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Unit 1: Integers HOMEWORK Page 31 Unit 1 Integers (Calculators will NOT be used) Homework SOL 7.1 - The student will: e) identify and describe absolute value for rational numbers SOL 7.3 - The student will: a) model addition, subtraction, multiplication and division of integers. b) Add, subtract, multiply and divide integers. Unit 1: Integers HOMEWORK Page 32 Integers and Absolute Value Homework Write an integer to represent the situation below. 1) sea level _______ 2) a withdraw of 42 dollars _______ 3) 14 degrees below 0 _______ 4) an increase in height of 3 inches______ Evaluate the problems below. 5) | 29 | = __________ 6) | - 15 | = __________ 7) | 9 | - | -2 | = __________ 8) | -50 | + | -7 | = __________ 9) What is the sum of the absolute value of -14 and 10? 10) | -30| - | -4 | + | 5 | = __________ Compare using > , < , or = 11) -32 14) | -9 | 14 |9| 12) 11 -4 13) | -14 | 15) -10 -12 16) | 4 + 7 | -14 13 Order the following from least to greatest. 17) -8 , 10 , 2 , -13 , -5 , 3 ________________________________________ 18) -22 , -11 , |11| , |0|, |-14|, 22 , -10 ________________________________________ Order the following from greatest to least. 19) -9 , -19 , 19 , 99 , -29 , -99 , 29 ________________________________________ My score is _________/19 Unit 1: Integers HOMEWORK Page 33 Unit 1: Integers HOMEWORK Page 34 Adding Integers Homework Add and Model Using +/- Signs making Zero Pairs where needed. 1) -4 + (-1) = _____ 2) 6 + (-4) = _____ 3) -3 + 8 = _____ 4) 7 + (-5) = _____ Interpret the following Models. 5) ______________ 6) ______________ 7) ______________ 8) ______________ Add and Model on a Number Line. (Draw a number line on your lined paper) 9) -2 + (-4) = _____ 10) -10 + 3 = _____ 11) 7 + (-2) = _____ 12) 8 + (-5) = _____ Evaluate each expression if a = -4, b = 7, and c = -6. 13) 6 + a = _____ 14) b + (-10) = _____ 15) c + (-2) = _____ 16) a + b = _____ 17) a + 0 = _____ 18) b + c + a = _____ Solve each word problem. 19) During the night, the average temperature on the moon is -140°C. By noon, the average temperature has risen 252°C. What is the average temperature on the moon at noon? 20) The starting balance in a checking account was $50. What was the balance after checks were written for $25 and for $32? My score is _________/20 Unit 1: Integers HOMEWORK Page 35 Unit 1: Integers HOMEWORK Page 36 Subtracting Integers Homework Subtract and Model Using +/- Signs making Zero Pairs where needed. 1) 3 – 8 = _____ 2) 6 – (-8) = _____ 3) -4 – 6 = _____ 4) -7 – (-10) = _____ Interpret the following Models. 5) ______________ 6) ______________ 7) ______________ 8) ______________ Subtract and Model on a Number Line. (Draw a number line on your lined paper) 9) -3 – 1 = _____ 10) 4 – (-6) = _____ 11) -5 – 4 = _____ 12) 6 – 10 = _____ Evaluate each expression if a = -8, b = 2, and c = -9. 13) 6 – a = _____ 14) b - (-12) = _____ 15) c - (-2) = _____ 16) a - b = _____ 17) a - 0 = _____ 18) b - c - a = _____ Solve each word problem. 19) During January, the normal high temperature in Duluth, Minnesota, is 16°F, and the normal low temperature is -2°F. Find the range of the temperatures. 20) The highest point in California is Mount Whitney, with an elevation of 14,494 feet. The lowest point is Death Valley, elevation -282 feet. Find the difference in the elevations. My score is _________/20 Unit 1: Integers HOMEWORK Page 37 Unit 1: Integers HOMEWORK Page 38 Multiplying and Dividing Integers Homework Solve the following by multiplying or dividing. 1) -3 · 4 = _____ 2) 54 ÷ (-9) = _____ 3) -5(-4)(6) = _____ 4) -60 ÷ 6 = _____ 5) -8(-11) = _____ 6) 480 ÷ (-12)= _____ 7) 6 · 9= _____ 8) Interpret the following Models. 10) ______________ 12) ______________ 175 −12 9) 2(-8)(-9)(10) = _____ = _____ 11) ______________ 13) ______________ Multiply and Model on a Number Line. (Draw a number line on your lined paper) 14) -7(2) = _____ 15) 4(-4) = _____ 16) -3 · 6 = _____ 17) 5 · (-3) = _____ Use multiplication or division to solve the problems below. 