Celé čísla ti pomôžu opísať všetko, čo je okolo teba... Show more
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Updated Mar 23, 2026
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Celé čísla: Úvod a Základné Pojmy
1 / 9
Úvod do celých čísel
Celé čísla používaš každý deň, aj keď si to možno neuvedomuješ. Keď je vonku -5°C alebo keď výťah ide do -2. podlažia, pracuješ s nimi.
Celé čísla sú všetky kladné prirodzené čísla (1, 2, 3...), nula (0) a všetky záporné čísla (-1, -2, -3...). Označujeme ich písmenom Z.
Kladné celé čísla sú väčšie ako nula - môžeš ich písať s + alebo bez neho . Záporné celé čísla sú menšie ako nula a vždy majú pred sebou mínus (-5). Nula nie je ani kladná, ani záporná - je presne v strede.
Tip: Predstav si záporné čísla ako dlh. Ak dlžíš 100€, je to horšie ako dlh 1€ - preto je -100 menšie ako -1!
Číselná os - tvoja najlepšia pomôcka
Číselná os je rovná čiara, ktorá ti ukáže, ako sú čísla usporiadané. Je to ako mapa čísel!
Ako ju nakresliť? Nakreslíš rovnú čiaru, označíš počiatok (tam bude nula), a potom odmeríš rovnaké vzdialenosti - to je jednotková úsečka. Doprava od nuly idú kladné čísla, doľava záporné.
| Typ čísla | Príklad | Kde na osi |
|---|---|---|
| Kladné | +3, 7, 12 | Doprava od nuly |
| Nula | 0 | V strede (počiatok) |
| Záporné | -2, -10 | Doľava od nuly |
Pamätaj si: Šípky na koncoch osi znamenajú, že čísla pokračujú do nekonečna oboma smermi!
Porovnávanie celých čísel
Na číselnej osi je porovnávanie super jednoduché - číslo, ktoré je viac vpravo, je vždy väčšie.
Tu sú pravidlá, ktoré ti uľahčia život:
- Kladné číslo je vždy väčšie ako záporné (5 > -100)
- Nula je väčšia ako každé záporné číslo (0 > -7)
- Pri záporných číslach: čím bližšie k nule, tým väčšie (-2 > -5)
Pozor na záporné čísla! -2 je väčšie ako -5, lebo -2 je bližšie k nule. Je to ako s dlhom - dlh 2€ je lepší ako dlh 5€.
Skúška: Ak si nie si istý, predstav si čísla na osi. Čo je vpravo, to je väčšie!
Riešené príklady krok za krokom
Príklad 1: Znázorni na číselnej osi: 3, -2, 0, 5, -4
Nakreslíš os, označíš nulu, zvolíš jednotkovú úsečku. Potom označíš: -4 (4 jednotky doľava), -2 (2 doľava), 0 (stred), 3 (3 doprava), 5 (5 doprava).
Príklad 2: Porovnaj čísla pomocou <, >, =
- 4 __ 9 → 4 < 9 (4 je vľavo od 9)
- -5 __ -2 → -5 < -2
- 0 __ -8 → 0 > -8 (nula je väčšia ako záporné)
Príklad 3: Usporiadaj od najmenšieho: 7, -3, 0, -5, 2, -1
Výsledok: -5, -3, -1, 0, 2, 7. Najprv záporné (od najmenšieho), potom nula, potom kladné.
Trik: Pri usporadúvaní si predstav všetky čísla na osi a "prečítaj" ich zľava doprava!
Celé čísla v bežnom živote
Celé čísla nie sú len školská záležitosť - stretávaš ich všade okolo seba! Teplomer používa záporné čísla pre teploty pod nulou. Výťah má záporné čísla pre podzemné poschodia.
Bankový účet - ak máš na konte 50€, je to +50. Ak dlžíš banke 20€, je to -20. Nadmorská výška - Gerlachovský štít má +2655 m, Mŕtve more má -420 m.
Toto učivo je základ pre všetko ďalšie počítanie s celými číslami. Keď si osvojíš porovnávanie a číselná os, sčítanie a odčítanie bude hračka.
Rýchle zhrnutie:
- Celé čísla = kladné + nula + záporné
- Na číselnej osi: čo je vpravo, to je väčšie
- Pri záporných: čím bližšie k nule, tým väčšie
Záver: Celé čísla ti pomôžu opísať svet presnejšie. Od zimnej teploty po výšku budov - sú všade!
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
Most popular content in Matematika
Most popular content
Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
Celé čísla: Úvod a Základné Pojmy
Celé čísla ti pomôžu opísať všetko, čo je okolo teba - od mrazivých teplôt v zime po výškové budovy s podzemím. Je to rozšírenie toho, čo už poznáš o číslach!
