Question

Describe integers and fractions.

Answer 1

Hint:Set of whole numbers that include positive, negative, and zero are known as integers. A fraction essentially indicates the number of parts that make up a whole. The slash that is written between the two numbers distinguishes a fraction as compared to integers.

Complete answer:
Integers: Integers are denoted without any fractional component. They are denoted by set symbol \[Z\] or \[\mathbb{Z}\] as follows:
\[Z = \{ ..., - 2, - 1,0,1,2,...\} \]
These numbers are used in addition, subtraction, multiplication, and division, among other arithmetic operations. Three types of integers are:
-Zero
-Positive Integers (Natural Numbers)
-Negative Integers (Additive Inverse of Natural Numbers)

Fractions: Fractions contains a numerator at the top and denominator at the bottom. The numerator and denominator are separated by horizontal lines. E.g., \[\dfrac{3}{4}\]is a fraction with \[3\] as numerator and \[4\] as denominator. There are six types of fractions-
Proper Fraction: When numerator is less than denominator e.g., \[\dfrac{6}{7}\].
Improper Fraction: When numerator is more than denominator e.g., \[\dfrac{7}{6}\].
Mixed Fraction: It contains a quotient and a remainder e.g., \[5\dfrac{1}{4}\].
Like Fraction: Here two fractions have a common denominator e.g., \[\dfrac{{10}}{3}\] and \[\dfrac{7}{3}\].
Unlike Fraction: Here two fractions have different denominators e.g., \[\dfrac{{10}}{3}\] and \[\dfrac{7}{4}\].
Equivalent Fraction: They are different fraction having different numerator and denominator but represents same part of the whole e.g., \[\dfrac{3}{6}\] and \[\dfrac{5}{{10}}\] both will be equivalent to \[\dfrac{1}{2}\].

Note:When you divide one integer by another, the result may be either an integer or a fraction. For example –\[10\] divided by \[5\] gives \[2\] which is an integer but \[10\]divided by \[3\]gives us fraction \[\dfrac{{10}}{3}\]. Real life examples of integers are currency - \[10,000/ - \], population, number of boys and girls in class room etc. Fractions example will be number of pizza slices divided equally, total boys out of total students in the classroom etc.