Section: 小数和整数的乘法 | 4.1小数和整数的乘法

Section outline

Mrs. Andersen is planning a field trip to the Science Museum for her sixth grade class. The group rate for a student ticket is $8.95 per ticket. If 22 students attend the field trip, how much money should Mrs. Andersen have to cover the cost of admission for the students?
::Andersen夫人正计划为她六年级的班级前往科学博物馆实地考察,学生机票集体费率为每张8.95美元,如果22名学生参加实地考察,Andersen夫人需要多少钱支付学生的入学费用?

In this concept, you will learn how to multiply decimals and whole numbers together.
::在这个概念中,你会学会如何乘以小数和整数。

Multiplying Decimals and Whole Numbers
::乘以十进数和整数

Multiplication is a short-cut for repeated addition. It is a way to add the same number of groups several or “multiple” times.
::乘法是重复加法的捷径,是增加相同数目的数组数或 " 倍数 " 次数的一种方式。

Here is a multiplication equation.
::这是一个乘法方程式。

$\begin{aligned} 4 \times 3 = 12 \end{aligned}$

This equation tells you that there are 3 groups of 4 or 4 groups of 3. Either grouping results in the same total. The product of 4 multiplied by 3 is 12. A product is the result of multiplying two or more numbers. You can also think of multiplying whole numbers and decimals as groups.
::此方程式告诉您, 共有三组 4 或四组 3 。任何一组的结果都相同。 4 乘以 3 的产物是 12 。产品是乘以两个或两个以上数字的结果。您也可以将整组数字和小数数按组计算。

Here is a whole number and decimal multiplication problem.
::这是整个数字和小数乘法的问题。

$\begin{aligned} 2 (0.25) = \underline{} \end{aligned}$

Remember that the parentheses tell you the order of operation and can also indicate multiplication. Think of 2 times 0.25 as two groups of twenty-five hundredths. Let’s look at this on a hundreds grid .
::记得括号里写着操作的顺序, 也可以表示乘法。想象一下, 2乘以0. 25 乘以 25 的两组。让我们在数百个网格上看一看这个。

Each color represents a group of twenty-five hundredths. Two groups of twenty-five hundredths total fifty hundredths.
::每种颜色代表二千五百总共二百五百

$\begin{aligned} 2 (0.25) = 0.50 \end{aligned}$

This is one way to multiply decimals and whole numbers. You can also multiply a decimal and a whole number just like you would two whole numbers. Afterwards, add the decimal point in the product the same number of places in the decimal number multiplier .
::这是乘以小数点和整数的一个方法。您也可以乘以小数点和整数,就像您会乘以两个整数一样。然后,在产品中加上小数点,在小数点乘数中加上相同的位数。

Here is another whole number and decimal multiplication problem.
::这是另一个整数和小数乘法问题。

$\begin{aligned} 4 (1.25) = \underline{} \end{aligned}$

First, ignore the decimal and multiply as if this were two whole numbers.
::首先,忽略小数点和乘法,仿佛这是两个完整的数字。

$\begin{aligned} 1.25 \\ \underline{\times 4} \\ 500 \end{aligned}$

Then, add the decimal point in the product. There are two decimal places in 1.25. Count two places from right to left and place the decimal point in the product.
::然后在产品中添加小数点。 1. 25 中小数点有两个位数。从右到左倒数两个位数,然后在产品中放置小数点。

$\begin{aligned} 1.25 \\ \underline{\times 4} \\ 5.00 \end{aligned}$

The product of 4 times 1.25 is 5.00.
::4乘以1.25的产物为5.00。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Mrs. Andersen’s field trip to the museum.
::Andersen夫人前往博物馆实地考察时,

Mrs. Andersen needs to find the total cost of 22 tickets that cost $8.95 each.
::Andersen夫人需要找到22张机票的总费用,每张机票费用为8.95美元。

First, write a multiplication problem to find the total cost.
::首先,写一个乘法问题来找出总成本。

$\begin{aligned} 22 (8.95) = \underline{} \end{aligned}$

Then, ignore the decimal and multiply as if this were two whole numbers.
::然后,忽略小数点,然后乘以两个整数。

$\begin{aligned} 8.95 \\ \underline{\times 22} \\ 1790 \\ \underline{+ 1790} \\ 19690 \end{aligned}$

Next, add the decimal point in the product. There are two decimal places in 8.95.
::接下来,在产品中添加小数点。8.95中小数点后有两个位数。

$\begin{aligned} 8.95 \\ \underline{\times 22} \\ 1790 \\ \underline{+ 1790} \\ 196.90 \end{aligned}$

The total cost for 22 student tickets at the group rate is $196.90.
::按集体费率计算的22张学生机票的总费用为196.90美元。

Example 2
::例2

Find the product for the following problem.
::为以下问题寻找产品。

9 friends decided to go to a movie on Friday night. They each paid the $8.50 for admission. How much money did they spend in all?
::9个朋友在星期五晚上决定去看电影,每人都付了8.50美元的入场费。他们花了多少钱?

