Chapter 22

Heartfelt Voice

Dance in front of the class? She wants me to be her entertainment? Is she trying to take revenge on me? Jiyeon blew out a quick breath and said, "I can't dance. Could you please ask me to do something else?"

Sohyun shook her head, that evil smile growing wider. "Don't go back on your words," she retorted, her voice full of authority. "Come to the centre-front and dance!"

"Go dance! Go dance! Go dance!" all students chanted in a singsong voice while tapping out a rhythm on the tables, with the tips of their fingers, except her lover and Chaeyeon. Her lover's annoyance was palpable. His upper lip curled up as Jaehyun stared at Sohyun, while Chaeyeon kept her head down and pressed her lips together.  

The students' chanting and the sound of fingers tapping on the tables irritated her. Jiyeon took a deep breath, trying to remain calm. She opened to speak, but her lover spoke first, just loud enough to attract attention, "Kim Sohyun, our teacher said she can't dance. Are you deaf?"

Sohyun jerked her gaze to Jaehyun. "Why do you suddenly defend her?" she snapped, slamming her fist on the table, anger lacing her voice. "Don't tell me you've fallen for her."

All the students, including Chaeyeon looked alternately at Jaehyun and Jiyeon, making her feel uncomfortable. Jaehyun scratched his forehead and looked nervous. His voice trembled as he stammered, "W-who says I've fallen for her...I just think what you're doing is disrespectful. She…she is our teacher whom we should respect."

Sohyun shook her head, disbelief clearly showing in her features. Before Sohyun could open , Jiyeon announced aloud, "Okay, guys. I'm going to dance." She stood up and dragged her feet to the centre-front of the room. She didn't want her students to suspect their relationship. She didn't want him to be mocked.

The class turned to silence, and everyone was looking straight ahead at her.

I don't know how to dance. Jiyeon closed her eyes briefly, and her lips curled into a tiny smile as the image of Taeyong dancing in the class flashed through her mind. She stood quietly at the centre-front for a while, staring into space as she tried to recall Taeyong's dance movements in detail. 

Slowly, Jiyeon's hands raised up her body, and some students' fingers began tapping out a rhythm on the tables. Her body merely swayed at first, her head dropping forward, allowing the fall of hair to hide her embarrassed face. Then her hips started to move, slowly at first, following the gentle drifting of her arms. She swayed her head in a circle allowing her hair to fall back again, revealing her face as her body and arms continued to move with the beat of drumming fingers on the tables. A loud roar erupted from the students.

Jiyeon found dancing enjoyable; her embarrassment faded while the excitement began building. Jaehyun's eyes lit up, and his mouth gaped open when she moved forward with a rolling double-hip , rotated her pelvis clockwise with a vertical shimmy, one arm over her head and the other at the leading hip. Imagining waves on the water's surface, she then moved backwards with shallow, precise undulations.

"That's pretty y!" the boys shouted, pumping their fists in the air. Simultaneously, the girls laughed and clapped their hands, with mingled disbelief and amazement.

"I thought you said you can't dance?" The fat male student's voice thundered through the room.

The class lapsed into silence as Jiyeon stood straight and tall, staring at them. For a minute or two, she just stood and fought to catch her breath. She switched her gaze to Sohyun and spoke, "I've done what you asked me to do. Are you satisfied?"

"I have to admit you've surprised me." Sohyun held her gaze. "I thought you couldn't dance."

I surprised myself, too. Jiyeon walked over to her, bent close to her and whispered in her ear, "And that's why you asked me to dance—you intended to embarrass me in front of your classmates, correct?"  

"You've been so unfair." Sohyun ducked her head down.

A sigh escaped her lips. "Any student who got caught cheating on the exam earned an F grade, Sohyun." Jiyeon gently patted Sohyun on the shoulder, then straightened up and went to the blackboard. She clapped her hands twice and like magic, the rumble in the room stopped. All the students sat straight up, folded their hands on top of their desks, and looked straight ahead at the blackboard.  

Seconds later, one hand shot up in the air, and Jaehyun said, "Teacher Park, I'm still waiting for you to answer my question, how to square two-digit numbers in your head so fast."

"Thank you for reminding me. I'm going to answer your question." Jiyeon smiled and grabbed a piece of chalk. "Let's say I want to square the number 14. Instead of multiplying 14 x 14, I'm going to use two numbers that are easier to multiply but also add to 28." She drew the table on the board.

Once Jiyeon finished drawing, she moved aside so that the students could see the table. They broke into excited whispering. They noticed that the products were getting smaller, and their difference from 196 was 1, 4, 9, 16, 25, or 12, 22, 32, 42, 52. They found this pattern astonishing. Jiyeon just watched them until they finished discussing.

