少广术曰：置全步及分母子，以最下分母遍乘诸分子及全步，各以其母除其子，置之於左。命通分者，又以分母遍乘诸分子，及已通者皆通而同之，并之为法。置所求步数，以全步积分乘之为实。实如法而一，得从步。请只用中文和英文翻译这段话，不要实现其他多余的内容
少广术是中国古代数学中用于处理分数通分的一种算法。具体操作是：将所有分子及它们的和（全步）乘以最小分母，然后用各自的原分母除以这个乘积，得到的结果放在一边。接着，让负责通分的人用分母再乘以每个分子，以及已经通分的项，确保它们通分到相同的分母，并将这些相加作为通分后的分母（法）。然后，将所求的步数（即分子的和）乘以所有分子的积分和，得到实（实际的分子）。最后，将实除以法（通分后的分母），得到从步（新的分子）。
The "Shao Guang" method is an ancient Chinese mathematical technique for the common denominator conversion of fractions. The procedure involves taking all numerators and their sum (the full step), multiplying them by the smallest denominator, and then dividing each product by its original denominator, placing these results aside. Next, the person responsible for the conversion multiplies each numerator again by the common denominator, ensuring that they all have the same denominator, and adds these to form the new common denominator (method). Then, the desired number of steps (sum of the numerators) is multiplied by the total integral of all numerators to obtain the actual numerator (reality). Finally, dividing reality by method yields the new numerator (following step).
〔一〕今有田广一步半。求田一亩，问从几何？
荅曰：一百六十步。
术曰：下有半，是二分之一。以一为二，半为一，并之得三，为法。置田二百四十步，亦以一为二乘之，为实。实如法得从步。
现在有一块田地，宽度是1.5步。如果要得到一亩田（古代中国一亩为240平方步），问需要多少步长？
答案是：160步。
解题方法：将1.5步视为三分之二步。以2代替1，以1代替半，合并后得到3作为计算的基准（法）。假设田地的长度是240步，也用2乘以它，得到实际长度（实）。通过实际长度除以基准得到所需的步长。
Now, there is a field that is 1.5 steps wide. If one wants to obtain an area of one mu (ancient Chinese unit of area, 1 mu = 240 square steps), how many steps in length does it need? The answer is: 160 steps. Solution method: Regard 1.5 steps as two-thirds of a step. Replace 1 with 2, and half with 1, adding them together to get 3 as the standard for calculation (method). Assume the length of the field is 240 steps, multiply it by 2 to get the actual length (reality). The required number of steps is obtained by dividing the actual length by the standard.
〔二〕今有田广一步半、三分步之一。求田一亩，问从几何？
荅曰：一百三十步、一十一分步之一十。
术曰：下有三分，以一为六，半为三，三分之一为二，并之得一十一为法。置田二百四十步，亦以一为六乘之，为实。实如法得从步。
现在有一块田地，宽度是1.5步又三分之一步。如果要得到一亩田（古代中国一亩为240平方步），问需要多少步长？
答案是：130又十分之一步。
解题方法：将1.5步又三分之一步视为六分之五步。以6代替1，以3代替半，以2代替三分之一，合并后得到11作为计算的基准（法）。假设田地的长度是240步，也用6乘以它，得到实际长度（实）。通过实际长度除以基准得到所需的步长。
Now, there is a field that is 1.5 steps and one-third of a step wide. If one wants to obtain an area of one mu (ancient Chinese unit of area, 1 mu = 240 square steps), how many steps in length does it need? The answer is: 130 and one-tenth of a step. Solution method: Regard 1.5 steps and one-third of a step as five-sixths of a step. Replace 1 with 6, half with 3, and one-third with 2, adding them together to get 11 as the standard for calculation (method). Assume the length of the field is 240 steps, multiply it by 6 to get the actual length (reality). The required number of steps is obtained by dividing the actual length by the standard.
