What is an Integer in Mathematics? 

In mathematics, an integer is a number that contains no fractional part (no decimals) or has a sign. It can be positive, negative, or zero. In addition, a number that is an integer can have a commutative property. This means that changing the position of a number’s operands in an operation will not affect the result. 

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Integers are whole numbers that do not contain fractions or decimals; they are also called the natural numbers. They include all positive and non-negative numbers, including the additive inverses. 

There are many types of integers, such as -1 and 0.

The number 0 is the centre of the integers on a number line; positive integers lie to the right of 0 and negative integers lie to the left. The distance between two integers on the number line is called their absolute value. For example, -4 is 4 units from zero and +4 is 4 units to the left of 0. 

There are other types of integers, including negative and decimal numbers. Negative integers are any whole number that is less than zero. They can be any number from -29 to 1,000,000,000. 

When adding and subtracting integers, the simplest rule is to use the sign of the first number to decide the order in which the operations are done. When subtracting, change the sign of the second number to make it the same as the first. 

Similarly, when multiplying integers, the same rule applies. For example, if you have a number with an absolute value of 2 and another with an absolute value of 5, the sum of the first two is 6. 

Mathematicians use integers to calculate many properties of numbers. These properties include the fundamental theorem of arithmetic, which says that all integers are the product of prime numbers. Integers are also used to count numbers, as well as to compute quotients and remainders during division and exponentiation. 

In addition to these properties, there are other important mathematical concepts that involve the use of integers. These include the commutative and multiplicative properties of addition and multiplication, as well as the additive inverse property, which states that any addition between a positive and a negative number will always produce a positive number. 

A lot of children have difficulty understanding this concept, which is why many teachers need to design problem-solving tasks and activities for students to learn it. A great resource to help with this is the Diving into Mastery Teaching Pack, which includes worksheets and a PowerPoint on this topic. 

How do children learn about integers?

In primary school, children are taught that the term ‘integer’ simply means a number. In particular, they will be taught that a number that has no fractional part and consists only of whole numbers is an integer. 

In Year 6 pupils will also start to learn how to add and subtract positive and negative integers together, and divide fractions by integers. This is an early precursor to more in-depth study of this topic later in the curriculum.