Natural Numbers and Integers
Natural numbers are the counting numbers 1, 2, 3 and so on, while integers also include zero and the negative whole numbers.
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Play with the controls to see the idea in action.
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Natural numbers are the counting numbers 1, 2, 3 and so on, while integers also include zero and the negative whole numbers.
- Integers extend the natural numbers to the left of zero
- Every integer has an opposite, such as 5 and -5
- Whole numbers have no fractional part
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Natural Numbers and Integers?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Natural Numbers and Integers. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Natural Numbers and Integers in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Natural Numbers and Integers gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Natural Numbers and Integers in detail
Natural numbers (1, 2, 3, …) are the numbers we use to count objects, while integers add zero and the negative whole numbers, giving the set …, -2, -1, 0, 1, 2, …. Picturing them on a number line shows that every integer has an opposite the same distance from zero on the other side.
Integers are needed whenever quantities can go below a starting point, such as temperatures below freezing, bank overdrafts or floors below ground level. Knowing which set a number belongs to also helps later, when you meet fractions, decimals and irrational numbers that sit between the integers.
How the interactive helps you understand Natural Numbers and Integers
Click a card to flip it and reveal the answer, then move on to the next one.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Natural Numbers and Integers.
Real-life uses and examples
- Explain Natural Numbers and Integers to a friend with a simple picture, such as a row of tiles or a bag of sweets.
- Spot Natural Numbers and Integers in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Natural Numbers and Integers by estimating first, then working it out step by step.
Common mistakes to avoid
- Memorising the steps for Natural Numbers and Integers without checking why they work.
- Forgetting units, signs or brackets when you apply Natural Numbers and Integers.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Natural Numbers and Integers
What is Natural Numbers and Integers?
Natural numbers are the counting numbers 1, 2, 3 and so on, while integers also include zero and the negative whole numbers.
What are the most important points about Natural Numbers and Integers?
The main points are: Integers extend the natural numbers to the left of zero; Every integer has an opposite, such as 5 and -5; Whole numbers have no fractional part.
Why is Natural Numbers and Integers useful?
Understanding Natural Numbers and Integers gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Natural Numbers and Integers?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Natural Numbers and Integers?
Related topics in Mathematics include Factors and Multiples, Highest Common Factor, Order of Operations.