如何添加具有不同分母的分数？

分数是 a/b 形式的数字，其中 a 和 b 是整数，其中 b ≠ 0。分数的一些示例是 2/5、3/7、3/1、6 等。整数，例如 6也是分数，因为 6 可以写成 6/1。

特性：

• 对于分数 a 和 b，a 和 b 都是整数，且 b ≠ 0。
• 所有整数都是分母等于 1 的分数
• 分数可以彼此相加、相减、相乘和相除。

分数的加法

添加分数的方法是：

• 交叉乘法：交叉乘以两个分数并将两个分数的分子部分相加得到答案的分子。分母部分可以相互相乘，得到答案的最终分母。由于它们可能不是简化的形式，我们可能需要将分子和分母除以一个公因数以获得适当的分数。

Consider two fractions a/b and c/d. Then, their sum can be done by:

a/b + c/d = (ad + bc) / bd

For example,

 3/5 + 2/7 = (7×3 + 2×5) / 5×7 = (21 + 10) / 35 = 31/35

• 分母的LCM：在这种方法中，我们需要找到分数的所有分母的LCM，然后将相同的因子与每个分数的分子和分母相乘，使得所有分数的分母都相同。然后我们需要将分数的所有新分子相加得到答案的分子。所有分母的 LCM 成为答案的分母。

Consider two fractions 3/8 and 2/3. To add the fractions, we need to find the LCM of 3 and 8.

Now, LCM of 3 and 8 is 24. Thus, we proceed as:

3/8 + 2/3 = (3×3 / 8×3) + (2×8 / 3×8) = 9/24 + 16/24 = 25/24

Thus, the sum is equal to 25/24.

示例问题

问题 1. 使用叉乘法求分数 2/5 和 3/4 之和。

解决方案：

To apply the cross multiplication method, we find the sum of numerators by cross multiplying them with other denominator.

Thus, the numerator of the answer = 2×4 + 3×5 = 23

The denominator of the answer = product of the denominators = 5×4 = 20

Thus, the sum is equal to 23/20.

问题 2. 使用 LCM 方法求分数 3/5 和 5/2 的和。

解决方案：

To apply the LCM method, we first need to find the LCM of the denominators 2 and 5. 

The LCM of 2 and 5 is 10.

Thus, we can write,

3/5 + 5/2 = 3×2 / 5×2 + 5×5 / 2×5 = 6/10 + 25/10

Thus, 3/5 + 5/2 = 31/10

问题 3. 求分数 3/5、6/7 和 3/2 的总和。

解决方案：

To find the sum of the three fractions, we need to first find the sum of the two fractions and add the answer to the third fraction. 

At first, we add 3/5 and 6/7 using the cross multiplication method. Thus,

3/5 + 6/7 = (3×7 + 6×5) / (5×7) = (21 + 30) / 35 = 51/35

Now, we add 51/35 with 3/2 using the same method to get out final answer.

51/35 + 3/2 = (51×2 + 35×3) / (35×2) = 207/70

Since 207/70 is a proper fraction and cannot be reduced further, the answer is 207/70.

问题 4. 找到要与 5/6 相加的分数，得到等于 3/2 的总和。

解决方案：

Let the fraction to be added be x. Then we can write

x + 5/6 = 3/2

x = 3/2 – 5/6

We can use the cross multiplication method to find the numerator of x and the denominator can be found by finding the product of both the denominators.

Thus, we can write

x = (3×6 – 5×2) / (2×6)

x = (18 – 10) / 12

x = 8/12

Since 8/12 is not in reduced form and can be further reduced by dividing both the numerator and denominator with their HCF.

HCF of 8 and 12 = 4

Thus, we can write

8/12 = (4×2) / (4×3) = 2/3

Thus, x = 8/12 = 2/3

So, 2/3 should be added with 5/6 to get a sum equal to 3/2.