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., $${\displaystyle \frac{3}{4}}$$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., $${\displaystyle \frac{6}{7}}$$.
Improper Fraction: When numerator is more than denominator e.g., $${\displaystyle \frac{7}{6}}$$.
Mixed Fraction: It contains a quotient and a remainder e.g., $$5{\displaystyle \frac{1}{4}}$$.
Like Fraction: Here two fractions have a common denominator e.g., $${\displaystyle \frac{10}{3}}$$ and $${\displaystyle \frac{7}{3}}$$.
Unlike Fraction: Here two fractions have different denominators e.g., $${\displaystyle \frac{10}{3}}$$ and $${\displaystyle \frac{7}{4}}$$.
Equivalent Fraction: They are different fraction having different numerator and denominator but represents same part of the whole e.g., $${\displaystyle \frac{3}{6}}$$ and $${\displaystyle \frac{5}{10}}$$ both will be equivalent to $${\displaystyle \frac{1}{2}}$$.

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 $${\displaystyle \frac{10}{3}}$$. 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.