There are four main properties which include commutative property, associative property, distributive property and identity property. Consider “m, n and r” are three real numbers. Then the above properties can be described using m, n, and r as shown below:
Commutative Property
If m and n are the numbers, then the general form will be m + n = n + m for addition and m.n = n.m for multiplication.
- Addition: m + n = n + m. For example, 5 + 3 = 3 + 5, 2 + 4 = 4 + 2
- Multiplication: m × n = n × m. For example, 5 × 3 = 3 × 5, 2 × 4 = 4 × 2
If m, n and r are the numbers. The general form will be m + (n + r) = (m + n) + r for addition(mn) r = m (nr) for multiplication.
- Addition: The general form will be m + (n + r) = (m + n) + r. An example of additive associative property is 10 + (3 + 2) = (10 + 3) + 2.
- Multiplication: (mn) r = m (nr). An example of a multiplicative associative property is (2 × 3) 4 = 2 (3 × 4).
For three numbers m, n, and r, which are real in nature, the distributive property is represented as:
m (n + r) = mn + mr and (m + n) r = mr + nr.
- Example of distributive property is: 5(2 + 3) = 5 × 2 + 5 × 3. Here, both sides will yield 25.
There are additive and multiplicative identities.
- For addition: m + 0 = m. (0 is the additive identity)
- For multiplication: m × 1 = 1 × m = m. (1 is the multiplicative identity)
Real Numbers Class 9 and 10
In real numbers Class 9, the common concepts introduced include representing real numbers on a number line, operations on real numbers, properties of real numbers, and the law of exponents for real numbers. In Class 10, some advanced concepts related to real numbers are included. Apart from what are real numbers, students will also learn about Euclid’s Division Lemma, Euclid’s Division Algorithm and the fundamental theorem of arithmetic in class 10.
