Course: 2.8使用前端估计的小数减法

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 使用前端估计的小数减法

Collapse Expand
使用前端估计的小数减法
Courtney’s house has a sour cherry tree in the backyard. Courtney loves picking the cherries and making jam with them. Her recipe for jam calls for 2.75 cups of sugar. Courtney just opened a new bag 3 pound bag of sugar that has 6.8571 cups of sugar in it. Courtney is planning to make one recipe’s worth of jam, but she wants to keep track of how much sugar she has in case she wants to make more jam. How can Courtney figure out approximately how much sugar she will have left after she makes one recipe’s worth of jam?
::Courtney的房子在后院里有一棵酸樱桃树。 Courtney喜欢摘樱桃和果酱。她的果酱配方需要2.75杯糖。 Courtney刚刚打开了一个新的袋子3磅糖袋,里面有6.8571杯糖。 Courtney正计划做一个配方的果酱,但她想了解她有多少糖,以防她想做更多的果酱。 Courtney如何知道她做一个配方后会留下多少糖呢?

In this concept, you will learn how to estimate decimal differences using front-end estimation .
::在此概念中,您将学会如何使用前端估计来估计小数点的差异。

Subtracting Decimals Using Front-End Estimation
::使用前期-后期估算法减减十进制

Recall that when you estimate you are finding an approximate solution to a problem.
::记得当你估计你正在找到解决问题的近似方法时

There are different methods for estimation . The front-end estimation method relies on focusing on only the first two digits of each number.
::估算方法各有不同。前端估算方法仅依靠每个数字的前两位数。

Here are the steps for front-end estimation with decimal number subtraction.
::这是前端估算的阶梯, 加上小数减法。

Arrange the numbers vertically so that the decimal points line up.
::垂直排列数字,使小数点排成一行。

Subtract the two front (left-most) pairs of digits at the same time.
::同时减前两对(最左)数字。

Here is an example.
::举一个例子。

Use front-end estimation to find the difference : $\begin{aligned} 0.55373 - 0.27449. \end{aligned}$
::使用前端估计值找出差额:0.55373 - 0.27449。

First, arrange the numbers vertically so that the decimal points line up.
::首先,垂直排列数字,使小数点排成一行。

0.55373

0.27449

Now, the two front pairs of digits are the digits in the tenths place and the digits in the hundredths place. Subtract these digits only. Note that you can ignore the ones place because those digits are both zero . Set up the subtraction problem.
::现在, 两对前两位数是十分位数的数字和百位数的数字。仅减这些位数。请注意, 您可以忽略这两个位数, 因为这两个位数都是零。设置减法问题。

$\begin{aligned} 0.55 \\ \underline{- 0.27} \end{aligned}$

Next, subtract. Start by borrowing from the 5 and subtracting 15 minus 7 to make 8. Then 4 minus 2 to make 2. Insert a decimal point into your answer under the decimal points in the original numbers.
::下一步,减去。从 5 开始从 5 开始借款,减去 15 减去 7 到 8 。然后 4 减去 2 到 2 。在您的答复中,在原数小数点的小数点下插入一个小数点。

$\begin{aligned} 0.55 \\ \underline{- 0.27} \\ 0.28 \end{aligned}$

The answer is $\begin{aligned} 0.55373 - 0.27449 \end{aligned}$ is approximately 0.28.
::答案为0.55373-0.27449约为0.28。

Here is another example.
::下面是另一个例子。

Use front-end estimation to find the difference: $\begin{aligned} 4.032 - 0.82 \end{aligned}$ .
::使用前端估计值找出差额:4.032 - 0.82。

First, arrange the numbers vertically so that the decimal points line up.
::首先,垂直排列数字,使小数点排成一行。

4.032

0.82

Now, the two front pairs of digits are the digits in the ones place and the digits in the tenths place. Subtract these digits only. Set up the subtraction problem.
::现在,两个前对位数是两个位数的位数,一个位数是位数,第十位数是位数。只减去这些位数。设置减法问题。

$\begin{aligned} 4.0 \\ \underline{- 0.8} \end{aligned}$
Next, subtract. Start by borrowing from the 4 and subtracting 10 minus 8 to make 2. Then 3 minus 0 to make 3. Insert a decimal point into your answer under the decimal points in the original numbers.