First, write a multiplication problem to find the total cost.
::首先,写一个乘法问题来找出总成本。

$\begin{aligned} 9 (8.50) = \underline{} \end{aligned}$

Then, ignore the decimal and multiply as if this were two whole numbers.
::然后,忽略小数点,然后乘以两个整数。

$\begin{aligned} 8.50 \\ \underline{\times 9} \\ 7650 \end{aligned}$

Next, add the decimal point in the product. There are two decimal places in 8.50.
::接下来,在产品中添加小数点。在8.50中小数点后有两个位数。

$\begin{aligned} 8.50 \\ \underline{\times 9} \\ 76.50 \end{aligned}$

The cost of 9 movie tickets was $76.50.
::9张电影票的费用为76.50美元。

Example 3
::例3

Find the product.
::找到产品。

$\begin{aligned} 3 (4.52) = \underline{} \end{aligned}$

First, ignore the decimal and multiply as if this were two whole numbers.
::首先,忽略小数点和乘法,仿佛这是两个完整的数字。

$\begin{aligned} 4.52 \\ \underline{\times 3} \\ 1356 \end{aligned}$

Then, add the decimal point in the product.
::然后在产品中添加小数点。

$\begin{aligned} 4.52 \\ \underline{\times 3} \\ 13.56 \end{aligned}$

The product of 3 times 4.52 is 13.56.
::3乘以4.52的产物是13.56。

Example 4
::例4

Find the product.
::找到产品。

$\begin{aligned} 5 (2.34) = \underline{} \end{aligned}$

First, ignore the decimal and multiply as if this were two whole numbers.
::首先,忽略小数点和乘法,仿佛这是两个完整的数字。

$\begin{aligned} 2.34 \\ \underline{\times 5} \\ 1170 \end{aligned}$

Then, add the decimal point in the product.
::然后在产品中添加小数点。

$\begin{aligned} 2.34 \\ \underline{\times 5} \\ 11.70 \end{aligned}$

The product of 5 times 2.34 is 11.70.
::5乘以2.34的产品为11.70。

Example 5
::例5

Find the product.
::找到产品。

$\begin{aligned} 7 (3.561) = \underline{} \end{aligned}$

First, ignore the decimal and multiply as if this were two whole numbers.
::首先,忽略小数点和乘法,仿佛这是两个完整的数字。

$\begin{aligned} 3.561 \\ \underline{\times 7} \\ 24927 \end{aligned}$

Then, add the decimal point in the product.
::然后在产品中添加小数点。

$\begin{aligned} 3.561 \\ \underline{\times 7} \\ 24.927 \end{aligned}$

The product of 7 times 3.561 is 24.927.
::7乘3.561的产品为24.927。

Review
::回顾

Find the product for the following problems.
::为以下问题寻找产品。

$\begin{aligned} 5 (1.24) = \underline{} \end{aligned}$

$\begin{aligned} 6 (7.81) = \underline{} \end{aligned}$

$\begin{aligned} 7 (9.3) = \underline{} \end{aligned}$

$\begin{aligned} 8 (1.45) = \underline{} \end{aligned}$

$\begin{aligned} 9 (12.34) = \underline{} \end{aligned}$

$\begin{aligned} 2 (3.56) = \underline{} \end{aligned}$

$\begin{aligned} 6 (7.12) = \underline{} \end{aligned}$

$\begin{aligned} 3 (4.2) = \underline{} \end{aligned}$

$\begin{aligned} 5 (2.4) = \underline{} \end{aligned}$

$\begin{aligned} 6 (3.521) = \underline{} \end{aligned}$

$\begin{aligned} 2 (3.222) = \underline{} \end{aligned}$

$\begin{aligned} 3 (4.223) = \underline{} \end{aligned}$

$\begin{aligned} 4 (12.34) = \underline{} \end{aligned}$

$\begin{aligned} 5 (12.45) = \underline{} \end{aligned}$

$\begin{aligned} 3 (143.12) = \underline{} \end{aligned}$

$\begin{aligned} 4 (13.672) = \underline{} \end{aligned}$

$\begin{aligned} 2 (19.901) = \underline{} \end{aligned}$

$\begin{aligned} 3 (67.321) = \underline{} \end{aligned}$

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

Multiplying Decimals and Whole Numbers ::乘以十进数和整数

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

Multiplying Decimals and Whole Numbers
::乘以十进数和整数

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