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Number Representation and Calculation – VII A Extending the Number Line Practice 1 Fill in the missing numbers. (−3) (a) 4 + (b) 3 – (9) (c) −6 + (−1) =1 (d) (−5) + 7= 2 = −6 (e) (−1) − 7 = −8 = −7 (f) 4 − (−3) Basic Rules for Multiplication/Division: Examples: positive × positive = positive (+5) × (+3) = +15 =7 (+8)/(+2) = +4 negative × negative = positive (-5) × (-3) = +15 (-8)/(-2) = +4 positive × negative = negative (+5) × (-3) = –15 (+8)/(-2) = -4 negative × positive = negative (-5) × (+3) = –15 (-8)/(+2) = -4 Note: • any number multiplied by ZERO is ZERO 0 × (–6) = 0 0 × (6) = 0 • any number divided by ZERO is undefined 7 ÷ 0 = undefined • ZERO divided by any number (≠ 0) is ZERO 0 ÷ 7 = 0 • ZERO divided by ZERO is undefined. 0 ÷ 0 = undefined Practice 2 (-3) (-2) ÷ (4) ÷ 1 = (answer: 1.5) (4 ÷ 8) (2) (-3) = (answer:-3) (answer: -7) = (answer: -1/5) = (e) -4 × 5 = - 20 (h) (−4) × (−8) (f) (−80) ÷ (−20) =4 (i) × (−3) = 12 (g) 16 × (−2) = -32 (j) 40 ÷ (−4) (−5) = 32 =− 8 3. Write down the next three terms in each of the sequences below. (a) 1, -2, 4, -8, 16, -32, 64, -128…. (b) -1, 2, -4, 8, -16, 32, -64, 128… 1 (c) 1, -10, 100, -1,000, 10,000, -100,000, 1,000,000 (d) -1, 5, -25, 125, - 625, 3125, -15625 Practice 4: Planting Zones Chart of Plant Hardiness Zones This chart is used to match the survival temperatures of a plant that you plan to buy with the coldest temperatures in the zone where you live, so that you can be assured that your plant will survive the coldest months in your area. a. Mark the range of average annual minimum temperatures in all zones on the following number line. −40 to 40 −40 −30 −20 −10 Zone 3 Zone 4 Zone 5 Zone 6 10 0 Zone 7 20 Zone 8 Zone 9 30 40 Zone 10 2 b. How much colder is the lowest minimum temperature in Zone 4 (most of the Northeast) than the lowest minimum temperature in Zone 9 (Florida)? 50 = 20 – (–30) Plant Scenarios-Will the Plants Survive the Winter? c. Daffodils grow in the spring and are very hardy. They even grow in Zone 3. Minnesota is in Zone 3. During a winter cold spell in northern Minnesota, the temperature rose to 5° and then dropped 50° at night for several days. Did the daffodils survive this unusual cold spell? Why or why not? –45°F = 5 – (50) No, it dropped below the minimum temperature in Zone 3. d. A flower catalogue advertised azalea shrubs that were hardy in Zones 6-9. All of Kentucky is Zone 6. One winter, the month of January was very cold. The daytime temperatures hovered around 35°, and at night, the temperatures dropped nearly 40 degrees. Would the plants be likely to survive? Why or why not? –5°F = 35 – (40) Yes, it is still above the minimum temperature in Zone 6. 5. Simplify 18 – (–16) – 3 – (–5) + 2 = 38 6. Simplify –43 – (–19) – 21 + 25 = –20. 7. Simplify 84 + (–99) + 44 – (–18) – 43 = 4. 8. Simplify (–2)(–3)(–4) = –24 9. Simplify (–1)(–2)(–1)(–3)(–4)(–2)(–1) = –48 10. Simplify 3