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Sana says |−9| is less than |7| because −9 is less than 7. Which reply is correct?

Class 6IntegersIntegers
  • AShe is right; |−9| is less than |7|.
  • BShe is right, because absolute value keeps the sign of the number.
  • CShe is wrong; |−9| = 9 and |7| = 7, so |−9| is the greater one.
  • DShe is wrong; the two absolute values are equal.

Step-by-Step Solution

As values, −9 really is less than 7. But the bars change the question to distance from zero: |−9| = 9 and |7| = 7, and 9 > 7. The trap is carrying the comparison of the signed numbers straight through the absolute-value bars instead of comparing the distances.
Answer: C) She is wrong; |−9| = 9 and |7| = 7, so |−9| is the greater one.

Key idea: Comparing integers

On the number line, the integer on the **right** is the **larger** one. So 5 > 2, but also −2 > −5. This often surprises students: even though 5 is bigger than 2, **−5 is smaller than −2**, because −5 is further to the left. Any positive integer is larger than any negative integer, and zero sits between them.

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