〔三〕今有田广一步半、三分步之一、四分步之一。求田一亩，问从几何？
荅曰：一百一十五步、五分步之一。
术曰：下有四分，以一为一十二，半为六，三分之一为四，四分之一为三，并之得二十五，以为法。置田二百四十步，亦以一为一十二乘之，为实。实如法而一，得从步。
现在有一块田地，宽度是1.5步、三分之一步、四分之一步。如果要得到一亩田（古代中国一亩为240平方步），问需要多少步长？
答案是：115又五分之一步。
解题方法：将1.5步、三分之一步、四分之一步视为十二分之七步。以12代替1，以6代替半，以4代替三分之一，以3代替四分之一，合并后得到25作为计算的基准（法）。假设田地的长度是240步，也用12乘以它，得到实际长度（实）。通过实际长度除以基准得到所需的步长。
Now, there is a field that is 1.5 steps, one-third of a step, and one-fourth of a step wide. If one wants to obtain an area of one mu (ancient Chinese unit of area, 1 mu = 240 square steps), how many steps in length does it need? The answer is: 115 and one-fifth of a step. Solution method: Regard 1.5 steps, one-third of a step, and one-fourth of a step as seven-twelfths of a step. Replace 1 with 12, half with 6, one-third with 4, and one-fourth with 3, adding them together to get 25 as the standard for calculation (method). Assume the length of the field is 240 steps, multiply it by 12 to get the actual length (reality). The required number of steps is obtained by dividing the actual length by the standard.
〔四〕今有田广一步半、三分步之一、四分步之一、五分步之一。求田一亩，问从几何？
荅曰：一百五步、一百三十七分步之一十五。
术曰：下有五分，以一为六十，半为三十，三分之一为二十，四分之一为一十五，五分之一为一十二，并之得一百三十七，以为法。置田二百四十步，亦以一为六十乘之，为实。实如法得从步。
现在有一块田地，宽度是1.5步、三分之一步、四分之一步、五分之一步。如果要得到一亩田（古代中国一亩为240平方步），问需要多少步长？
答案是：105又137分之15步。
解题方法：将1.5步、三分之一步、四分之一步、五分之一步视为六十分之五十五步。以60代替1，以30代替半，以20代替三分之一，以15代替四分之一，以12代替五分之一，合并后得到137作为计算的基准（法）。假设田地的长度是240步，也用60乘以它，得到实际长度（实）。通过实际长度除以基准得到所需的步长。
Now, there is a field that is 1.5 steps, one-third of a step, one-fourth of a step, and one-fifth of a step wide. If one wants to obtain an area of one mu (ancient Chinese unit of area, 1 mu = 240 square steps), how many steps in length does it need? The answer is: 105 and 137/15 of a step. Solution method: Regard 1.5 steps, one-third of a step, one-fourth of a step, and one-fifth of a step as fifty-five sixty-sixths of a step. Replace 1 with 60, half with 30, one-third with 20, one-fourth with 15, and one-fifth with 12, adding them together to get 137 as the standard for calculation (method). Assume the length of the field is 240 steps, multiply it by 60 to get the actual length (reality). The required number of steps is obtained by dividing the actual length by the standard.
〔五〕今有田广一步半、三分步之一、四分步之一、五分步之一、六分步之一。求田一亩，问从几何？
荅曰：九十七步、四十九分步之四十七。
术曰：下有六分，以一为一百二十，半为六十，三分之一为四十，四分之一为三十，五分之一为二十四，六分之一为二十，并之得二百九十四以为法。置田二百四十步，亦以一为一百二十乘之，为实。实如法得从步。
现在有一块田地，宽度是1.5步、三分之一步、四分之一步、五分之一步、六分之一步。如果要得到一亩田（古代中国一亩为240平方步），问需要多少步长？
答案是：97又49分之47步。
解题方法：将1.5步、三分之一步、四分之一步、五分之一步、六分之一步视为一百二十分之九十七步。以120代替1，以60代替半，以40代替三分之一，以30代替四分之一，以24代替五分之一，以20代替六分之一，合并后得到294作为计算的基准（法）。假设田地的长度是240步，也用120乘以它，得到实际长度（实）。通过实际长度除以基准得到所需的步长。
Now, there is a field that is 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, and one-sixth of a step wide. If one wants to obtain an area of one mu (ancient Chinese unit of area, 1 mu = 240 square steps), how many steps in length does it need? The answer is: 97 and 47/49 of a step. Solution method: Regard 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, and one-sixth of a step as ninety-seven one hundred and twenty-sixths of a step. Replace 1 with 120, half with 60, one-third with 40, one-fourth with 30, one-fifth with 24, and one-sixth with 20, adding them together to get 294 as the standard for calculation (method). Assume the length of the field is 240 steps, multiply it by 120 to get the actual length (reality). The required number of steps is obtained by dividing the actual length by the standard.
