Equations with rational numbers

Equations with rational numbers

1. Fraction to Decimal Conversion

   • A fraction can be converted into a decimal by dividing the numerator by the denominator. The numerator is the number on the top of the fraction, and the denominator is the number on the bottom. To do the conversion, we simply perform the division.
     • For example, if we have the fraction 3/4, we divide 3 by 4. The result is 0.75. This means that the fraction 3/4 is equal to the decimal 0.75.
     • This process works with any fraction. Sometimes the result is a terminating decimal, like 0.5 or 0.25. In other cases, the decimal repeats. Converting fractions to decimals helps us compare numbers and solve problems more easily.

2. Solving Equations with Fractions

   • When we solve equations with fractions, the process is similar to solving normal equations, but we need to work carefully with the fractions.
     • First, we need to find the least common denominator. The greatest common divisor helps us eliminate fractions from the equation. Next, we multiply each term by the GCD. This eliminates the fractions and makes solving the equation easier.
     • After that, we simplify the equation and combine like terms. Finally, we isolate the variable by using basic operations such as addition, subtraction, multiplication, or division.
       • This method helps us find the value of the variable and solve the equation correctly.

3. Rational Numbers

   • Rational numbers are numbers that can be written as a fraction in the form a/b, where a and b are integers and b is not zero. These numbers include many types of numbers that we use in mathematics.
     • Rational numbers can be positive or negative. They also include integers, fractions, and decimals.
     • For example, numbers like 1/2, 3/4, and -2/5 are rational numbers because they are fractions. Whole numbers such as 3, 5, and -8 are also rational numbers because they can be written as fractions like 3/1. Decimals such as 0.5 or 0.75 are also rational numbers because they come from fractions.
     • Understanding rational numbers helps us work with different types of numbers in equations and real-life situations.