Pointing her index finger to the fifth row, Jiyeon continued slowly, "I choose 10 x 18. To get the final answer, I just add 42 = 16 since 10 and 18 are each 4 away from 14. Thus, 142 = 180 + 16 = 196. The technique is diagrammed as follows—" She drew it on the board:

9d83f7.png

"Now let's see how this works for another square." She drew another diagram.

518274.png

"To square 79, add 1 to obtain 80 and subtract 1 to obtain 78. Next multiply 80 x 78. To get the final answer, add the square of 1, the number by which I climbed up and down from 79. Thus, 792 = 6,240 + 1 = 6,241."

Immediately, one hand was raised in the air, and the blunt sugar-bowl haired student spoke, "I understand your technique, but the problem is how to multiply 80 x 78 in your head that fast. Could you tell us the secret?"

"Thank you for asking that question." Jiyeon smiled. "To multiply 80 x 78, we just need to multiply 8 x 78 and tag one zero on the end. In our mental multiplication problem of 8 x 78, we solve this by treating 78 as 70 + 8 then distributing the 8 as follows,"

8 x 78 = 8 x (70 + 8) = (8 x 70) + (8 x 8) = 560 + 64 = 624. To get the product of 80 and 78, tag one zero on the end ⇒ 6,240.

Jiyeon circled the 624 and the 6,240 she had written and looked at him, saying, "Do you understand?"

He just nodded. Then another hand was raised, and Sohyun challenged, "Miss Park, square the number 94."

"Eighty-eight hundred," Jiyeon answered quickly and energetically, "thirty-six."

The class let out a collective gasp.

Jiyeon looked at the whole class, saying, "If you think squaring a big two-digit number in the high 90s, is an impossible problem to compute, you're totally wrong. Squaring these numbers is easier because they allow you to round up to 100." She turned to the board and drew another diagram. 

8af002.png

She moved aside. "Wasn't that easy? You should have rounded up by 6 to 100 and down by 6 to 88, and then multiplied 100 x 88 to get 8,800 and added the square of 6 to get the final answer, 8,836."

She took a deep breath before she continued speaking while scribbling down on the board:  

"Here is the algebraic relationship that works to explain this technique,

(n - d)2 = n2 – 2nd + d2 = n(n - 2d) + d2

Hence, to square 94, I set n = 100 and d = 6 to get

942 = (100 - 6)2 = 100 (100 - 12) + 62 = 8,836

Similarly,

(n + d)2 = n2 + 2nd + d2 = n(n + 2d) + d2

To find 142 when n = 10 and d = 4

(10 + 4)2 = 10 (10 + 8) + 42 = 196

Remember, n is the rounded number, and d is the distance from the number being squared to the rounded number. This technique is so efficient and with a little practice, it won't be long before you can beat someone with a calculator."   

Jiyeon clapped her hands, releasing chalk dust into the air. From the corner of her eye, she watched Jaehyun scribble in his notebook. I want to tell you my plan of going to Heartful Café with Yoona after teaching and ask you to join, but how do I tell you without being suspected by your classmates?

"Teacher Park, I can't see the blackboard properly. Could you move over a little?" one of the female students said politely, snapping her out of her thoughts.

"Sorry." Jiyeon walked over to the front of her desk and sat down on it, swinging her legs as she observed the students scribbling into their notebooks.

When they finished scribbling, Jiyeon cleared and announced, "Okay, guys. Let's play another number trick." She threw her arms open wide in an expansive gesture, smiling broadly. "Whoever can figure out the reason why the trick works will get their math grade raised."

Excitement filled the classroom. The students looked enthusiastic, gentle smiles decorating their faces as they waited for her words.

Jiyeon clapped her hands once and instructed, "Guys, write down any two-digit number on your notebooks and don't tell me what you have."

Ducking their heads, they wrote in their notebooks. From where she was sitting she couldn't see what their numbers were.

Looking up at the ceiling, Jiyeon continued, "Put a zero to the right of the number you picked. Now, you have a three-digit number. You need to make a six-digit number by writing that three-digit number twice. For example, if your number is 870, you'll have 870,870. Are you guys with me?"

"Yes," they said in unison.

"Divide that number by 7, and then divide that quotient by 10."

"Done!" Their voices rose in excitement.

Jiyeon shifted her gaze back towards them and said, "Now divide the previous quotient by 11, and then that quotient by 13." She watched their fingers punch the calculator and quickly added, "Ta-dah! You've got your number back!"

Their heads jerked up, and amazement dawned in their eyes. "How did you know that?" Admiration laced Jaehyun's voice. Jiyeon favored her lover with a bright smile, to which he responded with a slow smile of his own.

