Equivalent Fractions: Understanding and Identifying

6 Questions

下列哪个描述最准确？

当分数的分子和分母同时乘以同一个数字时，会得到一个等价分数。

如果我们将分数7/9的分子和分母同时乘以2，将得到什么等价分数？

14/18

通过将哪些数字同时乘以3，我们可以将3/6转化为等价分数？

在简化分数或解决问题时，等价分数对我们有什么重要作用？

允许我们比较和执行算术运算，而不改变它们的数学意义。

通过将7/9的分子和分母都除以3，我们会得到下列哪个等价分数？

7/27

哪种方法可以用来找到两个等价分数？

同时乘以某个数字来改变两个给定分数的大小。

Study Notes

Equivalent fractions are two or more fractions that represent the same value, despite having different numerators and denominators. Equivalence arises when the fractions are obtained either by multiplying both the numerator and denominator of a specific fraction by the same number, or by dividing both the numerator and denominator by the same number.

For instance, consider the fraction 3/6. By multiplying the numerator and denominator by the same number, such as 3, we obtain 9/18. Alternatively, dividing both the numerator and denominator by the same number, such as 3, yields 1/2. Both 3/6 and 9/18, as well as 1/2, represent the same value and are equivalent fractions.

To illustrate this concept with another example, consider the fraction 7/9. By multiplying both the numerator and denominator by a common factor, like 2, we can find an equivalent fraction: (7/9) × (2/2) = 14/18. Dividing both the numerator and denominator of 7/9 by 3 yields another equivalent fraction: 7/9 ÷ (3/3) = 7/27. Both 14/18 and 7/27 represent the same value as 7/9, making them equivalent fractions.

In summary, equivalent fractions provide alternative expressions for the same value, allowing us to compare and perform arithmetic operations on different fraction representations without changing their underlying mathematical significance. This property is essential in mathematics, particularly when simplifying fractions or expressing them in terms more convenient for solving specific problems.