Lesson 15
Adding and Subtracting with Scientific Notation
Problem 1
Evaluate each expression, giving the answer in scientific notation:
- \(5.3 \times 10^4 + 4.7 \times 10^4\)
- \(3.7 \times 10^6 - 3.3 \times 10^6\)
- \(4.8 \times 10^{\text-3} + 6.3 \times 10^{\text-3}\)
- \(6.6 \times 10^{\text-5} - 6.1 \times 10^{\text-5}\)
Solution
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Problem 2
- Write a scenario that describes what is happening in the graph.
- What is happening at 5 minutes?
- What does the slope of the line between 6 and 8 minutes mean?
![Coordinate plane, time in minutes, 0 to 8, distance in kilometers, 0 to 5. Line segments connect the origin to 2 comma 1, 2 point 5 comma 1, 4 point 5 comma 2, 5 point 5 comma 2, 8 comma 4 point 5.](https://cms-im.s3.amazonaws.com/Koa9yeYQerjR4gj4JKPAFaSE?response-content-disposition=inline%3B%20filename%3D%228-8.5.PP.C.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.PP.C.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T034309Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4e7d760799d4a881b737f3936ae1351281a4ed2a1904a7e26605ecb935c941e9)
Solution
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(From Unit 5, Lesson 10.)Problem 3
Apples cost $1 each. Oranges cost $2 each. You have $10 and want to buy 8 pieces of fruit. One graph shows combinations of apples and oranges that total to $10. The other graph shows combinations of apples and oranges that total to 8 pieces of fruit.
![Coordinate plane, x, number of apple, y, number of oranges.](https://cms-im.s3.amazonaws.com/hUBzFZuf5v81fxSZ4FWA4uie?response-content-disposition=inline%3B%20filename%3D%228-8.4.PP.C.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%278-8.4.PP.C.Image.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T034309Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c17523f067daa0704fffa92d53dc83fd0000b03b5afea2a9b4b39288e4b7a9b0)
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Name one combination of 8 fruits shown on the graph that whose cost does not total to $10.
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Name one combination of fruits shown on the graph whose cost totals to $10 that are not 8 fruits all together.
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How many apples and oranges would you need to have 8 fruits that cost $10 at the same time?
Solution
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(From Unit 4, Lesson 10.)Problem 4
Solve each equation and check your solution.
\(\text-2(3x-4)=4(x+3)+6\)
\(\frac12(z+4)-6=\text-2z+8\)
\(4w-7=6w+31\)
Solution
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(From Unit 4, Lesson 5.)