📚 Dividing Decimals | 小数除法
Division with decimals can look tricky, but the real meaning is the same as division with whole numbers: sharing a quantity into equal groups, or finding how many equal groups you can make. If you understand place value, you can divide decimals accurately and even check your answer with estimation.
小数除法看起来有点难，但其实它的含义和整数除法完全一样：把一个数量平均分成几份，或者求一个数里面有几个另一个数。只要理解位值，你就能准确计算小数除法，还能用估算来检验答案。
1. Fair Sharing: What Division Means | 1. 平均分：除法的真正含义
Suppose we want to divide 1.2 by 3. We are asking: if 1.2 is shared into 3 equal groups, how much is in one group? Write 1.2 in tenths: 1.2 is equal to 12 tenths. Then 12 tenths divided by 3 is 4 tenths.
例如：我们要计算 1.2 ÷ 3。这句话的意思是：把 1.2 平均分成 3 份，每份是多少？把 1.2 看成 12 个十分之一，12 个十分之一除以 3，等于 4 个十分之一。
12 tenths ÷ 3 = 4 tenths, so 1.2 ÷ 3 = 0.4
2. Number Line Model | 2. 数轴模型
A number line can show decimal division. For 0.8 ÷ 2, start at 0 and make two equal jumps to reach 0.8. Each jump is 0.4, so the quotient is 0.4. This matches fair sharing: two groups of 0.4 make 0.8.
数轴可以帮助我们理解小数除法。计算 0.8 ÷ 2 时，从 0 出发，分两次相等的跳跃到达 0.8。每一次跳 0.4，所以商是 0.4。这也验证了平均分：两个 0.4 合起来正好是 0.8。
0.8 ÷ 2 = 0.4, because 2 × 0.4 = 0.8
3. Money Model | 3. 钱币模型
Money is a helpful model because decimals are part of our everyday life. If 1.50 dollars is shared equally by 3 people, each person receives 0.50 dollars. We can think of 1.50 as 150 cents, and 150 cents divided by 3 is 50 cents.
钱币是学习小数的好模型，因为生活中经常用到小数。如果把 1.50 美元平均分给 3 个人，每个人得到 0.50 美元。我们可以把 1.50 看成 150 美分，150 美分 ÷ 3 = 50 美分。
$1.50 ÷ 3 = $0.50
4. Dividing a Decimal by a Whole Number | 4. 小数除以整数
To divide a decimal by a whole number, use the same long-division steps as with whole numbers. Place the decimal point in the quotient directly above the decimal point in the dividend. Then divide as usual.
计算小数除以整数时，步骤和整数除法一样。先把商的小数点对准被除数的小数点，然后按整数除法计算。
4.8 ÷ 4 = 1.2
s divided by 4 is 2 tenths. So 4.8 ÷ 4 = 1.2. Write extra zeros if needed: 1.5 ÷ 2 = 0.75.
计算 4.8 ÷ 4 时，可以这样想：4 个一除以 4 得 1 个一，8 个十分之一除以 4 得 2 个十分之一。所以 4.8 ÷ 4 = 1.2。如果必要，可以补 0 继续算，例如 1.5 ÷ 2 = 0.75。
5. Place Value and Powers of 10 | 5. 位值与10的幂
Multiplying or dividing by a power of 10 changes the place value of each digit. When you multiply by 10, every digit moves to the next higher place. When you divide by 10, every digit moves to the next lower place.
乘或除以 10 的幂时，每一位数字的位值会改变。乘 10 时，每个数字移到更高的数位；除以 10 时，每个数字移到更低的数位。
| 0.4 × 10 | 4 |
| 0.4 × 100 | 40 |
| 0.4 ÷ 10 | 0.04 |
This place-value idea is especially useful when the divisor is also a decimal.
这个位值变化规律在“除以小数”时特别有用。
6. Dividing by a Decimal | 6. 除以小数
When you divide by a decimal, first make the divisor a whole number. Multiply both the divisor and the dividend by the same power of 10. This does not change the quotient because you are multiplying both numbers by the same amount.
当除数是小数时，先把除数变成整数。给除数和被除数同时乘同一个 10 的幂，商不会改变，因为两个数同时扩大了相同的倍数。
2.4 ÷ 0.6 = 24 ÷ 6 = 4
: 0.6 × 4 = 2.4, so the quotient is correct. Another example: 1.35 ÷ 0.3 = 13.5 ÷ 3 = 4.5.
检验：0.6 × 4 = 2.4，所以商正确。另一个例子：1.35 ÷ 0.3 = 13.5 ÷ 3 = 4.5。
7. Estimation and Compatible Numbers | 7. 估算与简便数
Estimation helps you check if your answer is reasonable. Round the numbers to compatible numbers that are easy to divide mentally. For example, 5.8 ÷ 2.9 is close to 6 ÷ 3, which equals 2, and 5.8 ÷ 2.9 does equal 2.
估算可以帮助我们判断答案是否合理。把数看成容易心算的“简便数
Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图