Who understands? He traveled through time with a high-spec spatial ability.
Chapter 356 Arithmetic
Ji Yunchuan immediately wrote the poem on Xuan paper and had his page take it to a calligraphy and painting shop to have it carved into two plaques, which were then hung at the entrance of all the schools.
Then, eager to do something for Qiao Jingjing, he took the strange writings she had copied to the library, leaving Qiao Jingjing alone to wait in Yunshuiyao.
The sound of reading aloud drifted in from outside the window. Qiao Jingjing, having nothing else to do, followed the sound to the school next door.
More than twenty students sat together, bamboo slips spread out in front of them, their brows furrowed. A teacher of about fifty years old was explaining arithmetic, holding a ruler.
"Please look at this question: 'There is a field that is 15 paces wide and 16 paces long. How many paces is the field?' The Master tapped the table with his ruler. 'We should use the method of multiplying the width and length. 15 paces multiplied by 16 paces equals 240 paces.'"
Qiao Jingjing stood outside the window, observing with great interest. She saw the students picking up counting rods and arranging them on the ground. They first laid fifteen rods horizontally, then arranged sixteen vertically, and then counted the intersections one by one.
"This is too primitive..." Qiao Jingjing muttered to herself. She recalled the multiplication tables she had memorized as a child, and realized that such simple multiplication did not need to be so complicated.
With a sharp "smack," the ruler slammed heavily onto the desk.
"Du Mingyuan! You're wrong again!" The teacher's eyes widened in anger. "Fifteen times sixteen is clearly two hundred and forty, so why did you arrive at two hundred and thirty-eight?"
A well-mannered young student blushed and said, "I...I miscounted the intersection points..."
"Useless!" The teacher was so angry that his beard stood on end. "You can't even do such a simple multiplication problem correctly, how can you talk about passing the imperial examinations and entering officialdom?"
Qiao Jingjing watched this scene and a thought struck her. She gently knocked on the door, and the classroom immediately fell silent.
"Who is this young lady..." The teacher looked towards the door with a puzzled expression.
"My name is Qiao Jingjing. I apologize for disturbing your studies." She bowed slightly. "I noticed that you were all struggling with arithmetic. Would you allow me to introduce a simpler method?"
The classroom erupted in discussion. Du Mingyuan sized Qiao Jingjing up and down, a hint of disdain flashing in his eyes: "A woman knows arithmetic?"
Qiao Jingjing was not offended, but instead smiled slightly: "I know a little bit."
The teacher hesitated for a moment. Since it was not easy to enter the academy, and she had come from Yunshuiyao, she was very likely a distinguished guest of Headmaster Ji. So he nodded and said, "Please speak, young lady."
Qiao Jingjing walked to the center of the classroom, picked up a charcoal pencil, and wrote the five characters "Nine-Nine Multiplication Table" on the wooden board.
"This is the 'Nine-Nine Multiplication Table.' Once you memorize it, you can quickly calculate the multiplication of two numbers." As she spoke, she wrote the neat multiplication table on the wooden board.
"One times one equals one, one times two equals two...one times nine equals nine; two times one equals two, two times two equals four...nine times nine equals eighty-one."
The students stared wide-eyed, some already beginning to quietly recite along. Du Mingyuan, however, scoffed, "Nonsense! Arithmetic is a rigorous subject; how can one rely on these nursery rhymes to cheat?"
Qiao Jingjing had anticipated that someone would question her, so she calmly said, "How about we have a competition? Please give me a question, and I and this...Young Master Du will calculate at the same time to see who is faster and more accurate."
The Master became interested, stroked his beard, and said, "Good! Now I have a bolt of silk, priced at 320 coins. How much should I pay for seven bolts?"
Du Mingyuan immediately grabbed the counting rods and began to arrange them. Qiao Jingjing, however, stood still, closed her eyes and silently recited the incantation: "Three times seven is twenty-one, two times seven is fourteen..." In less than three breaths, she opened her eyes and said: "Two thousand two hundred and forty coins."
Du Mingyuan was still counting the counting rods when he heard the answer, his hand trembled, and the rods scattered all over the ground: "No... impossible!"
The teacher, after verifying the calculation with surprise, nodded: "The girl's answer is correct."
An uproar erupted in the classroom.
Qiao Jingjing seized the opportunity to say, "This is just the simplest multiplication. The multiplication tables also apply to larger numbers. For example, thirty-six multiplied by forty-eight..."
She turned and wrote the Arabic numerals 36 and 48 on the wooden board, then drew a framework for vertical multiplication.
"This is how I write numbers in my hometown; it's much simpler," she explained, demonstrating the steps of vertical multiplication. "Six times eight is forty-eight, write eight and carry over four; three times eight is twenty-four, add four and you get twenty-eight..."
The students stared in disbelief, even the teacher leaned closer for a closer look. Du Mingyuan's face turned ashen, and he suddenly shouted, "Sorcery! This must be sorcery! Arithmetic has always used counting rods, where have you ever heard of such strange symbols?"
Just as Qiao Jingjing was about to explain, a series of hurried footsteps came from outside the door. A middle-aged man in official robes strode in, his face grim: "Who is spreading heretical doctrines here?"
"Dr. Zheng!" The teacher quickly bowed. The visitor was none other than Zheng Shouren, the academy's mathematics doctor, known for his meticulousness.
Zheng Shouren glanced around, his gaze settling on the Arabic numerals on the blackboard. His brow furrowed. "What are these scribbles?" he asked.
Qiao Jingjing replied calmly and confidently, "These are numbers, a simpler way of counting than counting rods."
"Absurd!" Zheng Shouren shouted sternly. "Our Chinese arithmetic has a long and rich history. How can we allow foreign evil arts to taint it? Guards, wipe away this filth!"
Several students hesitated to step forward, but were stopped by Qiao Jingjing: "Dr. Zheng, knowledge knows no borders. If this method is indeed simple, why can't we learn it?"
Zheng Shouren sneered: "Simple? That's misleading! If you're truly proficient in arithmetic, dare you challenge me?"
The atmosphere in the classroom suddenly became tense. Qiao Jingjing knew this was the best opportunity to prove herself: "Please ask the professor to give me a question."
Zheng Shouren pondered for a moment, then said loudly, "There is an unknown number of objects. When counted in groups of three, there are two left over; when counted in groups of five, there are three left over; when counted in groups of seven, there are two left over. How many objects are there?"
This is a famous problem from the "Sun Tzu's Mathematical Classic," which usually requires complex calculations. The students all lowered their heads, and even Du Mingyuan looked troubled.
Qiao Jingjing's eyes lit up – wasn't this the "Han Xin Counting Soldiers" problem? She had learned how to solve it in a math interest class.
She picked up the chalk and wrote on the blackboard:
“70x2 + 21x3 + 15x2 = 140 + 63 + 30 = 233”
然后解释道:“此乃中国剩余定理。三、五、七两两互质,取5x7=35的倍数除以3余1者为70;同理得21和15。最后减去3x5x7=105的倍数,得最小解23。”
The entire school was silent. Zheng Shouren's eyes widened, his fingers trembling slightly: "You...how do you know such a secret technique?"
Qiao Jingjing smiled: "This is not a secret method, but the crystallization of wisdom. Doctor, the way of learning is to exchange and innovate, not to be stuck in the past."
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