〔六〕今有田广一步半、三分步之一、四分步之一、五分步之一、六分步之一、七分步之一。求田一亩，问从几何？
荅曰：九十二步、一百二十一分步之六十八。
术曰：下有七分，以一为四百二十，半为二百一十，三分之一为一百四十，四分之一为一百五，五分之一为八十四，六分之一为七十，七分之一为六十，并之得一千八十九，以为法。置田二百四十步，亦以一为四百二十乘之，为实。实如法得从步。
现在有一块田地，宽度是1.5步、三分之一步、四分之一步、五分之一步、六分之一步、七分之一步。如果要得到一亩田（古代中国一亩为240平方步），问需要多少步长？
答案是：92又121分之68步。
解题方法：将1.5步、三分之一步、四分之一步、五分之一步、六分之一步、七分之一步视为四百七十分之三百九十八步。以420代替1，以210代替半，以140代替三分之一，以105代替四分之一，以84代替五分之一，以70代替六分之一，以60代替七分之一，合并后得到1089作为计算的基准（法）。假设田地的长度是240步，也用420乘以它，得到实际长度（实）。通过实际长度除以基准得到所需的步长。
Now, there is a field that is 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, one-sixth of a step, and one-seventh of a step wide. If one wants to obtain an area of one mu (ancient Chinese unit of area, 1 mu = 240 square steps), how many steps in length does it need? The answer is: 92 and 68/121 of a step. Solution method: Regard 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, one-sixth of a step, and one-seventh of a step as three hundred and ninety-eight forty-seventieths of a step. Replace 1 with 420, half with 210, one-third with 140, one-fourth with 105, one-fifth with 84, one-sixth with 70, and one-seventh with 60, adding them together to get 1089 as the standard for calculation (method). Assume the length of the field is 240 steps, multiply it by 420 to get the actual length (reality). The required number of steps is obtained by dividing the actual length by the standard.
〔七〕今有田广一步半、三分步之一、四分步之一、五分步之一、六分步之一、七分步之一、八分步之一。求田一亩，问从几何？
荅曰：八十八步、七百六十一分步之二百三十二。
术曰：下有八分，以一为八百四十，半为四百二十，三分之一为二百八十，四分之一为二百一十，五分之一为一百六十八，六分之一为一百四十，七分之一为一百二十，八分之一为一百五，并之得二千二百八十三，以为法。置田二百四十步，亦以一为八百四十乘之，为实。实如法得从步。
现在有一块田地，宽度是1.5步、三分之一步、四分之一步、五分之一步、六分之一步、七分之一步、八分之一步。如果要得到一亩田（古代中国一亩为240平方步），问需要多少步长？
答案是：88又761分之232步。
解题方法：将1.5步、三分之一步、四分之一步、五分之一步、六分之一步、七分之一步、八分之一步视为八百四十分之七百四十八步。以840代替1，以420代替半，以280代替三分之一，以210代替四分之一，以168代替五分之一，以140代替六分之一，以120代替七分之一，以105代替八分之一，合并后得到2283作为计算的基准（法）。假设田地的长度是240步，也用840乘以它，得到实际长度（实）。通过实际长度除以基准得到所需的步长。
Now, there is a field that is 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, one-sixth of a step, one-seventh of a step, and one-eighth of a step wide. If one wants to obtain an area of one mu (ancient Chinese unit of area, 1 mu = 240 square steps), how many steps in length does it need? The answer is: 88 and 232/761 of a step. Solution method: Regard 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, one-sixth of a step, one-seventh of a step, and one-eighth of a step as seven hundred forty-eight eight hundred and forty-thirds of a step. Replace 1 with 840, half with 420, one-third with 280, one-fourth with 210, one-fifth with 168, one-sixth with 140, one-seventh with 120, and one-eighth with 105, adding them together to get 2283 as the standard for calculation (method). Assume the length of the field is 240 steps, multiply it by 840 to get the actual length (reality). The required number of steps is obtained by dividing the actual length by the standard.
