Open Middle®
Directions: Using the digits 1 to 9, at most one time each, place a digit in each box to make a true statement.
Hint
What digits would be bad choices for the denominators?
What digits would be good choices for the denominators?
What digits would be good choices for the denominators?
Answer
Answers found so far include:
2/8 + 1/4 + 3/6 = 1
2/4 + 3/9 + 1/6 = 1 (found by Koharu in Ms. Wilson’s class)
1/6 + 3/9 + 4/8 = 1
2/8 + 1/4 + 3/6 = 1
2/4 + 3/9 + 1/6 = 1 (found by Koharu in Ms. Wilson’s class)
1/6 + 3/9 + 4/8 = 1
Source: Owen Kaplinsky
1/3+1/3+1/3=1
can only use each digit one time
1/3 + 1/2 + 1/6
correct
1/3+1/3+1/3=1
I there only one answer? 1/4+2/8+3/6
Is there only one answer? 1/4+2/8+3/6
My students also found 4/8 + 3/9 + 1/6
Nice! I’ll add that to the answers.
4/8 + 3/9 + 1/6
1/3 + 1/3 + 1/3 =1
1/3 + 1/3 + 1/3
worng only use 1 once and 3 once from 1-9
2/8 + 1/4 + 3/6 = 1
2/8 + 1/4 + 3/6 = 1
2/8+1/4+3/6
2/8+1/4+3/6
2/8+5/8+1/8
1/4 + 2/8 + 3/6 = 1
3/9+3/9+3/9=1
1/3+1/3+1/3
The answer is 3/6+14+28=1
Hey Owen, this is nearly identical to the task I put up about 3 years ago, do you think we should take mine down or maybe collaborate? Your title is definitely better and I went all the way to 10 just because it provided a few more answers and touched on decimals. Also, I was inspired by the book The Wishing Club, which goes perfectly with these tasks.
This answer does not follow the rules with 1 digit in each box, but definitely answers the question. My student came up with 9/12 + 5/34 + 7/68
Oh! I didn’t realize that this is identical to yours! I think I should take mine down instead, because yours is the first one up. What do you think?
I would definitely leave yours up or we’d lose this great discourse thread!
This answer does not follow the rules with 1 digit in each box, but definitely answers the question. My student came up with 9/12 + 5/34 + 7/68
Gina, you should create that one and post it. It may already be on here already but by putting 1 box for numerator and 2 for each denominator you’ve created a pretty challenging task! I wonder if there is more than one answer?
Amazing!! How could you find the answer?? Just keep trial and errors??
i got 1/4 + 2/8 + 3/6
My answer is 1/4+4/8+4/16.
1/4+2/8+3/6
1/4+2/8+3/6
1/3, 1/3, 1/3
3/9, 2/4, 1/6
2/5 + 2/5 + 1/5 = 1
Wait no I’ll use
2/8 + 1/4 + 3/6
Because I can only use them once
2/8+1/4+3/6?
1/2 + 2/8 + 1/4 = 1
4/8 + 3/9 + 1/6
My fifth-grade student, Yuel, came up with 3 possibilities:
1/4 + 3/6 + 2/8 = 8/8
1/6 + 2/4 + 3/9 = 6/6
4/8 + 3/9 + 1/6 = 6/6
2/6 + 2/6 + 4/12
I need 3 numbers that have 1 as a numerator and all different denominators! HELP!
1/6 + 4/8 + 3/9 =1
G.D.
3/9 + 2/4 + 1/6 = 1
The unique solutions are
1/4 + 2/8 + 3/6
1/6 + 3/9 + 2/4
1/6 + 3/9 + 4/8
You can swap the numerators or the addends (fractions) around to get 6*6=36 times as many solutions.
Correction: You can swap the addends, but not the numerators, so only 3*6 = 18 solutions.
It is 1/4 1/4 and 1/5
no
Respect, a fundamental pillar of any healthy society, is the act of acknowledging and valuing the inherent dignity of every individual, regardless of their background, beliefs, or circumstances; it encompasses not only treating others with courtesy and consideration but also understanding and appreciating their perspectives, even when they differ from our own, thereby fostering positive interactions and building strong relationships.
At its core, respect involves actively listening to others, truly paying attention to what they have to say, and considering their viewpoints with an open mind. This means not interrupting, judging, or dismissing their opinions prematurely, but rather engaging in a dialogue where everyone feels heard and valued.
Self-respect, the foundation for respecting others, is the recognition of one’s own worth and the understanding of one’s personal boundaries. When we respect ourselves, we are more likely to set healthy limits, make positive choices, and treat others with the same dignity we accord ourselves.
Respect manifests in various ways, depending on the context. In the workplace, it means valuing colleagues’ contributions, respecting their time, and maintaining professional decorum. Within families, respect involves honoring family members’ opinions, even if they differ from our own, and treating everyone with kindness and consideration.
In our communities, respect means embracing diversity and appreciating the unique perspectives and experiences that different cultures bring. It entails challenging discriminatory behavior and actively promoting inclusivity, ensuring everyone feels welcomed and valued.
However, respect is not merely a passive concept; it requires active effort and conscious choices. It means speaking up against injustice, standing up for those who may be marginalized, and challenging behaviors that undermine respect.
The absence of respect can lead to harmful consequences, including conflict, tension, and a breakdown in communication. When people feel disrespected, they may become withdrawn, defensive, or even aggressive, hindering positive interactions and damaging relationships.
