This document discusses operations with rational numbers such as addition, subtraction, multiplication, and division. It explains that for addition and subtraction of rational numbers with common denominators, only the numerators are added or subtracted. For different denominators, the lowest common denominator must first be found before adding or subtracting the numerators. Multiplication of rational numbers is done by multiplying the numerators and denominators. Division can be performed by multiplying the first number by the reciprocal of the second number.

1. Rational Numbers

2. Understanding Rational Numbers

3. Adding Rational Numbers with CommonDenominatorsTo add rational numbers that have a common denominator, we add the numerators, but we do not add the denominators.

4. Adding Rational Numbers with DifferentDenominatorsTo add rational numbers with different denominators, first we equalize the denominators by enlarging each rational number by the lowest common denominator (LCD). Then we add the numerators.

5. Subtracting Rational Numbers with Common DenominatorsSubtraction is the inverse operation of addition. To subtract rational numbers that have a common denominator, we subtract the numerator, but we do not subtract the denominators.

6. Subtracting Rational Numbers with Different DenominatorsTo subtract rational numbers with different denominators, first equalize the denominators and then subtract the numerators.

7. Multiplying Rational NumbersMultiplying Two Rational NumbersTo multiply two rational numbers, we multiply the numerators to get the new numerator and multiply the denominators to get the new denominatorFor example:

8. Multiplying a Rational Number by a Whole NumberTo find the product of a whole number and a rational number, first write the whole number as an improper fraction, and then multiply. This is the same as multiplying the numerator of the fraction by whole number .

9. Multiplying Mixed NumbersWhen we multiply two mixed numbers, first we express each mixed number as an improper fraction, then we find the product.

10. DIVISION IN RATIONAL NUMBERS