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Put the rational numbers in order on the timeline. Drag and drop them into their correct box.(4 points)

Drop target 1
Drop target 2
Drop target 3
Drop target 4
Answers:
-4.5
2.25
-1/2
-2 1/2

5 answers

To order the rational numbers on a timeline, we first need to convert them into a consistent format, typically decimal form or improper fractions. Here are the numbers you've provided:

  1. -4.5 (which is -4.5)
  2. 2.25 (which is 2.25)
  3. -1/2 (which is -0.5)
  4. -2 1/2 (which as an improper fraction is -5/2 or decimal form is -2.5)

Now, let's convert the fractions for better comparison:

  • -4.5
  • -2.5 (from -2 1/2)
  • -0.5 (from -1/2)
  • 2.25

Next, we will order them from least to greatest:

  1. -4.5
  2. -2.5
  3. -0.5
  4. 2.25

Now we can drop them into their correct boxes:

Drop target 1: -4.5
Drop target 2: -2.5
Drop target 3: -0.5
Drop target 4: 2.25

Select whether each statement is TRUE or FALSE.

Calculators are not allowed in Unit 2.

(4 points)
True False
62 = 12


82 = 8×8

49−−√ = 7
because 7×7=49

12−−√= 6
because 6×2 =12

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Let's evaluate each statement one by one to determine if they are TRUE or FALSE.

  1. 62 = 12

    • FALSE
    • \( 6^2 = 36 \), not 12.

  2. 82 = 8×8

    • TRUE
    • \( 8^2 = 64 \), and \( 8 \times 8 = 64 \).

  3. 49−−√ = 7 because 7×7=49

    • TRUE
    • \( \sqrt{49} = 7 \) because \( 7 \times 7 = 49 \).

  4. 12−−√= 6 because 6×2 =12

    • FALSE
    • \( \sqrt{12} \) is approximately 3.464, not 6. The equation \( 6 \times 2 =12 \) is true, but it does not provide the correct square root.

Here's the summary:

  1. 62 = 12 - FALSE
  2. 82 = 8×8 - TRUE
  3. 49−−√ = 7 because 7×7=49 - TRUE
  4. 12−−√= 6 because 6×2 =12 - FALSE
Use the rules of adding rational numbers to solve. Calculators are not allowed.

−212+623
(1 point)
Responses

413
4 and 1 third

−416
negative 4 and 1 sixth

916
9 and 1 sixth

416
4 and 1 sixth
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To solve the addition of the rational numbers \(-212 + 623\), we need to first express them as improper fractions.

  1. Convert \(-212\) and \(623\) to improper fractions.
    • \(-212\) is simply \(-212\) (it remains the same).
    • \(623\) is also simply \(623\).

Now we compute:

\[ -212 + 623 = 623 - 212 \]

Calculating it step by step:

  1. Subtract \(212\) from \(623\): \[ 623 - 212 = 411 \]

So, we have:

\[ -212 + 623 = 411 \]

Now let's check the options given:

  1. 413
  2. 4 and 1 third
  3. −416
  4. negative 4 and 1 sixth
  5. 916
  6. 9 and 1 sixth
  7. 416
  8. 4 and 1 sixth

The correct answer is 411, which is not explicitly listed but is closest to 416 in terms of options. However, as it cannot be found directly, if we just proceed with the addition, we arrive at 411 which is a positive rational number.

Nonetheless, if you want the closest match provided, consider checking the problem again, as 411 does not match the options.

If the arithmetic was intended to be in a different format or if the options contain a typographical error for expected results, generally the computation leads us to 411. Hence clarification or rechecking the problem prompt could provide further insight.