Article in English: It is usually easier to reduce fractions before squaring them. Remember, to reduce a fraction means to divide it by a common factor until the number one is the only number that can be evenly divided into both the numerator and denominator. Reducing the fraction first means you don’t have to reduce it at the end when the numbers will be larger.  For example: (12/16)2  12 and 16 can both be divided by 4. 12/4 = 3 and 16/4 = 4; therefore, 12/16 reduces to 3/4. Now, you will square the fraction 3/4. (3/4)2 = 9/16, which cannot be reduced. To prove this, let’s square the original fraction without reducing:  (12/16)2 = (12 x 12/16 x 16) = (144/256) (144/256) has a common factor of 16. Dividing both the numerator and denominator by 16 reduces the fraction to (9/16), the same fraction we got from reducing first. When working with more complex equations, you may be able to simply cancel one of the factors. In this case, it is actually easier to wait before you reduce the fraction. Adding an additional factor to the above example illustrates this.  For example: 16 × (12/16)2  Expand out the square and cross out the common factor of 16: 16 * 12/16 * 12/16Because there is one 16 whole number and two 16’s in the denominator, you can cross ONE of them out.  Rewrite the simplified equation: 12 × 12/16  Reduce 12/16 by dividing through by 4: 3/4  Multiply: 12 × 3/4 = 36/4 Divide: 36/4 = 9 Another way to solve the same example is to simplify the exponent first. The end result is the same, it’s just a different way to solve.  For example: 16 * (12/16)2  Rewrite with the numerator and denominator squared: 16 * (122/162) Cancel out the exponent in the denominator: 16 * 122/162Imagine the first 16 has an exponent of 1: 161. Using the exponent rule of dividing numbers, you subtract the exponents. 161/162, yields 161-2 = 16-1 or 1/16.  Now, you are working with:  122/16  Rewrite and reduce the fraction: 12*12/16 = 12 * 3/4. Multiply: 12 × 3/4 = 36/4 Divide: 36/4 = 9

Summary in Chinese:
计算平方前先看看分数是否能够约分。 学会判断什么时候应该先不约分。 了解如何使用指数来做快捷计算。