Course: 2.7 小数减法 | The Way To Learn

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2.7 小数减法
Owen likes to help his mom cut out coupons from the paper on Sunday mornings. This week he found 5 coupons that will save them $4.10 on their purchases at the grocery store. Once Owen and his mom get to the grocery store, they fill up their cart with everything on their list. At the cash register, their total is $85.91 before Owen hands over the coupons. How could Owen determine what the new total is going to be after the coupons are applied?
::Owen喜欢帮助他妈妈在星期天早上从报纸上剪掉优惠券。本周他发现5张优惠券,在杂货店的购物中可以省下他们4.10美元。一旦Owen和他妈妈来到杂货店,他们就会把清单上的所有东西都装满车。在现金登记簿上,在Owen交出优惠券之前,他们的总数是85.91美元。Owen如何确定在应用优惠券之后新的总额会是多少?

In this concept, you will learn how to subtract decimals with and without rounding .
::在这个概念中,你将学会如何在不四舍五入的情况下减去小数。

Subtracting Decimals
::减减十进制

Recall that in a decimal number, the decimal point divides the whole part of the number from the fractional part of the number.
::回顾在小数点数中,小数点将数字的整个部分与数字的分数部分分开。

To subtract decimal numbers:
::减去小数数字:

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。

Add zeros for any missing spaces so that each number has the same number of digits to the right of the decimal point.
::为任何缺失的空格添加零,使每个数字在小数点右侧的位数相同。

Subtract from right to left, borrowing as necessary just as if you were subtracting whole numbers .
::从右到左的减法, 借入和借入一样必要, 就像你在减去整数一样。

Insert a decimal point into your answer so that it lines up with the decimal points of the original numbers.
::在您的答复中插入小数点,使其与原始数字的小数点一致。

Here is an example.
::举一个例子。

Subtract 4.5 from 18.98.
::从18.98中减去4.5。

First, notice that you are going to find 18.98 minus 4.5.
::首先,请注意你会发现18.98减4.5

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

$\begin{aligned} 18.98 \\ \underline{- 4.5} \end{aligned}$

Next, add a zero after the 5 in the second number so that both numbers have two digits to the right of the decimal point.
::接下来,在第二个数字的5之后加上0,这样两个数字在小数点右侧有两个位数。

$\begin{aligned} 18.98 \\ \underline{- 4.50} \end{aligned}$

Now, subtract from right to left. Start by subtracting 8 minus 0 to make 8. Then 9 minus 5 to make 4. Then 18 minus 4 to make 14. Insert a decimal point into your answer directly under the decimal points in the original numbers.
::现在, 从右向左减。以减去 8 减去 0 开始。然后 9 减 5 得出 4 ; 然后 18 减 4 得出 14 。在您的答复中直接插入一个小数点, 在原数的小数点的小数点下插入一个小数点。

$\begin{aligned} 18.98 \\ \underline{- 4.50} \\ 14.48 \end{aligned}$

The answer is $\begin{aligned} 18.98 - 4.5 = 14.48 \end{aligned}$ .
::答案是18.98 - 4.5 = 14.48。

Sometimes you will want to round numbers before subtracting them. Rounding is useful when you only need an approximate answer instead of an exact answer. Read the problem carefully to determine if you should round before or after you subtract.
::有时,您会想要在减去数字之前进行圆数。当您只需要大致答案而不是精确答案时,圆数是有用的。仔细阅读问题以确定您在减去之前还是之后应该圆圆。

Here is an example.
::举一个例子。

Round each number to the nearest tenth and then find the difference .
::每一回合到最近的第十回合,然后找出差数。

$\begin{aligned} 72.953 - 52.418 \end{aligned}$

First, round each number to the nearest tenth. Remember that the tenths place is the first digit to the right of the decimal point. Look at each digit in the tenths place and then the digit to the right of that to decide if you will need to round up the digit in the tenths place or keep it the same.
::首先,将每个数字四舍五入到最接近的十分点。记住, 十分位数是小数点右侧的第一个位数。看看十位数中的每个位数, 然后将数字移到十位数右位数, 以决定您是否需要将位数四舍五入到十分位数, 或者保持原位数不变。

72.953 rounds to 73.0
::72.953发子弹至73.0

52.418 rounds to 52.4
::52.418发炮弹至52.4

Now, subtract the rounded numbers. Start by arranging the numbers vertically so that the decimal points line up.
::现在, 减去四舍五入的数字。从垂直排列数字开始, 这样小数点就会排队。

