Lesson 15

Adding and Subtracting with Scientific Notation

Let’s add and subtract using scientific notation to answer questions about animals and the solar system.

Problem 1

Evaluate each expression, giving the answer in scientific notation:

  1.  \(5.3 \times 10^4 + 4.7 \times 10^4\)
  2. \(3.7 \times 10^6 - 3.3 \times 10^6\)
  3. \(4.8 \times 10^{\text-3} + 6.3 \times 10^{\text-3}\)
  4. \(6.6 \times 10^{\text-5} - 6.1 \times 10^{\text-5}\)

Problem 2

  1. Write a scenario that describes what is happening in the graph.
  2. What is happening at 5 minutes?
  3. 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.
(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.

  1. Name one combination of 8 fruits shown on the graph that whose cost does not total to $10.

  2. Name one combination of fruits shown on the graph whose cost totals to $10 that are not 8 fruits all together.

  3. How many apples and oranges would you need to have 8 fruits that cost $10 at the same time?

(From Unit 4, Lesson 10.)

Problem 4

Solve each equation and check your solution.

\(\text-2(3x-4)=4(x+3)+6\)

\(\frac12(z+4)-6=\text-2z+8\)

\(4w-7=6w+31\)

(From Unit 4, Lesson 5.)