"You're too shameless! Stop flirting with him!" Baekwoon's voice echoed in her ears, which Jiyeon shook it off.

Jiyeon's smile widened when two hands shot up in the air. Chaeyeon and Sohyun looked at each other; then Chaeyeon quickly dropped her hand down on the table and lowered her head. In order to avoid being accused of acting unjustly again, Jiyeon asked, "Guys, who raised their hands first, Chaeyeon or Sohyun?"

"Chaeyeon!" some students shouted, while the others stayed silent, their eyes were glued to their notebooks, seemingly trying to figure out the math behind the trick. Sohyun's eyes narrowed in displeasure.

"Chaeyeon," Jiyeon called out. Chaeyeon lifted her head and looked at her. She added softly, "Go ahead and speak."

"I…I think I know how you did that." Her voice shook a little bit. Chaeyeon looked down at her notebook and continued, "Let's say our number is 72 and we add a zero. We get 720. When we repeat this number in the same order, we get 720,720. The secret of the trick is in this number. This number when divided by 7, 10, 11, and 13, will be the original number. The beautiful thing about this trick is that you always come up with the original number and not a variation of it."

The classroom erupted into applause, which Sohyun silenced by challenging Chaeyeon aloud, "Chaeyeon, come up to the blackboard and explain mathematically how it happens."

Chaeyeon remained silent for a moment, then stared at Sohyun. "You think I'm afraid to do it, don't you? I'm not, I will." Her lower lip trembled, but her voice held steady.

Go Chaeyeon! Don't let anyone oppress you. Jiyeon smiled proudly, looking at Chaeyeon as she rose to her feet and went to the blackboard. She ducked her head down and tapped her right foot lightly on the floor as if trying to hide her nervousness.

"The reason that—"

"Don't speak to the floor. Speak to us," Sohyun said aloud. Jiyeon shot her an incredulous look and shook her head.

Chaeyeon straightened up, stood tall and stared straight ahead at her classmates. She tapped her right foot lightly on the floor as she spoke, "The reason that this works as it does is that to form the six-digit number we actually multiplied the original two-digit number by 10,010."

She turned to the blackboard and picked up a piece of chalk. Her hand trembled as she wrote on the board:

72 x 10,010 = 72 x (10,000 + 10) = 72 x 10,000 + 720 = 720,000 + 720 = 720,720.

"But the four prime factors of 10,010 are 7, 10, 11, and 13."

10,010 = 7 x 10 x 11 x 13.

Chaeyeon moved aside, turned back to face her classmates and continued, "Therefore, by dividing successively by 7, 10, 11, and 13, we have undone the original multiplication by 10,010, leaving the original number."

"That's correct," Jiyeon responded, clapping her hands.

All students erupted in cheers, except Sohyun, who was staring at her notebook, gripping the pencil tightly. A wave of applause carried Chaeyeon to her seat. She sat upright, looking at Jiyeon; her entire face lit up with her smile. She looked so proud of herself. Jiyeon smiled, giving her thumbs-up.

Jiyeon continued showing off 'magic' number tricks. She enjoyed watching her students' jaws drop when they saw her guess their secret number correctly again and again. Her students really got into it because they truly wanted to learn how to do it themselves.

She looked down at her watch, noting the time. Jiyeon then paced around the front of the room while speaking, "The addition trick I'm going to performance is fun. It will amaze you guys." She sat down on the edge of her desk, looking at the students. "I need a volunteer. Who wants to be my volunteer?"

Six hands shot in the air. Jaehyun was the first student who raised his hand. Jiyeon gulped before speaking, "Jaehyun, come to the blackboard."

Jaehyun sprang to his feet, ran to the blackboard and picked up the chalk. He gave her his charming smile, exposing two dimples on either side of his face. His dimpled smile warmed her blood and made her heart beat faster. The slow, deep breath she took calmed her heart rate.

"Jaehyun, write down any three-digit number with no two like digits: omitting zero," Jiyeon instructed calmly.

He wrote 957 on the board.

"Please, make five other numbers with those same digits."

He did as he was told. He wrote the numbers in a vertical column:

957

975

795

759

597

579

Just as Jaehyun finished writing the last number, Jiyeon announced aloud, "The sum of those six numbers is 4,662. I could actualy determine the sum after the first number Jaehyun offered."

A look of stricken surprise and total astonishment crossed the students' faces. Jiyeon obviously couldn't help but laugh at their expression. Her laughter ceased when they began discussing how she did that. It brought satisfaction to her heart.  

"Teacher Park, how can this be done so fast?" Jaehyun's voice held such quiet awe. Simultaneously, a few of her students groaned.

"I have no cule how you did that."     "You make it sound so easy. Tell us, what's the secret?"