〔八〕今有田广一步半、三分步之一、四分步之一、五分步之一、六分步之一、七分步之一、八分步之一、九分步之一。求田一亩，问从几何？
荅曰：八十四步、七千一百二十九分步之五千九百六十四。
术曰：下有九分，以一为二千五百二十，半为一千二百六十，三分之一为八百四十，四分之一为六百三十，五分之一为五百四，六分之一为四百二十，七分之一为三百六十，八分之一为三百一十五，九分之一为二百八十，并之得七千一百二十九，以为法。置田二百四十步，亦以一为二千五百二十乘之，为实。实如法得从步。
现在有一块田地，宽度是1.5步、三分之一步、四分之一步、五分之一步、六分之一步、七分之一步、八分之一步、九分之一步。如果要得到一亩田（古代中国一亩为240平方步），问需要多少步长？
答案是：84又7129分之5964步。
解题方法：将1.5步、三分之一步、四分之一步、五分之一步、六分之一步、七分之一步、八分之一步、九分之一步视为二千五百二十分之一千九百八十五步。以2520代替1，以1260代替半，以840代替三分之一，以630代替四分之一，以504代替五分之一，以420代替六分之一，以360代替七分之一，以315代替八分之一，以280代替九分之一，合并后得到7129作为计算的基准（法）。假设田地的长度是240步，也用2520乘以它，得到实际长度（实）。通过实际长度除以基准得到所需的步长。
Now, there is a field that is 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, one-sixth of a step, one-seventh of a step, one-eighth of a step, and one-ninth of a step wide. If one wants to obtain an area of one mu (ancient Chinese unit of area, 1 mu = 240 square steps), how many steps in length does it need? The answer is: 84 and 5964/7129 of a step. Solution method: Regard 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, one-sixth of a step, one-seventh of a step, one-eighth of a step, and one-ninth of a step as one thousand nine hundred eighty-five two thousand five hundred and twenty-ninths of a step. Replace 1 with 2520, half with 1260, one-third with 840, one-fourth with 630, one-fifth with 504, one-sixth with 420, one-seventh with 360, one-eighth with 315, and one-ninth with 280, adding them together to get 7129 as the standard for calculation (method). Assume the length of the field is 240 steps, multiply it by 2520 to get the actual length (reality). The required number of steps is obtained by dividing the actual length by the standard.
〔九〕今有田广一步半、三分步之一、四分步之一、五分步之一、六分步之一、七分步之一、八分步之一、九分步之一、十分步之一。求田一亩，问从几何？
荅曰：八十一步、七千三百八十一分步之六千九百三十九。
术曰：下有一十分，以一为二千五百二十，半为一千二百六十，三分之一为八百四十，四分之一为六百三十，五分之一为五百四，六分之一为四百二十，七分之一为三百六十，八分之一为三百一十五，九分之一为二百八十，十分之一为二百五十二，并之得七千三百八十一，以为法。置田二百四十步，亦以一为二千五百二十乘之，为实。实如法得从步。
现在有一块田地，宽度是1.5步、三分之一步、四分之一步、五分之一步、六分之一步、七分之一步、八分之一步、九分之一步、十分之一步。如果要得到一亩田（古代中国一亩为240平方步），问需要多少步长？
答案是：81又7381分之6939步。
解题方法：将1.5步、三分之一步、四分之一步、五分之一步、六分之一步、七分之一步、八分之一步、九分之一步、十分之一步视为二千五百二十分之二千零四十八步。以2520代替1，以1260代替半，以840代替三分之一，以630代替四分之一，以504代替五分之一，以420代替六分之一，以360代替七分之一，以315代替八分之一，以280代替九分之一，以252代替十分之一，合并后得到7381作为计算的基准（法）。假设田地的长度是240步，也用2520乘以它，得到实际长度（实）。通过实际长度除以基准得到所需的步长。
Now, there is a field that is 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, one-sixth of a step, one-seventh of a step, one-eighth of a step, one-ninth of a step, and one-tenth of a step wide. If one wants to obtain an area of one mu (ancient Chinese unit of area, 1 mu = 240 square steps), how many steps in length does it need? The answer is: 81 and 6939/7381 of a step. Solution method: Regard 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, one-sixth of a step, one-seventh of a step, one-eighth of a step, one-ninth of a step, and one-tenth of a step as two thousand and forty-eight two thousand five hundred and twentieths of a step. Replace 1 with 2520, half with 1260, one-third with 840, one-fourth with 630, one-fifth with 504, one-sixth with 420, one-seventh with 360, one-eighth with 315, one-ninth with 280, and one-tenth with 252, adding them together to get 7381 as the standard for calculation (method). Assume the length of the field is 240 steps, multiply it by 2520 to get the actual length (reality). The required number of steps is obtained by dividing the actual length by the standard.
