Properties of Rational Numbers

Rational numbers are closed under addition, subtraction and multiplication. They are commutative and associative under addition and multiplication i.e., reordering and regrouping of operands does not change the result.

Rational Numbers

A rational number is defined as a number that can be expressed in the form p/q , where p and q are integers and q ≠ 0. The word ‘rational’ arises from the term ‘ratio’ & 'Q' comes from the word 'quotient'. The decimal numbers can be written as an ordinary fraction and, hence, are rational numbers. The integers can be written as a fraction with denominator 1 and, hence, are rational numbers.

Multiplication & Division of Decimals

While Multiplying the decimal numbers we multiply the numbers normally as integers without decimal point. We add the number of digits after decimal points in decimals (let it be n). Then, we put the decimal point in answer before n digits from right.

Decimals

Numbers having both integral part and fractional part is called decimal numbers or simply decimals. To differentiate between integral part and fractional part in a decimal, we put a point (or dot) called decimal point in between.

Multiplication & Division of Fractions

Here we will learn the various methods for Multiplication and Division of Fractions | Multiplication of a fraction by a whole number | Multiplication of a Fraction by a Fraction | Division of a Whole Number by a Fraction | Division of a Fraction by a Whole Number | Division of a Fraction by Another Fraction.

Fractions – Their Types, Comparison & Sum

A fraction is a number representing parts of a whole. The Whole may be a single object or group of objects but the Parts have to be equal. A fraction is written as parts above whole and horizontal line or slash in between, e.g., a/b.

Multiplication and Division of Integers

Product of two integers of same sign result in positive integer whereas product of two integers of different signs result in negative integer. Division of two integers of same sign result in positive number whereas division of integers of different signs result in negative number.

Integers

When we include negative numbers to the collection of whole numbers we got new set of numbers called Integers. Z = {..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ...}.

HCF & LCM

The Highest Common factor (HCF) or Greatest Common Divisor of two or more numbers is the highest (or greatest ) of their common factors. The Lowest Common factor (LCM) of two or more numbers is the lowest (or smallest) of their common multiples.

Factors & Multiples of Whole numbers

A factor of a number is an exact divisor of that number. A number can be expressed as a product of its factors. Multiple of a number is the product of the number itself with another number. A number is multiple of each of its factors.