$\begin{aligned} 73.0 \\ \underline{- 52.4} \end{aligned}$

Next, subtract from right to left. Borrow from the 3 and then subtract 10 minus 4 to make 6. Then subtract 2 minus 2 to make 0. Finally subtract 7 minus 5 to make 2. Insert a decimal point into your answer directly under the decimal points in the original numbers.
::下一步,从右到左。从 3 中借款,然后减去 10 减 4,然后减去 6 。然后减去 2 减 2 减 2 减 0 。最后减去 7 减 5 减 5 减 2 。在您的答复中,在原数小数小数点的小数点下直接插入小数点。

$\begin{aligned} 73.0 \\ \underline{- 52.4} \\ 20.6 \end{aligned}$

The answer is $\begin{aligned} 73.0 - 52.4 = 20.6 \end{aligned}$ .
::答案是73.0-52.4=20.6。

Examples
::实例

Example 1
::例1

Earlier, you were given a problem about Owen, who likes clipping coupons with his mom.
::之前,你得到一个问题关于欧文, 谁喜欢剪贴券与他的母亲。

This week Owen found $4.10 worth of coupons. At the store, their items cost $85.91 before the coupons are applied. Owen wants to determine what their total will be after he gives the coupons to the cashier.
::本周欧文发现了价值4.10美元的优惠券。在商店,在实行优惠券之前,他们的物品成本为85.91美元。欧文想确定在向出纳员提供优惠券之后,他们的总价值是多少。

First, Owen needs to realize that he will need to subtract 85.91 minus 4.10.
::首先,欧文需要意识到他需要减去85.91减4.10

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

$\begin{aligned} 85.91 \\ \underline{- 4.10} \end{aligned}$

Now, he should subtract from right to left. First subtract 1 minus 0 to make 1. Then 9 minus 1 to make 8. Then 85 minus 4 to make 81. He needs to insert a decimal point into his answer directly under the decimal points in the original numbers.
::现在,他应该从右向左减一。首先减1减去0,再减1,再减9减1,再减8,再减85减4,再减81,他需要在回答中直接插入小数点,在原数小数点的小数点下插入小数点。

$\begin{aligned} 85.91 \\ \underline{- 4.10} \\ 81.81 \end{aligned}$

The answer is $\begin{aligned} 85.91 - 4.10 = 81.81 \end{aligned}$ . The total will be $81.81 after the coupons are applied.
::答案是85.91-4.10=81.81,在采用优惠券后,总额将为81.81美元。

Example 2
::例2

Subtract $\begin{aligned} 4.56 - 2.37 \end{aligned}$ .
::减号4.56 - 2.37

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。

$\begin{aligned} 4.56 \\ \underline{- 2.37} \end{aligned}$

Now, subtract from right to left. Start by borrowing from the 5 and then subtracting 16 minus 7 to make 9. Then subtract 4 minus 3 to make 1. Finally subtract 4 minus 2 to make 2. Insert a decimal point into your answer directly under the decimal points in the original numbers.
::现在, 从右向左减。从 5 开始从 5 开始借款, 然后从 16 减 7 开始, 然后从 9 减 16 减 7 到 9 。然后减 4 减 3 到 1 。最后减 4 减 2 到 2 。在您的答复中直接插入一个小数点, 在原数小数点的小数点下插入一个小数点。

$\begin{aligned} 4.56 \\ \underline{- 2.37} \\ 2.19 \end{aligned}$

The answer is $\begin{aligned} 4.56 - 2.37 = 2.19 \end{aligned}$ .
::答案是4.56 - 2.37 = 2.19。

Example 3
::例3

Subtract $\begin{aligned} 5.674 - 2.5 \end{aligned}$ .
::减号 5.674 - 2.5

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。

$\begin{aligned} 5.674 \\ \underline{- 2.5} \end{aligned}$

Next, add two zeros after the 5 in the second number so that both numbers have three digits to the right of the decimal point.
::接下来,在第二个数字的5之后加上两个零,使两个数字在小数点右侧有三个位数。

$\begin{aligned} 5.674 \\ \underline{- 2.500} \end{aligned}$

Now, subtract from right to left. Start by subtracting 4 minus 0 to make 4. Then 7 minus 0 to make 7. Then 6 minus 5 to make 1. Finally 5 minus 2 to make 3. Insert a decimal point into your answer directly under the decimal points in the original numbers.
::现在, 从右向左减。开始减 4 减 0 得出 4 。然后 7 减 0 得出 7 。然后 6 减 5 得出 1 。最后 5 减 2 得出 3 。在您的答复中直接插入一个小数点, 在原数的小数点的小数点下。

$\begin{aligned} 5.674 \\ \underline{- 2.500} \\ 3.174 \end{aligned}$

The answer is $\begin{aligned} 5.674 - 2.5 = 3.174 \end{aligned}$ .
::答案是5.674 - 2.5 = 3.174。