〔十〕今有田广一步半、三分步之一、四分步之一、五分步之一、六分步之一、七分步之一、八分步之一、九分步之一、十分步之一、十一分步之一。求田一亩，问从几何？
荅曰：七十九步、八万三千七百一十一分步之三万九千六百三十一。
术曰：下有一十一分，以一为二万七千七百二十，半为一万三千八百六十，三分之一为九千二百四十，四分之一为六千九百三十，五分之一为五千五百四十四，六分之一为四千六百二十，七分之一为三千九百六十，八分之一为三千四百六十五，九分之一为三千八十，一十分之一为二千七百七十二，一十一分之一为二千五百二十，并之得八万三千七百一十一，以为法。置田二百四十步，亦以一为二万七千七百二十乘之，为实。实如法得从步。
现在有一块田地，宽度是1.5步、三分之一步、四分之一步、五分之一步、六分之一步、七分之一步、八分之一步、九分之一步、十分之一步、十一分之一。如果要得到一亩田（古代中国一亩为240平方步），问需要多少步长？
答案是：79又83711分之39631步。
解题方法：将1.5步、三分之一步、四分之一步、五分之一步、六分之一步、七分之一步、八分之一步、九分之一步、十分之一步、十一分之一视为二万七千七百二十分之一万九千七百四十七步。以27720代替1，以13860代替半，以9240代替三分之一，以6930代替四分之一，以5544代替五分之一，以4620代替六分之一，以3960代替七分之一，以3465代替八分之一，以3080代替九分之一，以2772代替一十分之一，以2520代替十一分之一，合并后得到83711作为计算的基准（法）。假设田地的长度是240步，也用27720乘以它，得到实际长度（实）。通过实际长度除以基准得到所需的步长。
Now, there is a field that is 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, one-sixth of a step, one-seventh of a step, one-eighth of a step, one-ninth of a step, one-tenth of a step, and one-eleventh of a step wide. If one wants to obtain an area of one mu (ancient Chinese unit of area, 1 mu = 240 square steps), how many steps in length does it need? The answer is: 79 and 39631/83711 of a step. Solution method: Regard 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, one-sixth of a step, one-seventh of a step, one-eighth of a step, one-ninth of a step, one-tenth of a step, and one-eleventh of a step as one thousand nine hundred seventy-four seventieths of a step. Replace 1 with 27,720, half with 13,860, one-third with 9,240, one-fourth with 6,930, one-fifth with 5,544, one-sixth with 4,620, one-seventh with 3,960, one-eighth with 3,465, one-ninth with 3,080, one-tenth with 2,772, and one-eleventh with 2,520, adding them together to get 83,711 as the standard for calculation (method). Assume the length of the field is 240 steps, multiply it by 27,720 to get the actual length (reality). The required number of steps is obtained by dividing the actual length by the standard.
〔一一〕今有田广一步半、三分步之一、四分步之一、五分步之一、六分步之一、七分步之一、八分步之一、九分步之一、十分步之一、十一分步之一、十二分步之一。求田一亩，问从几何？
荅曰：七十七步、八万六千二十一分步之二万九千一百八十三。
术曰：下有一十二分，以一为八万三千一百六十，半为四万一千五百八十，三分之一为二万七千七百二十，四分之一为二万七百九十，五分之一为一万六千六百三十二，六分之一为一万三千八百六十，七分之一为一万一千八百八十，八分之一为一万三百九十五，九分之一为九千二百四十，一十分之一为八千三百一十六，十一分之一为七千五百六十，十二分之一为六千九百三十，并之得二十五万八千六十三，以为法。置田二百四十步，亦以一为八万三千一百六十乘之，为实。实如法得从步。
现在有一块田地，宽度是1.5步、三分之一步、四分之一步、五分之一步、六分之一步、七分之一步、八分之一步、九分之一步、十分之一步、十一分之一、十二分之一。如果要得到一亩田（古代中国一亩为240平方步），问需要多少步长？
答案是：77又86021分之29183步。
解题方法：将1.5步、三分之一步、四分之一步、五分之一步、六分之一步、七分之一步、八分之一步、九分之一步、十分之一步、十一分之一、十二分之一视为八万三千一百六十分之四万七千零三十九步。以83160代替1，以41580代替半，以27720代替三分之一，以27900代替四分之一，以16632代替五分之一，以13860代替六分之一，以11880代替七分之一，以13950代替八分之一，以9240代替九分之一，以8316代替十分之一，以7560代替十一分之一，以6930代替十二分之一，合并后得到258063作为计算的基准（法）。假设田地的长度是240步，也用83160乘以它，得到实际长度（实）。通过实际长度除以基准得到所需的步长。