18) The research submarine Alvin, used to locate the 19) The highest recorded temperature in Columbus wreck of the Titanic, descends at a rate of about Ohio, is 104°F. The lowest recorded temperature is 100 feet per minute. What integer describes the -22°F. What is the difference between the highest distance Alvin travels in 5 minutes? and lowest temperatures? 20) The low temperatures for 7 days in January were -2, 0, 5, -1, -4, 2, and 0. Find the average for the 7-day period. My score is _________/20 Unit 1: Integers HOMEWORK Page 39 Unit 1: Integers HOMEWORK Page 40 Integer Test Study Guide Absolute Value • Integers are any numbers from a set of whole numbers and their opposites o (Examples: …., -4, -3, -2, -1, 0, 1, 2, 3, 4….) • The absolute value of an integer is the distance from zero (it is always positive) 1) Write an integer that represents a withdrawal of $15 2) |-13| – |-8| 4) Fill in with <,>,= 6) Order the numbers from least to greatest. -7 5) Fill in with <,>,= -4 8 | -10 | 7) Order the numbers from greatest to least. -38, -1, 5, 42, |-37| , 43 3) Fill in with <,>, = 27 |-27| -9, 9, 0, 1, -10, -3, 3 8) On the same day, a thermometer registered 10 degrees in Paris and -5 degrees in Rome. Which European city was warmer? Adding Integers Step 1: Look at the signs are they the same or different? (-4) + (-3) ⇒ Same signs (-7) + 2 ⇒ Different signs If Signs are the SAME: If Signs are different: Step 2: Add the numbers: Step 2: Subtract the numbers: (-4) + (-3) = 4+3=7 (-7) + 2= 7-2= 5 Step 3: Keep the sign the same Step 3: Keep the sign of the larger number (-4) + (-3)= (-7) For #s 9 – 12, Evaluate if x = -5, y = 10, and z = -3. 9) x + y 10) x + y + z 13) Jason owed his mom $7. He borrowed $25 more to go to the movies. How much money does Jason have? (-7) +2 = 5 (7 is larger than 2, so the answer is negative) 11) z + x 12) z + y 14) The members of the Investment Club purchased a stock for $60. The next day the price of the stock dropped $16. On the second and third days, the price dropped another $15 and then rose $20. How much was the stock worth at the end of the third day? 15) Model using +/- signs -3 + 7 = _____ Unit 1: Integers HOMEWORK Page 41 16) Solve and model using the number line. -10 + 13 = _____ Example: (-4) – (-3) = ? Subtracting Integers • Minus Minus becomes a GIANT Plus Sign (-4) + 3 = -1 For #s 17 – 20, Evaluate if x = -5, y = 10, and z = -3. 17) 12 – (-y) 18) x + y – z 19) -y – x 20) z – x 21) The average temperature in Calgary, Canada, is 22 degrees Celsius in July and -11 degrees Celsius in January. What is the range of the temperatures? 22) James has negative $50 in the bank and Rico has $70 in the bank $70. What is the difference in the amount of money the boys have? 23) Model using +/- signs 24) Solve and model using the number line. -5 – (-3) = _____ 7 - 12 = _____ Multiplying and Dividing Integers Positive • or ÷ Positive= Positive Negative • or ÷ Negative = Positive EVEN # of negative signs the answer is POSITIVE Positive • or ÷ Negative= Negative ODD # of negative signs the answer is NEGATIVE Negative • or ÷ Positive = Negative 25) -6(-12) Unit 1: Integers HOMEWORK Page 42 27) (-4)(-22) 28) 45 ÷ (-15) For # 29 – 32, Evaluate if x = -5, y = 10, and z = -3. 29) -2(3z) xy 31) xyz 32) 2y(-3) 30) 2 33) McCarthy Middle School’s enrollment has decreased by 500 students over the past 5 years. What is the average change per year? 34) A hose can drain a pool at the rate of 225 gallons per hour. How much water can be drained in 5 hours? -65 = 5 26) = Multiply and model on the number line. 35) -4 · 6 = _____ Don’t Forget to Check your Homework Online and Review the Notes Section of your Binder! Your test is next class! My score is _________/35 Unit 1: Integers HOMEWORK Page 43 Unit 1: Integers HOMEWORK Page 44 Unit 1: Integers HOMEWORK Page 45 Unit 1: Integers HOMEWORK Page 46