$\begin{aligned} 4.0 \\ \underline{- 0.8} \\ 3.2 \end{aligned}$

The answer is $\begin{aligned} 4.032 - 0.82 \end{aligned}$ is approximately 3.2.
::答案是4.032-0.82约为3.2。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Courtney and her cherry jam.
::早些时候,你得到一个问题关于Courtney和她的樱桃果酱。

Her new bag of sugar has 6.8571 cups of sugar in it and Courtney is planning to use 2.75 cups of sugar to make cherry jam. She needs to know approximately how many cups of sugar she will have left after making the jam.
::她的新袋糖里有6.8571杯糖,Courtney正计划用2.75杯糖做樱桃果酱,她需要知道在做果酱后她会离开多少杯糖。

First, Courtney should arrange the numbers vertically so that the decimal points line up.
::首先,Courtney应该垂直排列数字,使小数点排成一行。

6.8571

2.75

Now, the two front pairs of digits are the digits in the ones place and the digits in the tenths place. Courtney will subtract these digits only. Set up the subtraction problem.
::现在,两个前对位数是两个位数的位数,一个是位数,第十位是位数。Courtney将只减去这些位数。设置减法问题。

$\begin{aligned} 6.8 \\ \underline{- 2.7} \end{aligned}$
Next, subtract. Start by subtracting 8 minus 7 to make 1. Then 6 minus 2 to make 4. Courtney should insert a decimal point into her answer under the decimal points in the original numbers.

$\begin{aligned} 6.8 \\ \underline{- 2.7} \\ 4.1 \end{aligned}$

The answer is $\begin{aligned} 6.8571 - 2.75 \end{aligned}$ is approximately 4.1. Courtney will have approximately 4.1 cups of sugar left after making her jam.
::答案是6.8571-2.75约为4.1.Courtney做果酱后将剩下大约4.1杯糖。

Example 2
::例2

Use front-end estimation to find the difference: $\begin{aligned} 0.22281 - 0.1946. \end{aligned}$
::使用前端估计值找出差额:0.2281 - 0.1946。

First, arrange the numbers vertically so that the decimal points line up.
::首先,垂直排列数字,使小数点排成一行。

0.22281

0.1946

Now, the two front pairs of digits are the digits in the tenths place and the digits in the hundredths place. Subtract these digits only. Set up the subtraction problem.
::现在,两对前两位数是十分位数的数字和百位数的数字。仅减这些位数。设置减法问题。

$\begin{aligned} 0.22 \\ \underline{- 0.19} \end{aligned}$

Next, subtract. Start by borrowing from the 2 and subtracting 12 minus 9 to make 3. Then 1 minus 1 to make 0. Insert a decimal point into your answer under the decimal points in the original numbers.
::下一步,减去。从 2 中借款开始,减去 12 减 9 得出 3 。然后 1 减 1 减 1 得出 0 。在您回答的原数小数点小数点下插入一个小数点。

$\begin{aligned} 0.22 \\ \underline{- 0.19} \\ 0.03 \end{aligned}$
The answer is $\begin{aligned} 0.22281 - 0.1946 \end{aligned}$ is approximately 0.03 .

Example 3
::例3

Use front-end estimation to find the difference: $\begin{aligned} 4.6712 - 1.34. \end{aligned}$
::使用前端估计值发现差异:4.6712 - 1.34。

First, arrange the numbers vertically so that the decimal points line up.
::首先,垂直排列数字,使小数点排成一行。

4.6712

1.34

Now, the two front pairs of digits are the digits in the ones place and the digits in the tenths place. Subtract these digits only. Set up the subtraction problem.
::现在,两个前对位数是两个位数的位数,一个位数是位数,第十位数是位数。只减去这些位数。设置减法问题。

$\begin{aligned} 4.0 \\ \underline{- 1.3} \end{aligned}$

Next, subtract. Start by borrowing from the 4 and subtracting 10 minus 3 to make 7. Then 3 minus 1 to make 2. Insert a decimal point into your answer under the decimal points in the original numbers.
::下一步,减去。开始从 4 中借款,减去 10 减 3 以作出 7 。然后 3 减 1 以作出 2 。在您的答复中,在原数小数点的小数点下插入一个小数点。

