• Multiplication
  RULE 1: A positive integer compounded by a negative integer produces a negative integer.
  RULE 2: When multiplying two positive integers, the result is positive.
  RULE 3: When multiplying two negative integers, the answer is positive.
• Division
  RULE 1: A positive integer’s quotient with a negative integer is negative.
  RULE 2: When two positive integers are quotients, the result is positive.
  RULE 3: When two negative integers are multiplied together, the quotient is positive.

Integers have a few properties that dictate how they are used. Many equations may be solved using these rules or properties. Any positive or negative number, even zero, is an integer. The properties of these integers can assist in easily simplifying and addressing a sequence of integer operations.

The following are the five significant properties of operation for integers:

• Closure property
• Associative property
• Commutative property
• Distributive property
• Identity property

Any number can be expressed as p/q, where q≠0 is a rational number in mathematics. We may also classify any fraction as a rational number if the denominator and numerator are both integers and the denominator is not equal to zero. As a rational number (i.e., a fraction) is split, the output is in decimal form and may be ending or repeating.

Check the criteria below to see whether a number is logical or not.

• It’s written as p/q, where q≠0.
• The p/q ratio can be condensed further and displayed in decimal form.

Rather than expressing rational numbers as fractions, they may be expressed in decimal form. They can conveniently be converted to decimals by dividing the numerator “p” by the denominator “q” (as rational numbers are written in the form p/q).

A terminating or non-terminating, repeating decimal may be used to express a rational number.

Compared to improper rational fractions, the representation of rational numbers in decimal fractions allows calculations to be more straightforward.

A fraction is a numerical value that denotes the components of a larger whole. If a number is separated into four sections, it is represented by the symbol x/4. As a result, the fraction x/4 denotes 1/4th of the integer x. Fractions have a significant role in our everyday lives. There are several instances of a fraction as an operator that you can find in daily life.

They are as follows:

• Proper fractions
  Proper fractions have a numerator that is smaller than the denominator. Since “numerator < denominator,” 8/9 is a proper fraction.
• Improper fractions
  A fraction with an incorrect numerator is one in which the numerator is greater than the denominator. 9/8, for example, is an improper fraction since the “denominator” is smaller than the “numerator.”
• Mixed fractions
  A mixed fraction comprises two parts: an integer and a proper fraction. A mixed fraction is also known as a mixed numeral.
• Like fractions
  Like fractions are fractions that are related or equal. Take the fractions 4/8 and 2/4, for example; they are similar because you get the same fraction when you simplify them mathematically.
• Unlike fractions
  Those that are dissimilar are unlike fractions. 3/7 and 1/3, for example, are diametrically opposed fractions.
• Equivalent fractions
  If one of the two fractions is identical to the other after simplification, the two fractions are equivalent. 2/3 and 4/6, for example, are equivalent fractions.

In this chapter, we learned about number systems. We learned about fractions and the reciprocal of a fraction. We can further use this knowledge for problem-solving using operations.

1. What are fractions, precisely?
   Fractions are integer quantities that are a percentage of a whole number. As a number or an object is separated into equivalent sections, each component becomes a fraction of the total. Where an is the numerator and b is the denominator, a fraction is written as a/b.
   
2. What’s the correct way to solve fractions?
   When adding or subtracting fractions, we must first decide if the denominators are the same or different. When the denominators are the same, we may add or remove the numerators while leaving the denominator the same. However, if the denominators vary, we must find the LCM to reduce them.
   
3. Is the number 0 rational?
   Yes, 0 is a rational number since it is an integer we can write in various ways, including 0/1, 0/2, and 0/3, where b is a non-zero integer. It can be expressed in the following way: p/q = 0/1. As a result, we may claim that 0 is a rational number.
   
4. Is seven a rational number?
   Since it can be written as a ratio, such as 7/1, 7 is a rational number.
   
5. What is the significance of the number system?
   The number scheme helps to depict numbers in a minimal symbol range.