"All right," Jiyeon said, smiling broadly. "All I have to do is to get the sum of the digits of the original number. Here I get 9 + 5 + 7 = 21 and then multiply 21 by 222 to get 4,662, which is the required sum."

The students let out a collective gasp, followed by exclamations of "Cool!" "Awesome!" and "That's indeed easy!"

Then one hand shot up in the air, and Sohyun questioned, a hint of curiosity lacing her voice, "Why 222?"

"That's good question!" Jiyeon clapped her hands once and let her eyes roam around the classroom. "Does anyone want to try to answer?"   

No student raised their hands. Her eyes landed on Chaeyeon, who was scribbling in her notebook, moving like she was talking inaudibly to herself. Jiyeon cleared to get her attention, and Chaeyeon raised her head to look at her. Jiyeon smiled. "Chaeyeon, how about you? You want to try?"

Chaeyeon looked at her in silence for a moment, then nodded. Quietly, she said, "I think I can do it."

"Yes, you can do it," Jiyeon said as she raised her fist in front of her chest, lightly shaking it in a gesture of encouragement. Then she shifted her gaze to the whole class and announced, "Guys, Chaeyeon is going to try to answer Sohyun's question. Pay attention to her, okay?"

They nodded enthusiastically and looked straight ahead at the blackboard in silence, ready to listen.   

Jiyeon looked back at Chaeyeon and said, "Chaeyeon, come up to the blackboard."

Chaeyeon took a deep breath before she rose to her feet and went to the blackboard. Jaehyun handed her the chalk, which she took it hesitantly. Then he grabbed the eraser from the ledge and erased everything that was on the board.

"Jaehyun, go back to your seat," Jiyeon told him once he finished erasing. He nodded, put the eraser back on the blackboard ledge and walked back to his seat.

"I'm going to use simple algebra to answer Sohyun's question," Chaeyeon began after a moment's silence. Her voice sounded calm and steady as she spoke while writing on the board,

"Consider the number xyz = 100x + 10y + z, where x, y, z can be any of the digits 1, 2, 3, ..., 9. The sum of the digits is x + y + z. I then represent all of the six numbers of these digits on my list:

100x + 10y + z

100x + 10z + y

100y + 10x + z

100y + 10z + x

100z + 10x + y

100z + 10y + x

This equals to

100(2x + 2y + 2z) + 10(2x + 2y + 2z) + 1(2x + 2y + 2z)

= 200(x + y + z) + 20(x + y + z) + 2(x + y + z)

= 222(x + y + z)

which is 222 times of the sum of the digits."

Chaeyeon moved aside and turned to face her classmates. "That's all."

Her classmates erupted in applause that sounded genuine, while Sohyun accepted the explanation with resignation. "What can I say? You're clever!"

With a bright smile adorning her face, Jiyeon stood up and approached her. "You did a good job." She put her arm around Chaeyeon's shoulder and squeezed it lightly.

Chaeyeon looked up at her and smiled. "Thank you, Teacher Park." Then she went back to her seat.

The class went quiet again and then the bell rang, indicating the end of the school day. Students rushed out, talking excitedly, while Jiyeon walked back to her desk and sat down on the chair. Now there were only Jiyeon, Chaeyeon and Jaehyun in the classroom.

Smiling, Jaehyun rose to his feet. Jiyeon felt all her senses come alive as she watched him walk towards her. To her surprise, Jaehyun sat down on the chair beside Chaeyeon. Jiyeon snorted at the slight wave of disappointment that washed over her.

Chaeyeon looked uncomfortable; she kept her head down. Jaehyun cleared his throat. "Chaeyeon, could I ask you something?"

Chaeyeon just nodded. Jaehyun patted her arm gently. "I noticed when you spoke in front of class, you—"

"Tapping my foot on the floor helped me reduce nervousness," Chaeyeon interjected, looking up at the ceiling.

"Oh, I—"

"Chae, let's go home."

They turned their heads in the voice's direction and found Taeyong stand in the doorway, leaning against the door frame.


 

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KimmyNurry
692 streak #1
Chapter 40: Congrats on the bid! ^^
lovelyfeisty
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Chapter 40: Congratulations on the highest bid and I'll be reading soon!
WR_Supplier
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Chapter 34: Congrats on the ad bid feature!
dreamshun
1813 streak #4
Chapter 34: Congrats^^
Damia_Song123 #5
Chapter 34: Congratulations on winning the bid ^^
Ghad20
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Chapter 34: Congratulations
sabirah
#7
Chapter 34: Wow the whole story is so overwhelming ,i would likely to digest the gist of it ...Love it as it's been a long time that i read this kind of story before 😍