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Name:_______________________________ 1.4 Adding and Subtracting Integers on the Number Line When we ADD, we move RIGHT on the number line. When we SUBTRACT, we move LEFT on the number line. Adding Integers -3 Starting point + Subtracting integers 2 -3 Moving 2 steps to the right – Starting point 2 Moving 2 steps to the left –5 + 3 = –5 + 5 = –5 + 7 = –2 + 3 = 2–3= –4 + 2 = –1 – 1 = 4+7= –8 + 9 = 3–7= –2 – 4 = –4 – 4 = WHAT IF we need to add or subtract a negative number? There are two signs next to each other! Change the double signs to a single sign: + – will become – – – will become + 0 + (–4) = -4 + (–3) = 1 + (–5) = 3 – (–6) = –2 – (–3) = 4 – (–6) = –3 – (–1) = –7 – (–5) = –1 + (–8) = -5 – (-2) = –4 + (–4) = –12 – (–0) = 3 + (–8) = (–9) – (–4) = 7–5= 8 + (–1) = 6 – (–4) = (–4) – (–2) = (–4) – 10 = –3 – (–3) = Review: An integer and its opposite add up to give __________ , that is why we also call them _______________________________________________. Inverse means ___________________. -7 + (+7) = -3 + 3 = 100 + (–100) = |–6 + 17|= |–3 – 14|= |7 – 14|= –78 + 20 = –26 – (–46) = –100 – 22 = Distance on the Number Line A distance between two points on a number line can be calculated as the absolute value of the __________________ between their coordinates. Graph each pair of points on the number line. Then write an expression using absolute value to find the distance between the points. Find the distance. 19. H at –4 and G at 2 20. X at –5 and Y at –1 21. A at 3 and B at –3 22. How far away is the plane from the submarine? ___________ 23. A diver that was located 7 meters below the sea level ascends 3 meters. What is his new location? Write an expression using absolute value to find the distance between the given points. Find the distance. a) 4 and 10 b) –2 and –8 c) –12 and –3 d) +7 and –3 e) –12 and 12 f) 0 and –5 Use the number line to demonstrate the expressions. Simplify and circle your answer. 19) –4 + 6 20) –1 – 2 Use the given models to write at least two corresponding integer expressions. 21) 22) 23) 24) HOMEWORK 1.4 1. Circle ALL expressions below that can be represented by the given model. –3 + 8 –3 – (– 8) 0 + –3 + 8 0–3 –3 + 5 –3 – (+8) 5 – (–3) –3 – 8 2. Model (show) –2 + 5 on the number line. Then model it with counters. The answer is ____ 3. Evaluate 8 − (−2) = 1 – (–7) = 4+2= (–2) + 6 = (−4) − 4 = 9 − (−7) = (−18) − 0 = 87 − 65 = (–35) + (−10) = (−12) − (−23) = (−5) − (−26) = 19 – (−19) = |–43| + 2 = |5| – |–3|= −|−12| = |– 5 + 13| 4. Find the opposite of 7 ______ 5. Find the additive inverse of 7 ______ 6. Find the abs. value of 7 _____ 7. Before you went to sleep last night, the temperature was –3°F. During the night the temperature dropped by 5°F. What was the temperature at the end of the night? 8. A pilot descended 100 meters to avoid a thunderstorm, then ascended 150 meters. Write an addition expression to describe this situation, and then find the sum and explain its meaning. The elevation of the plane became _____ meters __________(higher? lower?) than the original elevation. 9. Find the distance between the points on the number line: a) 5 and –17 b) –8 and –14