.80
::答案是0.80

Example 4
::例4

If you have 15 nickels and 20 dimes, what is the sum?
::如果你有15个硬币和20个硬币, 金额是多少?

First, write an expression to represent the dollar value of some number of nickels added to some number of dimes:
::首先,写一个表达式,表示一些硬币中添加的一些镍币的美元价值:

$\begin{aligned} .05 n + .10 d \end{aligned}$

Next, substitute the number of nickels and dimes in place of the variables.
::其次,取代变量的镍和硬币数量。

$\begin{aligned} .05 n + .10 d \\ .05 (15) + .10 (20) \end{aligned}$

Finally, simplify the expression using the correct order of operations.
::最后,使用正确的操作顺序简化表达式。

$\begin{aligned} .05 (15) + .10 (20) \\ .75 + 2 \\ 2.75 \end{aligned}$
The sum is $2.75.

Example 5
::例5

If you have 35 dimes and 12 quarters, what is the sum?
::如果你有35美分和12个季度, 数额是多少?

First, write an expression to represent the dollar value of some number of dimes and quarters
::首先,写一个表达式,表示一些硬币和硬币的美元价值。

$\begin{aligned} .10 d + .25 q \end{aligned}$

Then, substitute the given number of dimes and quarters into the expression.
::然后,用给定数目的硬币和硬币换成表达式。

$\begin{aligned} .10 d + .25 q \\ .10 (35) + .25 (12) \end{aligned}$

Finally, simplify the expression.
::最后,简化表达方式。

$\begin{aligned} .10 (35) + .25 (12) \\ 3.50 + 3 \\ 6.50 \end{aligned}$

The sum is $6.50.
::总额是6.50美元。

Review
::回顾

Write an expression for each money amount and evaluate it using the given information.
::为每一笔金额写一个表达式, 并使用给定的信息来评估它。

15 quarters
::15个季度

10 dimes and 3 quarters
::10美元零3个季度

30 nickels and 15 dimes
::30镍和15角

6 quarters and 60 nickels
::6个季度和60个镍

21 quarters and 14 dimes
::21个季度和14分

6 dimes, 10 nickels and 120 pennies
::6角、10分和120分

18 quarters and 12 half-dollars
::18个季度和12个半美元

32 dimes, 16 nickels and 11 quarters
::32分、16分和11个季度

18 nickels, 33 dimes and 39 quarters
::18个镍、33个角和39个季度

27 dimes, 87 pennies, 12 quarters
::27分 87分 12个季度

10 pennies, 15 nickels, 9 dimes and 27 quarters
::10 便、15 镍、9 便、27 个季度

35 quarters and 98 nickels
::35个季度和98个镍

95 dimes, 27 nickels and 82 quarters
::95角、27镍和82个季度

77 dimes, 15 nickels and 81 quarters
::77分、15分和81分

70 nickels, 63 dimes, 82 pennies and 55 quarters
::70个镍、63个角、82个便分和55个季度

12 nickels, 33 dimes, 17 pennies and 80 quarters
::12个镍、33个角、17个便分和80个季度

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

描述模式的词汇

Describing Patterns ::描述模式

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

Describing Patterns
::描述模式

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