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September 10, 2015 1.5: Rational Numbers A rational number is a number that can be written as a quotient of two integers, where the divisor is not 0. Examples: 2/5, 0.3, -6, 3 1/2 Comparing Rational Numbers -1/2 and -3/4 Method 1: Use a number line Method 2: Re-write with common denominator Your Turn ... -2/3 and -1/6 September 10, 2015 Comparing Decimals Example: Compare -4.4 and 4.7 Method 1: Use Number Sense Method 2: Use a Number Line to illustrate Ordering Rational Numbers The peaks of four mountains or seamounts are located either below or above sea level as follows: 1/4 mi, -0.2 mi, -2/9 mi, 1.1 mi. Put them in order from least to greatest please. The following temperatures were recorded during a science project: 12 1/2ºC, -4ºC, 6.55ºC, and -6 1/4ºC. Order the integers from least to greatest. September 10, 2015 1-6: Adding and Subtracting Rational Numbers The distance between two numbers on a number line is the absolute value of their distance. -5 -4 -3 -2 -1 0 1 2 3 4 5 Find the distance between -1.4 and 2.8 *Check by counting the distance on the number line. Adding Rational Numbers Same Sign The sum of two positive rational numbers is positive. a. 1 3/4 + 2 1/8 = Different Sign Find the absolute value of each addend. Subtract the lesser from the greater. The sum has the sign of the addend with the greater absolute value. c. 1 3/4 + (-2 1/8) The sum of two negative rational numbers is negative. b. -3.5 + (-4.25) = d. -3.5 + 4.25 September 10, 2015 Your Turn .... 1. -6.25 + (-8.55) 2. 4 3/5 + (-3 2/5) Subtracting Rational Numbers To subtract a rational number, add its opposite. a. Find 6 2/3 - (-3 1/3) b. Find -4.68 - (-5.79) Your Turn ... c. -3 2/5 - (- 2 4/5) d. -13.45 - 12.25