Now, there is a field that is 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, one-sixth of a step, one-seventh of a step, one-eighth of a step, one-ninth of a step, one-tenth of a step, one-eleventh, and one-twelfth of a step wide. If one wants to obtain an area of one mu (ancient Chinese unit of area, 1 mu = 240 square steps), how many steps in length does it need? The answer is: 77 and 29183/86021 of a step. Solution method: Regard 1.5 steps, one-third of a step, one-fourth of a step, one-fifth of a step, one-sixth of a step, one-seventh of a step, one-eighth of a step, one-ninth of a step, one-tenth of a step, one-eleventh, and one-twelfth of a step as forty-seven thousand and thirty-nine 83160ths of a step. Replace 1 with 83160, half with 41580, one-third with 27720, one-fourth with 27900, one-fifth with 16632, one-sixth with 13860, one-seventh with 11880, one-eighth with 13950, one-ninth with 9240, one-tenth with 8316, one-eleventh with 7560, and one-twelfth with 6930, adding them together to get 258063 as the standard for calculation (method). Assume the length of the field is 240 steps, multiply it by 83160 to get the actual length (reality). The required number of steps is obtained by dividing the actual length by the standard.
〔一二〕今有积五万五千二百二十五步。问为方几何？
荅曰：二百三十五步。
现在有一块正方形田地的面积是五万五千二百二十五平方步。问边长是多少？
答案是：235步。
解题方法：由于正方形的面积等于边长的平方，所以要求边长，就需要计算平方根。将55225步开平方，得到235步。因此，这块正方形田地的边长是235步。
Now, there is a square field with an area of 55,225 square steps. What is the length of its side? The answer is: 235 steps. Solution method: Since the area of a square is equal to the square of its side length, to find the side length, we need to calculate the square root. Taking the square root of 55,225 steps, we get 235 steps. Therefore, the side length of this square field is 235 steps.
〔一三〕又有积二万五千二百八十一步。问为方几何？
荅曰：一百五十九步。
又有面积为二万五千二百八十一步的正方形。问边长多少步？
答案是：159步。
There is also a square with an area of 25,281 steps. How long is the side? The answer is: 159 steps.
〔一四〕又有积七万一千八百二十四步。问为方几何？
荅曰：二百六十八步。
现在有一块正方形田地的面积是七万一千八百二十四平方步。问边长是多少？
答案是：268步。
解题方法：由于正方形的面积等于边长的平方，所以要求边长，就需要计算平方根。将71824步开平方，得到268步。因此，这块正方形田地的边长是268步。
Now, there is a square field with an area of 71,824 square steps. What is the length of its side? The answer is: 268 steps. Solution method: Since the area of a square is equal to the square of its side length, to find the side length, we need to calculate the square root. Taking the square root of 71,824 steps, we get 268 steps. Therefore, the side length of this square field is 268 steps.
〔一五〕又有积五十六万四千七百五十二步、四分步之一。问为方几何？
荅曰：七百五十一步半。
又有面积为五十六万四千七百五十二步又四分之一步的正方形。问边长多少步？
答案是：751步半。
There is also a square with an area of 25,281 steps. How long is the side? The answer is: 159 steps.