Úvod do celých čísel
Celé čísla používaš každý deň, aj keď si to možno neuvedomuješ. Keď je vonku -5°C alebo keď výťah ide do -2. podlažia, pracuješ s nimi.
Celé čísla sú všetky kladné prirodzené čísla (1, 2, 3...), nula (0) a všetky záporné čísla (-1, -2, -3...). Označujeme ich písmenom Z.
Kladné celé čísla sú väčšie ako nula - môžeš ich písať s + alebo bez neho . Záporné celé čísla sú menšie ako nula a vždy majú pred sebou mínus (-5). Nula nie je ani kladná, ani záporná - je presne v strede.
Tip: Predstav si záporné čísla ako dlh. Ak dlžíš 100€, je to horšie ako dlh 1€ - preto je -100 menšie ako -1!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Číselná os - tvoja najlepšia pomôcka
Číselná os je rovná čiara, ktorá ti ukáže, ako sú čísla usporiadané. Je to ako mapa čísel!
Ako ju nakresliť? Nakreslíš rovnú čiaru, označíš počiatok (tam bude nula), a potom odmeríš rovnaké vzdialenosti - to je jednotková úsečka. Doprava od nuly idú kladné čísla, doľava záporné.
| Typ čísla | Príklad | Kde na osi |
|---|---|---|
| Kladné | +3, 7, 12 | Doprava od nuly |
| Nula | 0 | V strede (počiatok) |
| Záporné | -2, -10 | Doľava od nuly |
Pamätaj si: Šípky na koncoch osi znamenajú, že čísla pokračujú do nekonečna oboma smermi!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Porovnávanie celých čísel
Na číselnej osi je porovnávanie super jednoduché - číslo, ktoré je viac vpravo, je vždy väčšie.
Tu sú pravidlá, ktoré ti uľahčia život:
- Kladné číslo je vždy väčšie ako záporné (5 > -100)
- Nula je väčšia ako každé záporné číslo (0 > -7)
- Pri záporných číslach: čím bližšie k nule, tým väčšie (-2 > -5)
Pozor na záporné čísla! -2 je väčšie ako -5, lebo -2 je bližšie k nule. Je to ako s dlhom - dlh 2€ je lepší ako dlh 5€.
Skúška: Ak si nie si istý, predstav si čísla na osi. Čo je vpravo, to je väčšie!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Riešené príklady krok za krokom
Príklad 1: Znázorni na číselnej osi: 3, -2, 0, 5, -4
Nakreslíš os, označíš nulu, zvolíš jednotkovú úsečku. Potom označíš: -4 (4 jednotky doľava), -2 (2 doľava), 0 (stred), 3 (3 doprava), 5 (5 doprava).
Príklad 2: Porovnaj čísla pomocou <, >, =
- 4 __ 9 → 4 < 9 (4 je vľavo od 9)
- -5 __ -2 → -5 < -2
- 0 __ -8 → 0 > -8 (nula je väčšia ako záporné)
Príklad 3: Usporiadaj od najmenšieho: 7, -3, 0, -5, 2, -1
Výsledok: -5, -3, -1, 0, 2, 7. Najprv záporné (od najmenšieho), potom nula, potom kladné.
Trik: Pri usporadúvaní si predstav všetky čísla na osi a "prečítaj" ich zľava doprava!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Celé čísla v bežnom živote
Celé čísla nie sú len školská záležitosť - stretávaš ich všade okolo seba! Teplomer používa záporné čísla pre teploty pod nulou. Výťah má záporné čísla pre podzemné poschodia.
Bankový účet - ak máš na konte 50€, je to +50. Ak dlžíš banke 20€, je to -20. Nadmorská výška - Gerlachovský štít má +2655 m, Mŕtve more má -420 m.
Toto učivo je základ pre všetko ďalšie počítanie s celými číslami. Keď si osvojíš porovnávanie a číselná os, sčítanie a odčítanie bude hračka.
Rýchle zhrnutie:
- Celé čísla = kladné + nula + záporné
- Na číselnej osi: čo je vpravo, to je väčšie
- Pri záporných: čím bližšie k nule, tým väčšie
Záver: Celé čísla ti pomôžu opísať svet presnejšie. Od zimnej teploty po výšku budov - sú všade!
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
We thought you’d never ask...
What is the Knowunity AI companion?
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
Where can I download the Knowunity app?
You can download the app in the Google Play Store and in the Apple App Store.
Is Knowunity really free of charge?
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
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Most popular content in Matematika
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Can't find what you're looking for? Explore other subjects.
Students love us — and so will you.
4.6/5
App Store
4.7/5
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️
Thomas R
iOS user
Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE Knowunity AI. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!
Paul T
iOS user