Add Rational Numbers Quick Check

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Question
Use the image to answer the question.

Four number lines are arranged vertically and range from negative 10 to 10 in increments of 1. The first number line is labeled Option 1 and has a closed point plotted at negative 7. An arrow extends right from the closed point to 8. The second number line is labeled Option 2 and has a closed point plotted at negative 7. An arrow extends right from the closed point to 1. The third number line is labeled Option 3 and has a closed point plotted at negative 7. An arrow extends right from the closed point to negative 1. The fourth number line is labeled Option 4 and has a closed point plotted at 8. An arrow extends left from the closed point to negative 7.

Which number line correctly represents −7+8 ?

(1 point)
Responses

Option 2
Option 2

Option 1
Option 1

Option 4
Option 4

Option 3
Option 3

5 answers

To solve the problem of representing the sum \(-7 + 8\), we first need to calculate the result:

\[ -7 + 8 = 1 \]

Next, we look at the provided number lines to find the correct representation for this sum.

  • Option 1 shows the interval from \(-7\) to \(8\) which represents adding a larger positive number. At the end point of the arrow, it goes to \(8\); however, \(-7 + 8\) equals \(1\), not \(8\).

  • Option 2 shows the interval from \(-7\) to \(1\), which correctly represents \(-7 + 8\) because it includes the closed point at \(-7\) and extends to \(1\).

  • Option 3 shows the interval from \(-7\) to \(-1\), which does not represent \(-7 + 8\).

  • Option 4 shows the interval from \(8\) to \(-7\), which is not relevant for calculating \(-7 + 8\).

Based on this analysis, the correct option that represents \(-7 + 8\) is:

Option 2.

what the correct answer

The correct answer is Option 2. This option correctly represents the sum \(-7 + 8\), which equals \(1\).

are you sure

Yes, I am sure.

To clarify the reasoning:

  1. The expression you're evaluating is \(-7 + 8\), which equals \(1\).
  2. Option 2 represents the action of moving from \(-7\) to \(1\), which aligns with the result of the operation.
  3. The other options either do not reach \(1\) or represent sums that do not correspond to \(-7 + 8\).

Therefore, the correct answer is indeed Option 2.