〔一六〕现在有一块正方形田地的面积是三十九亿七千二百一十五万六百二十五平方步。问边长是多少？
答案是：63025步。
解题方法：这是一道开方的问题。首先，将给定的面积作为被除数（实）。然后，借一个算筹作为除数，使其超过当前位数。接着，估算得到的商，将借来的算筹乘以1作为除法的除数，进行除法运算。完成除法后，将除数翻倍作为定法。然后继续进行除法，将除数折半并下拉。再次放置借来的算筹，重复之前的操作，将得到的副数加到定法上，再进行除法。将得到的副数与定法合并，继续进行除法和折半操作。如果开方不尽，则为不可开，应以命面的方式表示。如果实数有分数部分，通分后加入子数作为定实。然后进行开方，完成后，开其母报除。如果母数不可开，则以母数乘以定实，再进行开方，直至结果能整除母数为止。
现在有丝一斤，价值343钱。现在有丝7两12铢，问可以卖多少钱？
答案是：可以卖161钱又23/32钱。
解题方法：以一斤丝的铢数为比例（法），用一斤丝的价格乘以现有的丝的重量（7两12铢）作为实际得分（实）。实际得分除以比例得到可以卖的钱的数量。
Now, there is a square field with an area of 3,972,115,625 square steps. What is the length of its side? The answer is: 63,025 steps. Solution method: This is a problem of square root extraction. First, take the given area as the dividend (actual). Then, borrow a counting rod as the divisor, making it exceed the current digit place. Next, estimate the quotient, multiply the borrowed counting rod by 1 to serve as the divisor for the division, and perform the division. After completing the division, double the divisor to establish a fixed method. Continue with the division, halving and pulling down the divisor. Place the borrowed counting rod again, repeating the previous steps, and add the obtained subsidiary number to the fixed method before performing the division. Combine the obtained subsidiary number with the fixed method and continue with the division and halving operations. If the square root cannot be completely extracted, it is considered irreducible and should be indicated by naming the face. If the actual number has a fractional part, integrate the fraction into the numerator to establish a fixed actual. Then proceed with the square root extraction, and after completion, extract the square root of the denominator and divide accordingly. If the denominator cannot be extracted, multiply the denominator by the fixed actual, then extract the square root, and continue until the result can be evenly divided by the denominator.
〔一七〕今有积一千五百一十八步、四分步之三。问为圆周几何？
荅曰：一百三十五步。
现在有一个圆的面积为一千五百一十八步四分之三，问这个圆的周长是多少步？
答案是：135步。
Now, there is a circle with an area of 1518 and three-quarters of a step. What is the circumference of this circle in steps? The answer is: 135 steps.
〔一八〕今有积三百步。问为圆周几何？
荅曰：六十步。
开圆术曰：置积步数，以十二乘之，以开方除之，即得周。
现在有一块圆形田地的面积是300平方步。问圆的周长是多少？
答案是：60步。
解题方法：将给定的面积步数乘以12，然后开方，即可得到圆的周长。
Now, there is a circular field with an area of 300 square steps. What is the circumference? The answer is: 60 steps. Solution method: Take the number of square steps of the area, multiply it by 12, and then extract the square root to obtain the circumference.
〔一九〕今有积一百八十六万八百六十七尺。问为立方几何？
荅曰：一百二十三尺。
现在有一个立方体的体积为一百八十六万八百六十七尺。问这个立方体的边长是多少尺？
答案是：123尺。
Now, there is a cube with a volume of 1,868,667 cubic feet. What is the length of the edge of this cube? The answer is: 123 feet.
〔二０〕今有积一千九百五十三尺、八分尺之一。问为立方几何？
荅曰：一十二尺半。
现在有一个立方体的体积是一千九百五十三尺加上八分之一尺。问这个立方体的边长是多少？
答案是：12.5尺。
Now, there is a cube with a volume of 1,953 feet and one-eighth of a foot. What is the length of the edge of the cube? The answer is: 12.5 feet. Solution method: Convert the given volume to feet, calculate the cube root, and you will obtain the length of the edge of the cube.
〔二一〕今有积六万三千四百一尺、五百一十二分尺之四百四十七。问为立方几何？
荅曰：三十九尺、八分尺之七。
现在有一个立方体的体积为六万三千四百一尺五百一十二分之四百四十七。问这个立方体的边长是多少？
答案是：三十九尺八分七。
Now, there is a cube with a volume of 63,401 feet and 447/512 of a foot. What is the length of the edge of this cube? The answer is: 39 feet and 7/8 of a foot.
〔一一〕今有丝一斤价直三百四十三。今有丝七两一十二銖，问得钱几何？
荅曰：一百六十一钱、三十二分钱之二十三。
术曰：以一斤銖数为法，以一斤价数，乘七两一十二銖为实。实如法得钱数。
现在有丝一斤，价值343钱。现在有丝7两12铢，问可以卖多少钱？
答案是：可以卖161钱又23/32钱。
解题方法：以一斤丝的铢数为比例（法），用一斤丝的价格乘以现有的丝的重量（7两12铢）作为实际得分（实）。实际得分除以比例得到可以卖的钱的数量。
Now, one jin (a unit of weight) of silk is valued at 343 coins. If one has 7 liang and 12 zhu of silk now, how much money can be made? The answer is: 161 coins and 23/32 of a coin can be obtained. Solution method: Use the number of zhu per jin as the ratio (law), multiply this price by the weight of silk available (7 liang and 12 zhu) to get the actual amount (real). Dividing the actual amount by the ratio yields the amount of money that can be made.
