Rational Addition/Subtraction

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Rational Addition/Subtraction · Grade 7 · Worksheet 3

1. Liam is tracking his stock portfolio. On Monday, his investment gained 3/8 of its value. On Tuesday, it lost 1/4 of its new value. On Wednesday, it gained another 5/16 of its value. What was the total fractional change in the value of his investment over the three days? Answer: 1/2 Solution: To find the total change after multiple percentage or fractional increases and decreases, it is often helpful to model the value after each step. An increase means you multiply by a number greater than 1 (e.g., 1 + the fraction), and a decrease means you multiply by a number less than 1 (e.g., 1…
   Full step-by-step solution

   To find the total change after multiple percentage or fractional increases and decreases, it is often helpful to model the value after each step. An increase means you multiply by a number greater than 1 (e.g., 1 + the fraction), and a decrease means you multiply by a number less than 1 (e.g., 1 - the fraction). The overall change is found by multiplying these factors together and comparing the final result to the starting point.

2. Emma is tracking the altitude of a research drone as it flies over a mountain range. The drone starts at an altitude of 135 meters above sea level. It first descends 87 meters to avoid a cliff, then ascends 63 meters to catch a thermal updraft, and finally descends 49 meters to land on a plateau. What is the drone's final altitude relative to sea level? Answer: 62 Solution: Start at 135 meters. Descend 87 meters: 135 - 87 = 48 meters. Ascend 63 meters: 48 + 63 = 111 meters.
   Full step-by-step solution

   Step 1: Start at 135 meters. Step 2: Descend 87 meters: 135 - 87 = 48 meters. Step 3: Ascend 63 meters: 48 + 63 = 111 meters. Step 4: Descend 49 meters: 111 - 49 = 62 meters. The final altitude is 62 meters above sea level.

3. Charlotte is tracking the depth of a research submarine during an underwater expedition. The submarine starts at -250.75 feet relative to sea level. It then descends (goes deeper) by 185.5 feet to investigate a coral reef. After exploring the reef, it ascends (goes up) by 312.25 feet to avoid an underwater canyon. Finally, it descends again by 98.4 feet to collect samples near the ocean floor. What is the final depth of the submarine relative to sea level? Answer: -222.4 Solution: Start at -250.75 feet. Descend 185.5 feet means subtract 185.5: -250.75 - 185.5 = -436.25 feet. Ascend 312.25 feet means add 312.25: -436.25 + 312.25 = -124 feet.
   Full step-by-step solution

   Step 1: Start at -250.75 feet. Descend 185.5 feet means subtract 185.5: -250.75 - 185.5 = -436.25 feet. Step 2: Ascend 312.25 feet means add 312.25: -436.25 + 312.25 = -124 feet. Step 3: Descend 98.4 feet means subtract 98.4: -124 - 98.4 = -222.4 feet. The final depth is -222.4 feet.

4. Tane is hiking in the mountains and tracking his altitude changes. He starts at an elevation of 12450 feet above sea level. He climbs up 2850 feet to reach a peak. Then he descends 6200 feet into a valley. Finally, he climbs up 1950 feet to reach a campsite. What is Tane's final elevation above sea level? Answer: 11050 Solution: Start with the initial elevation: 12450 feet. Climb up 2850 feet: 12450 + 2850 = 15300 feet. Descend 6200 feet: 15300 - 6200 = 9100 feet.
   Full step-by-step solution

   Step 1: Start with the initial elevation: 12450 feet. Step 2: Climb up 2850 feet: 12450 + 2850 = 15300 feet. Step 3: Descend 6200 feet: 15300 - 6200 = 9100 feet. Step 4: Climb up 1950 feet: 9100 + 1950 = 11050 feet. The final elevation is 11050 feet above sea level.

5. Aroha is monitoring the depth of a diving spot near a coral reef. The water depth starts at -37.5 feet relative to sea level (meaning it is 37.5 feet below sea level). A tidal wave causes the water level to rise by 21.75 feet. Then, an underwater current pulls the water down by 45.25 feet. Finally, a second tidal wave lifts the water up by 33.5 feet. What is the final depth of the water relative to sea level? Answer: -27.5 Solution: Start with initial depth: -37.5 feet First tidal wave rises water by 21.75 feet: -37.5 + 21.75 = -15.75 feet Underwater current pulls water down by 45.25 feet: -15.75 - 45.25 = -61 feet Second tidal wave lifts water by 33.5 feet: -61 + 33.5 = -27.5 feet The final water depth is -27.5 feet below…
   Full step-by-step solution

   Step 1: Start with initial depth: -37.5 feet Step 2: First tidal wave rises water by 21.75 feet: -37.5 + 21.75 = -15.75 feet Step 3: Underwater current pulls water down by 45.25 feet: -15.75 - 45.25 = -61 feet Step 4: Second tidal wave lifts water by 33.5 feet: -61 + 33.5 = -27.5 feet The final water depth is -27.5 feet below sea level.

6. Emma is tracking the value of her cryptocurrency investment. On Monday, her portfolio is worth -$350.00 (meaning she is in debt). On Tuesday, the value increases by $125.50. On Wednesday, it drops by $200.75. On Thursday, it rises by $85.25. What is the value of Emma's portfolio after all these changes? Answer: -340.00 Solution: Start with the initial value: -$350.00 Add Tuesday's increase: -350.00 + 125.50 = -224.50 Subtract Wednesday's drop: -224.50 - 200.75 = -425.25 Add Thursday's rise: -425.25 + 85.25 = -340.00 The final value of Emma's portfolio is -$340.00.
   Full step-by-step solution

   Step 1: Start with the initial value: -$350.00 Step 2: Add Tuesday's increase: -350.00 + 125.50 = -224.50 Step 3: Subtract Wednesday's drop: -224.50 - 200.75 = -425.25 Step 4: Add Thursday's rise: -425.25 + 85.25 = -340.00 The final value of Emma's portfolio is -$340.00.

7. (-7/8 + 3/4) - (-5/6 + 2/3) = ? Answer: 1/8 Solution: Calculate the first parentheses: -7/8 + 3/4 Find common denominator for 8 and 4: 8 -7/8 = -7/8 3/4 = 6/8 -7/8 + 6/8 = -1/8 Calculate the second parentheses: -5/6 + 2/3 Find common denominator for 6 and 3: 6 -5/6 = -5/6 2/3 = 4/6 -5/6 + 4/6 = -1/6 Subtract the results: (-1/8) - (-1/6) Subtracting…
   Full step-by-step solution

   Step 1: Calculate the first parentheses: -7/8 + 3/4 Find common denominator for 8 and 4: 8 -7/8 = -7/8 3/4 = 6/8 -7/8 + 6/8 = -1/8 Step 2: Calculate the second parentheses: -5/6 + 2/3 Find common denominator for 6 and 3: 6 -5/6 = -5/6 2/3 = 4/6 -5/6 + 4/6 = -1/6 Step 3: Subtract the results: (-1/8) - (-1/6) Subtracting a negative is adding: -1/8 + 1/6 Step 4: Find common denominator for 8 and 6: 24 -1/8 = -3/24 1/6 = 4/24 -3/24 + 4/24 = 1/24 The answer is 1/24.