In conclusion, respect is a cornerstone of a harmonious society, where everyone feels valued and empowered. By actively practicing respect in our personal and professional lives, we create a more positive and inclusive environment for ourselves and those around us.
Integrity, a cornerstone of ethical conduct, signifies the quality of being honest and adhering to strong moral principles, even when faced with challenging situations where personal gain might tempt one to deviate from the right path. It is a fundamental trait that underpins trust, reliability, and a person’s overall character, making it crucial in personal, professional, and societal spheres.
The Essence of Integrity
At its core, integrity involves aligning one’s actions with one’s beliefs, demonstrating consistency between words and deeds. This means being truthful even when it is inconvenient, taking responsibility for one’s mistakes, and upholding ethical standards regardless of external pressures. People with integrity are known for their reliability, as they can be counted on to do what they say they will do, even when no one is watching.
Importance in Personal Life
Integrity is vital in personal relationships, fostering trust and creating a foundation for genuine connections. When individuals demonstrate integrity, they earn respect from others and build strong bonds based on mutual understanding and honesty. This quality also contributes to a positive self-image, as individuals feel confident in their actions and choices, knowing they are acting in accordance with their values.
Professional Integrity
In the workplace, integrity is paramount for building a reputable organization. Employees with integrity are seen as trustworthy and reliable, leading to increased productivity and collaboration. Ethical conduct within a company, including transparency in decision-making and adherence to company policies, fosters a positive work environment and enhances customer loyalty.
Challenges to Integrity
Maintaining integrity can be challenging, especially in situations where personal gain may be at stake. Ethical dilemmas, peer pressure, and the temptation to cut corners can all test a person’s commitment to their values. However, by actively reflecting on one’s moral compass and making conscious decisions, individuals can navigate these challenges and uphold their integrity.
Developing Integrity
Cultivating integrity is a lifelong process that begins with self-awareness and a commitment to personal growth. Role models who demonstrate high ethical standards can serve as inspiration, while actively seeking feedback and engaging in open dialogue can help individuals identify areas where they need to improve.
Impact on Society
When individuals within a society prioritize integrity, it creates a culture of trust and accountability. This is essential for fostering a just and equitable society, where individuals feel empowered to hold institutions and leaders accountable for their actions.
Conclusion
Integrity is a fundamental human value that serves as a guiding principle for ethical decision-making in all aspects of life. By consistently choosing to act with honesty and moral courage, individuals can build strong relationships, contribute to a positive workplace environment, and create a more trustworthy society.
Perseverance, often described as “grit” or unwavering determination, is a crucial attribute that allows individuals to navigate life’s obstacles and achieve their goals despite setbacks and challenges; it is the ability to keep striving forward even when faced with adversity, demonstrating resilience and a steadfast commitment to one’s aspirations. This essay will explore the concept of perseverance, highlighting its significance in personal growth, the role of mindset in fostering perseverance, and real-life examples of individuals who have demonstrated remarkable tenacity in the face of difficulty.
The Power of Perseverance in Personal Growth
Perseverance is a catalyst for personal growth, enabling individuals to learn from their mistakes and evolve as they encounter challenges. When faced with failure, a persistent individual does not view it as a dead end but rather as an opportunity to adapt and improve their approach. By consistently pushing past comfort zones and embracing challenges, perseverance fosters a sense of accomplishment and self-efficacy, which are essential components of a positive self-image.
The Role of Mindset in Perseverance
A growth mindset is fundamental to perseverance. Individuals with a growth mindset believe that their abilities can be developed through hard work and dedication, whereas a fixed mindset often leads to discouragement when faced with obstacles. Cultivating a positive outlook and a willingness to learn from failures are key to fostering perseverance and achieving long-term success.
Historical Examples of Perseverance
Throughout history, countless individuals have demonstrated extraordinary perseverance in the face of adversity. Nelson Mandela, the South African anti-apartheid revolutionary, spent decades imprisoned yet never wavered in his pursuit of equality and justice. Similarly, Helen Keller, who overcame blindness and deafness to become a renowned author and activist, exemplifies the power of perseverance in the face of significant challenges.
Overcoming Obstacles in Daily Life
Perseverance is not limited to grand feats; it is equally important in everyday situations. A student struggling with a challenging subject can develop perseverance by actively seeking help, practicing consistently, and refusing to give up. Similarly, an athlete facing setbacks during training can use perseverance to push through pain and continue working towards their goals.
The Importance of Support Systems
A strong support system can significantly enhance an individual’s perseverance. Family, friends, mentors, and communities can provide encouragement, motivation, and a sense of belonging, which are crucial when facing challenging times.
Perseverance in the Workplace
In the professional world, perseverance is vital for career advancement. Employees who demonstrate tenacity in the face of complex projects or challenging deadlines are often recognized for their dedication and commitment.
Developing Perseverance
To cultivate perseverance, individuals can set realistic goals, celebrate small wins, and develop strategies to manage setbacks. Practicing resilience through mindfulness and self-awareness can also help individuals bounce back from challenges and maintain a positive outlook.
Conclusion
Perseverance is a powerful attribute that enables individuals to overcome obstacles, achieve their goals, and live fulfilling lives. By embracing a growth mindset, seeking support, and consistently striving forward despite setbacks, individuals can harness the transformative power of perseverance and reach their full potential.
pneumonoultramicroscopicsilicovolcanoconiosis
It is a disease in the lungs caused by silica dust.
I just realized that i have the first comment of 2025, W’s, today is early-out too, w day lez goooooooo!
Btw it says this was posted at 9:52 but its really 10:52
what’s up my friends its me 4 years later
I mean 5 years later