〔二二〕又有积一百九十三万七千五百四十一尺、二十七分尺之一十七。问为立方几何？
荅曰：一百二十四尺、太半尺。
开立方术曰：置积为实。借一算步之，超二等。议所得，以再乘所借一算为法，而除之。除已，三之为定法。復除，折而下。以三乘所得数置中行。復借一算置下行。步之，中超一，下超二等。復置议，以一乘中，再乘下，皆副以加定法。以定法除。除已，倍下、并中从定法。復除，折下如前。开之不尽者，亦为不可开。若积有分者，通分內子为定实。定实乃开之，讫，开其母以报除。若母不可开者，又以母再乘定实，乃开之。讫，令如母而一。
现在有一个立方体的体积是一百九十三万七千五百四十一尺加上二十七分之一十七尺。问这个立方体的边长是多少？
答案是：124尺又三分之二尺。
解题方法：将给定的体积作为被除数（实）。借一个算筹作为除数，使其超过当前位数两等。估算得到的商，将借来的算筹乘以2作为除法的除数，进行除法运算。完成除法后，将除数乘以3作为定法。然后继续进行除法，将除数折半并下拉。将得到的3倍的商放在中行。再次借一个算筹放在下行。进行除法，中行超过一等，下行超过两等。重复放置估算值，将中行乘以1，下行乘以2，都加到定法上。用定法进行除法。完成除法后，将下行的2倍与中行相加合并到定法。继续进行除法和折半操作。如果开立方不尽，则为不可开，应以命面的方式表示。如果实数有分数部分，通分后加入子数作为定实。然后进行开方，完成后，开其母报除。如果母数不可开，则以母数乘以定实，再进行开方，直至结果能整除母数为止。
Now, there is a cube with a volume of 1,937,541 feet and one-seventeenth of twenty-seven thousandths of a foot. What is the length of the edge of the cube? The answer is: 124 feet and two-thirds of a foot. Solution method: Take the given volume as the dividend (actual). Borrow a counting rod as the divisor, making it exceed the current digit place by two ranks. Estimate the quotient, multiply the borrowed counting rod by 2 to serve as the divisor for the division, and perform the division. After completing the division, triple the divisor to establish a fixed method. Continue with the division, halving and pulling down the divisor. Place the obtained tripled quotient in the middle row. Borrow another counting rod and place it in the lower row. Perform the division, with the middle row exceeding by one rank and the lower row by two ranks. Repeat the process of placing estimates, multiply the middle row by 1 and the lower row by 2, and add them both as subsidiaries to the fixed method. Divide by the fixed method. After completing the division, double the lower row and combine it with the middle row into the fixed method. Continue with the division and halving operations as before. If the cube root cannot be completely extracted, it is considered irreducible and should be indicated by naming the face. If the actual number has a fractional part, integrate the fraction into the numerator to establish a fixed actual. Then proceed with the extraction of the cube root, and after completion, extract the cube root of the denominator and divide accordingly. If the denominator cannot be extracted, multiply the denominator by the fixed actual, then extract the cube root, and continue until the result can be evenly divided by the denominator.
〔二三〕今有积四千五百尺。问为立圆径几何？
荅曰：二十尺。
现在有一个直立圆柱体的体积为四千五百尺。问这个圆柱体的底面直径是多少？
答案是：20尺。
Now, there is a vertical cylinder with a volume of 4,500 cubic feet. What is the diameter of the base of this cylinder? The answer is: 20 feet.
〔二四〕又有积一万六千四百四十八亿六千六百四十三万七千五百尺。问为立圆径几何？
荅曰：一万四千三百尺。
开立圆术曰：置积尺数，以十六乘之，九而一，所得开立方除之，即丸径。
现在有一个球体的体积是一万六千四百四十八亿六千六百四十三万七千五百尺。问这个球的直径是多少？
答案是：14300尺。
解题方法：将给定的体积乘以16，然后除以9，得到的结果开立方根，即可得到球的直径。
Now, there is a sphere with a volume of 16,448,664,375,000 feet. What is the diameter of the sphere? The answer is: 14,300 feet. Solution method: Take the number of cubic feet, multiply it by 16, then divide by 9, and extract the cube root of the result to obtain the diameter of the sphere.