Lesson 6 Subtracting real numbers Inverse property of

Lesson 6 Subtracting real numbers

Inverse property of addition • For every real number a, • a + (-a) = (-a) + a = 0 • Two numbers with the same absolute value but different signs are opposites. • Another name for opposite is additive inverse.

Rules for subtracting real numbers • To subtract a number, add its inverse- then follow the rules for addition. • Any subtraction problem can be turned into an addition problem by adding the opposite. • 3 -5 = 3 + (-5)= -2

Find each difference • • (-13) -8 (-32) -(-22) 4. 5 -(-8. 2) (-6/7) -(-1/7) 3. 2 -(-5. 1) (-19)-(-8) (-12) -21 (-3/5) -(-1/5)

Lesson 7 simplifying and comparing expressions with symbols of inclusion • To simplify an expression with multiple symbols of inclusion, begin inside the innermost symbol of inclusion and work outward. • Symbols of inclusion include: parentheses, brackets, fraction bar, absolute value symbol

Simplify using order of operations

Simplify with brackets

Compare expressions • Use <, >, or =

Lesson 8 using unit analysis to convert measures • Unit analysis converts measures into different units by using a unit ratio, or conversion factor, that names the same amount. • Examples of unit ratios: 12 in = 1 foot • 1 meter = 100 cm. • 3 ft= 1 yard • 60 min = 1 hour 5280 ft= 1 mile 1000 meters= 1 kilometer 1 inch = 2. 54 cm. 60 sec= 1 min

Unit ratios • Since the amounts used in a unit ratio are equal to each other, if we write them in fraction form, a unit ratio is always equal to 1 • Example: • A cheetah ran at a rate of 105, 600 yards per hour. How fast did the cheetah run in miles per hour? • 105600 yards -----? Miles

example • An elephant can charge at speeds of about 25 miles per hour. How fast can an elephant charge in feet per hour?

Converting units of area • Area is measured in square units • Example: yd 2 = yd. • So when converting area measurements, we must use each unit conversion twice • Ex: a gym measures 8. 5 meters by 14 meters. The owner bought mats to cover the floor. Each mat is 110 cm. square. If 95 mats were purchased, are there enough mats to cover the floor? • 1. Find the area of the floor • 2. convert the area to cm. square • 3. find the area of the mats • 4. compare the areas

Converting units of volume • Volume is measured in cubic units • Ex: yd 3 = yd yd yd • So whenever we are converting volume measurements, we must use 3 unit ratios. • Ex: A hose with a flow rate of 41, 472 cubic inches per hour is filling up a pool. The volume of the pool is 1104 cubic feet. How many hours will it take to fill the pool? • 1. change cubic inches to cubic feet • 2. divide volume of pool by volume per hour.

Lesson 9 evaluating and comparing algebraic expressions • An algebraic expression containing only numbers and operations is a numeric expression • An algebraic expression is an expression with variables and/or numbers that use operations, add, subt, mult or div. • Evaluate means to substitute values for the variables and to use the order of operations to simplify

Evaluate • 1. evaluate the expression when x =3 and a =1 • 3 x - 4 x + ax • 2. evaluate when x =2 and y=5 • 2 x + 3 y -xy • 3. evaluate when y = 2 and z = 4 • 3(z-y)2 - 4 y 3 • 4. evaluate when a = 3 and z = 2 • 2(a+z)3 - z 2

Comparing algebraic expressions • 2 algebraic expressions are equivalent if they can be simplified to the same value. • • Compare when b= 3 and a = 4, use <, >, or = 3 a 2 + 2 b - 4 b 3 ------ 2 a 2 b 2 Compare when b=5 and c= 2 4 b 3 -3 c + 2 b 2 ------- 3 b 2 c 3

application • A company charges $60 per month and $4 per movie rented. How much will it cost to rent 7 movies in a month? • 1. write the expression • 2. substitute values for the variables • 3. solve

adding and subtracting real numbers • When solving a problem containing addition and subtraction of signed numbers, begin by writing the problem as addition only. • Then group and add terms with like signs. • Then add the terms with unlike signs • Ex. 79. 5 +(-3. 12) + 7. 34 - 6. 18 • 79. 5 + (-3. 12) + 7. 34 + (-6. 18) • 79. 5 + 7. 34 + (-3. 12) + (-6. 18) • 86. 84 + - 9. 30 • 77. 54

Ordering rational numbers • It is easiest to order numbers if they are all fractions or all decimals • Order from least to greatest: • 7/8, -2, . 125, 1/2 • 3/5, -1/4, -. 75, 0

Comparing rational expressions • Use <, >, = • 3/8 + ( -5/8) - 1/8 ____ -2. 75 +6. 25 - 3. 75 • 7/9 - 1/9 + (-2/9) _____ 2. 15 - 4. 27 + 2. 56

Check for understanding • 1. Why might you use a number line to order rational numbers? • 2. Explain how to evaluate an expression. • 3. Explain how to write a unit ratio to convert 45 inches to yards. • 4. What is the order of operations? • 5. How do you find the opposite of a real number?