Module 1 Ratios and Proportional Relationships Topic B

Module 1: Ratios and Proportional Relationships: Topic B: Unit Rate and Constant of Proportionality What is a “rate”? What is a “unit rate”? rate: a ratio that compares two quantities measured in different units. Example: 120 miles is read as “ 120 miles ‘per’ or ‘each’ 4 hours” 4 hours unit rate: the rate in which the denominator is 1 (rate ‘per’ 1 unit of a given quantity) - Unit rate is used in everyday life to determine the best value. It can be found by simplifying the fraction to a denominator of “ 1” or simply dividing the numerator (top number) by the denominator (bottom number. Example: 120 miles 4 4 hours 4 = 30 miles 1 hours or 120 4 = 30 mph The above unit rate is read as “ 30 miles ‘per’ hour” (30 m/h or 30 mph) PRE-ALGEBRA

Module 1: Ratios and Proportional Relationships: Topic B: Unit Rate and Constant of Proportionality PRE-ALGEBRA

Module 1: Ratios and Proportional Relationships: Topic B: Unit Rate and Constant of Proportionality What is an “equation”? What is a “true equation”, “false equation”, and “open sentence”? equation – a number sentence with an “equal” sign Examples: 9 + 2 = 11 a numerical expression equal to a numerical expression x + 7 = 37 or 37 = x + 7 an algebraic expression equal to a numerical expression (or vice versa) a + (-3) = 2 a + 5 an algebraic expression equal to an an algebraic expression true equation – an equation in which both sides equal one another Example: 6 + 12 = 18 false equation – an equation in which both sides don’t equal one another Example: 6 ≠ 3 + 4 open sentence – an equation with one or more variables Example: Write the equation “nine times the opposite of five is forty-five. ” State whether the equation is true, false or an open sentence. Words nine 9 times x the opposite of five (-5) is = forty-five 45 The equation is false, because 9 x (-5) = -45, and -45 ≠ 45 PRE-ALGEBRA

Module 1: Ratios and Proportional Relationships: Topic B: Unit Rate and Constant of Proportionality PRE-ALGEBRA

Module 1: Ratios and Proportional Relationships: Topic B: Unit Rate and Constant of Proportionality PRE-ALGEBRA

Module 1: Ratios and Proportional Relationships: Topic B: Unit Rate and Constant of Proportionality PRE-ALGEBRA

Module 1: Ratios and Proportional Relationships: Topic B: Unit Rate and Constant of Proportionality PRE-ALGEBRA

Module 1: Ratios and Proportional Relationships: Topic B: Unit Rate and Constant of Proportionality PRE-ALGEBRA

Module 1: Ratios and Proportional Relationships: Topic B: Unit Rate and Constant of Proportionality POTD Find each unit rate. 1. You pay $4. 50 for 2 gallons of orange juice. $2. 25/gal 2. You pay $21. 60 for a 20 -lb bag of dog food. $1. 08/lb 3. A bird flies at a speed of 384 in. /s. What is its 1, 920 ft/min speed in units of ft/min? 4. A job takes 96 person-days. How many workers are needed to complete the job in 24 days? 4 PRE-ALGEBRA

Module 1: Ratios and Proportional Relationships: Topic B: Unit Rate and Constant of Proportionality Lesson Quiz 1. Is b + 3 b – 1 = 15 true, false, or an open sentence? open sentence 2. Write an equation for A number added to seven times the number is the opposite of thirty-two. Is the equation true, false, or an open 7 x + x = – 32; open sentence? yes 3. Is 25 a solution of the equation 175 – x = 150? 4. no Can you stack eight books that are each 3 in. thick inside a box that is 18 in. tall? PRE-ALGEBRA