1-3Real Number System & Absolute Value :1-3Real Number System & Absolute Value Real Numbers—Any number that fits into one of the following two categories: Rational Numbers—Any number that be written I n the form of a fraction a/b. Whole Number— 0, 1, 2, 3, …….. Integer— -2, -1, 0, 1, 2, ……… Fractions—Both proper, improper, and mixed TERMINATING Decimals—Decimals that STOP Irrational Numbers—Any number that CANNOT be written in the form of a fraction a/b. NON-Terminating Decimals—Decimals that do NOT end Non-Perfect Squares— √3, √12


1-3Real Number System & Absolute Value :1-3Real Number System & Absolute Value Absolute Value—The distance from a number to zero on the number line. Absolute Values are ALWAYS positive because it is a DISTANCE Strategies For Comparing Rational Numbers: 1. Compare “apples to apples” and “oranges to oranges” ie. If you are comparing a fraction to a decimal, either: a. Change the fraction to a decimal or b. Change the decimal to a fraction 2. If comparing two decimals, compare place values 3. If comparing two fractions, CROSS MULTIPLY (see examples)


1-3Real Number System & Absolute Value :1-3Real Number System & Absolute Value Identify ALL groups each real number is classified to. 1. -9 2. 2/3 3. √25 4. -3.12 5. √10 Real Real Rational Integer Real Rational Integer Whole Rational Real Rational Irrational 6. 15/3 Real Real Rational Whole Integer


1-3Real Number System & Absolute Value :1-3Real Number System & Absolute Value 5. Compare. SHORTCUT! Don’t find common denominators! Use cross multiplication! -12 -3 REMEMBER! The negatives on fractions can be placed in the numerator or denominator! We will always use the numerator. -12 < -3, so the answer is <


1-3Real Number System & Absolute Value :1-3Real Number System & Absolute Value 6. Order from least to greatest. Remember! Apples to apples! We’ll change fractions to decimals. .88 .8888 Now….rewrite to all the same place values! Apples to apples! .88000 .88888 .88880 1 3 2 .8888


Slide 6:Write each number in rational (a/b) form. 7. 16.4 1-3Real Number System & Absolute Value 8. 9. 5


1-3Real Number System & Absolute Value :1-3Real Number System & Absolute Value Evaluate each expression. 10.


1-4 & 1-5Adding & Subtracting Rational Numbers :1-4 & 1-5Adding & Subtracting Rational Numbers Evaluate each expression. -3.7 + 18.2 14.5 -9.2 – (-6.4) -9.2 + (+6.4) -2.8 -17 + (-13) -30 4. It’s OK to leave your fractions in IMPROPER FORM! Do NOT convert them into a mixed fraction or decimal! ALL FRACTIONS in algebra are in simplified form when they are reduced and in either proper or improper form. NO DECIMAL OR MIXED FRACTION CONVERSIONS. It is acceptable, though, if a problem BEGINS with a mixed fraction or decimal, you may leave final answer in that form.


1-4 & 1-5Adding & Subtracting Rational Numbers :1-4 & 1-5Adding & Subtracting Rational Numbers Evaluate each expression. 5. 6. We cannot subtract so we must borrow!