A Rational Number is a quotient of two integers A Rational Number is a quotient of two integers. A rational number is a number which can be written in the form of a/b where b cannot be equal to 0. Examples: Terminating decimals are also rational numbers because they can be rewritten as fractions. Examples: Non-Terminating decimals can also be written as rational numbers if it has a repeating pattern. (converting repeating decimals to fractions will be covered in college algebra.) Integers are also rational numbers. (The denominator is a 1.) Examples: Real numbers: The combination of the sets of rational and irrational numbers. Irrational numbers: Numbers that cannot be written in fractional form, and when written in decimal notation are not terminating nor repeating.

Adding Rational Numbers with Common Denominators If are denominators are common (the same), simplify ( + or  ) numerators. Write the result over the common denominator. Reduce if possible. Example 1. Add: Solutions: Your Turn Problem #1 Add: Answers:

3. Simplify numerators and place in a single fraction over the LCM. Adding and/or subtracting rational numbers with unlike (not common) denominators. 1. Find the LCM of the denominators—also called the Least Common Denominator (LCD). 2. Determine equivalent form of each fraction using LCM as a denominator of each. 3. Simplify numerators and place in a single fraction over the LCM. 4. If possible, reduce resulting fraction to simplest form. Adding Rational Numbers with Unlike Denominators Example 2. Add: Solutions: LCD =24 LCD =24 LCD =30 Your Turn Problem #2 Add: Answers:

Multiplying Rational Numbers in Fractional Form: To multiply fractions: 1. Reduce vertically and/or diagonally if possible. 2. Multiply horizontally remaining factors. 3. Reduce if necessary. Example 3. Multiply: Solutions: 4 3 5 1 3 2 1 2 Your Turn Problem #3 Multiply: Answers:

Dividing Rational Numbers in Fractional Form: To divide fractions: 1. Rewrite the first fraction. 2. Change the division symbol to a multiplication symbol. 3. Invert the fraction that follows the division symbol. 4. Follow the rules for multiplying fractions Example 4. Divide: Solutions: 4 3 4 3 Your Turn Problem #4 Divide: Answers:

Adding Rational Numbers in Decimal Notation When adding rational numbers in decimal notation, align the decimal points vertically; then proceed by process of adding or subtracting integers (depending on the signs). Adding Rational Numbers in Decimal Notation Example 5. Simplify the following: a) –4.2 – 3.87 b) 6.38 + (–15.2) Since the signs are different, we will need to subtract. When subtracting, place the larger number on top for borrowing . 1st change to addition. Since both signs are negative, write vertically and add. Then attach the negative. –4.2 + (–3.87) Answer: –8.07 Answer: –8.82 Remember to keep the sign of the larger number. Your Turn Problem #5 Simplify: Answers:

When multiplying rational numbers in decimal notation, multiply the numbers. Place decimal point in product so that the number of decimal places in the product equals the sum of the decimal places in the original factors. Then attach the sign following the rules of multiplication. Multiplying Rational Numbers in Decimal Notation Example 6. Simplify the following: a) 6.2 (–5.63) b) –0.35 (–0.28) Answer: –34.906 3 decimals places  34.906 Answer: 0.098 Your Turn Problem #6 Simplify: Answers:

Dividing Rational Numbers in Decimal Notation 1. Determine sign of quotient (answer). 2. Move the decimal point in divisor (number in front) to right to make a whole number 3. Move decimal point in the dividend (number under division box) the same number of places as #2. 4. Place decimal point in quotient directly over decimal point in dividend. 5. Divide as whole numbers. Example 7. Simplify the following: –4.362  (–1.34). Round off to 100ths. Solution: Quotient will be positive. Move the decimal point in the divisor 2 places to the right which will make it a whole number. Then move the decimal point in the dividend the same number places to the right. Your Turn Problem #7 The End B.R. 4-26-07