Two fractions are multiplied by multiplying their numerators and denominators separately and writing the product as product of numerators by product of denominators. For example, 2/3 x 5/7 = (2 x 5) / (3 x 7) = 10 / 21
A fraction acts as an operator ‘of’. Example, ½ of 2 is 1/2 x 2 = 1
Integers are a bigger collection of numbers which is formed by whole numbers and their negatives.
All natural numbers are whole numbers and all whole numbers are integers.
Properties satisfied by addition and subtraction of integers
Integers are closed for addition and subtraction both. a + b and a – b are again integers, where a and b are any integers.
Addition is commutative for integers, i.e., a + b = b + a for all integers a and b.
Addition is associative for integers, i.e., (a + b) + c = a + (b + c) for all integers a, b and c.
Integer 0 is the identity under addition. That is, a + 0 = 0 + a = a for every integer a.
Product of a positive and a negative integer is a negative integer, whereas the product of two negative integers is a positive integer. For example, – 2 × 7 = – 14 and – 3 × – 8 = 24.
Product of even number of negative integers is positive, whereas the product of odd number of negative integers is negative.
Following are the properties of Integers under multiplication.
Integers are closed under multiplication. That is, a × b is an integer for any two integers a and b.
Multiplication is commutative for integers. That is, a × b = b × a for any integers a and b.
The integer 1 is the identity under multiplication, i.e., 1 × a = a × 1 = a for any integer a.
Multiplication is associative for integers, i.e., (a × b) × c = a × (b × c) for any three integers a, b and c.
Integers show distributive property under multiplication and addition. That is, a × (b + c) = a × b + a × c for any three integers a, b and c.
Properties of division of integers:
When a positive integer is divided by a negative integer, the quotient obtained is a negative integer and vice-versa.
Division of a negative integer by another negative integer gives a positive integer as quotient.
For any integer a, we have
a / 0 is not defined
a / 1 = a
Absolute value of a number is the positive value of the number.