Example 4
::例4

Take 5.67 from 12.378.
::从12 378拿5.67

First, notice that you are going to find 12.378 minus 5.67.
::首先,请注意你会发现12 378减去5.67

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

$\begin{aligned} 12.378 \\ \underline{- 5.67} \end{aligned}$

Next, add a zero after the 7 in the second number so that both numbers have three digits to the right of the decimal point.
::接下来,在第二个数字的7后面加上0,这样两个数字在小数点右侧都有3位数。

$\begin{aligned} 12.378 \\ \underline{- 5.670} \end{aligned}$

Now, subtract from right to left. Start by subtracting 8 minus 0 to make 8. Then 7 minus 7 to make 0. Then borrow from the 2 and subtract 13 minus 6 to make 7. Finally subtract 11 minus 5 to make 6. Insert a decimal point into your answer directly under the decimal points in the original numbers.
::现在, 从右向左减。以减去 8 减 0 开始。 8 减 8 减 7 减 7 减 0 。然后从 2 中借款, 减去 13 减 6 减 7 。最后减去 11 减 5 减 6 。在您的答复中, 在原数小数点的小数点下直接插入一个小数点。

$\begin{aligned} 12.378 \\ \underline{- 5.670} \\ 6.708 \end{aligned}$

The answer is $\begin{aligned} 12.378 - 5.67 = 6.708 \end{aligned}$ .
::答案是12 378 - 5.67 = 6.708。

Example 5
::例5

Round to the nearest tenth and then subtract: $\begin{aligned} 83.56 - 1.258 \end{aligned}$ .
::圆到最接近的十分之一,然后减去:83.56 - 1.258。

First, round each number to the nearest tenth. Remember that the tenths place is the first digit to the right of the decimal point. Look at each digit in the tenths place and then the digit to the right of that to decide if you will need to round up the digit in the tenths place or keep it the same.
::首先,将每个数字四舍五入到最接近的十分点。记住, 十分位数是小数点右侧的第一个位数。看看十位数中的每个位数, 然后将数字移到十位数右位数, 以决定您是否需要将位数四舍五入到十分位数, 或者保持原位数不变。

83.56 rounds to 83.6
::83.56发至83.6发子弹

1.258 rounds to 1.3
::1.258发炮弹至1.3

Now, subtract the rounded numbers. Start by arranging the numbers vertically so that the decimal points line up.
::现在, 减去四舍五入的数字。从垂直排列数字开始, 这样小数点就会排队。

$\begin{aligned} 83.6 \\ \underline{- 1.3} \end{aligned}$

Next, subtract from right to left. Subtract 6 minus 3 to make 3. Then 83 minus 1 to make 82. Insert a decimal point into your answer directly under the decimal points in the original numbers.
::下一步,从右到左减。减号 6 减号 3 到 3 。再减号 83 减号 1 到 82 。在您的答复中,在原数小数点的小数点下直接插入小数点。

$\begin{aligned} 83.6 \\ \underline{- 1.3} \\ 82.3 \end{aligned}$

The answer is $\begin{aligned} 83.6 - 1.3 = 82.3 \end{aligned}$ .
::答案是83.6-1.3=82.3。

Keep practicing on your own!
::继续自己练习!

Review
::回顾

Find each difference.
::找出每个不同之处

$\begin{aligned} 6.57 - 5.75 \end{aligned}$

$\begin{aligned} .0826 - .044 \end{aligned}$

$\begin{aligned} 19.315 - 6.8116 \end{aligned}$

$\begin{aligned} 2056.04 - 2044.1 \end{aligned}$

$\begin{aligned} 303.45 - 112.05 \end{aligned}$

$\begin{aligned} 16.576 - 8.43 \end{aligned}$

$\begin{aligned} 199.2 - 123.45 \end{aligned}$

$\begin{aligned} 1.0009 - .234 \end{aligned}$

$\begin{aligned} 789.12 - .876 \end{aligned}$

$\begin{aligned} 102.03 - .27 \end{aligned}$

Find the difference after rounding each decimal to the nearest hundredth.
::将每个小数点四舍五入到最接近的百分百位后, 查找差数。

$\begin{aligned} 63.385 - 50.508 \end{aligned}$

$\begin{aligned} .535 - .361 \end{aligned}$

$\begin{aligned} 747.005 - 47.035 \end{aligned}$

$\begin{aligned} .882 - .546 \end{aligned}$

$\begin{aligned} .9887 - .0245 \end{aligned}$

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

General

2.7 小数减法

Subtracting Decimals ::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)

Resources ::资源

Subtracting Decimals
::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)

Resources
::资源