$\begin{aligned} 4.0 \\ \underline{- 1.3} \\ 2.7 \end{aligned}$

The answer is $\begin{aligned} 4.6712 - 1.34 \end{aligned}$ is approximately 2.7 .
::答案是4.6712-1.34约为2.7。

Example 4
::例4

Use front-end estimation to find the difference $\begin{aligned} 6.789 - 3.45. \end{aligned}$
::使用前端估计值找出差额6.789-3.45。

First, arrange the numbers vertically so that the decimal points line up.
::首先,垂直排列数字,使小数点排成一行。

6.789

3.45

Now, the two front pairs of digits are the digits in the ones place and the digits in the tenths place. Subtract these digits only. Set up the subtraction problem.
::现在,两个前对位数是两个位数的位数,一个位数是位数,第十位数是位数。只减去这些位数。设置减法问题。

$\begin{aligned} 6.7 \\ \underline{- 3.4} \end{aligned}$
Next, subtract. Start by subtracting 7 minus 4 to make 3. Then 6 minus 3 to make 3. Insert a decimal point into your answer under the decimal points in the original numbers.

$\begin{aligned} 6.7 \\ \underline{- 3.4} \\ 3.3 \end{aligned}$

The answer is $\begin{aligned} 6.789 - 3.45 \end{aligned}$ is approximately 3.3.
::答案是6.789-3.45约为3.3。

Example 5
::例5

Use front-end estimation to find the difference: $\begin{aligned} 5.023 - 2.346. \end{aligned}$
::使用前端估计值找出差异:5.023 - 2.346。

First, arrange the numbers vertically so that the decimal points line up.
::首先,垂直排列数字,使小数点排成一行。

5.023

2.346

Now, the two front pairs of digits are the digits in the ones place and the digits in the tenths place. Subtract these digits only. Set up the subtraction problem.
::现在,两个前对位数是两个位数的位数,一个位数是位数,第十位数是位数。只减去这些位数。设置减法问题。

$\begin{aligned} 5.0 \\ \underline{- 2.3} \end{aligned}$
Next, subtract. Start by borrowing from the 5 and subtracting 10 minus 3 to make 7. Then 4 minus 2 to make 2. Insert a decimal point into your answer under the decimal points in the original numbers.

$\begin{aligned} 5.0 \\ \underline{- 2.3} \\ 2.7 \end{aligned}$
The answer is $\begin{aligned} 5.023 - 2.346 \end{aligned}$ is approximately 2.7.

Review
::回顾

Use front-end estimation to estimate the following differences.
::使用前端估计来估计以下差异。

$\begin{aligned} 4.57 - 2.34 \end{aligned}$

$\begin{aligned} 2.123 - 1.136 \end{aligned}$

$\begin{aligned} 8.913 - 2.047 \end{aligned}$

$\begin{aligned} 8.7651 - 2.345 \end{aligned}$

$\begin{aligned} 2.436 - 1.267 \end{aligned}$

$\begin{aligned} 18.527 - 9.431 \end{aligned}$

$\begin{aligned} 8.414 - 7.3214 \end{aligned}$

$\begin{aligned} 12.637 - 2.456 \end{aligned}$

$\begin{aligned} .671 - .41 \end{aligned}$

$\begin{aligned} .643 - .123 \end{aligned}$

$\begin{aligned} .912 - .367 \end{aligned}$

$\begin{aligned} .456 - .023 \end{aligned}$

$\begin{aligned} .48218 - .1927 \end{aligned}$

$\begin{aligned} 10.5765 - 6.421192 \end{aligned}$

$\begin{aligned} .5075412 - .45601 \end{aligned}$

Review (Answers)
::回顾(答复)

Section outline

General

使用前端估计的小数减法

Subtracting Decimals Using Front-End Estimation ::使用前期-后期估算法减减十进制

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)

Subtracting Decimals Using Front-End Estimation
::使用前期-后期估算法减减十进制

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)