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...
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Where can I download the Knowunity app?
You can download the app from Google Play Store and 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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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 a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
Where can I download the Knowunity app?
You can download the app from Google Play Store and 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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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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
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
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
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
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
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 apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user