Negative numbers and absolute value

Advanced Math 6 · Unit 4 · integers-absolute-value · Teacher edition

integers-absolute-value

Name ______________________________Date ______________

1.
A submarine is at an elevation of $-250$ metres. How far is it from the surface, in metres?
Answer: ______________
2.
Which list is in order from least to greatest?
1. (A)
  $-\dfrac{3}{2},\ -2,\ -2.5,\ 0,\ \dfrac{1}{2}$
2. (B)
  $0,\ \dfrac{1}{2},\ -\dfrac{3}{2},\ -2,\ -2.5$
3. (C)
  $-2.5,\ -2,\ -\dfrac{3}{2},\ 0,\ \dfrac{1}{2}$
4. (D)
  $-2,\ -2.5,\ -\dfrac{3}{2},\ 0,\ \dfrac{1}{2}$
3.
At 6 a.m. the temperature was $-7^\circ$ C. At noon it was $-3^\circ$ C. Which statement is correct?
1. (A)
  $-7 > -3$ , so 6 a.m. was warmer.
2. (B)
  $-3 > -7$ , so noon was warmer.
3. (C)
  $\lvert -7 \rvert < \lvert -3 \rvert$ , so 6 a.m. was warmer.
4. (D)
  Both are below $0$ , so they are equally cold.
4.
Compute $\lvert -4 \rvert + \lvert 3 \rvert - \lvert -2 \rvert$ .
Answer: ______________
5.
On a number line, point $A$ is at $-6$ and point $B$ is at $-1$ . How many units apart are $A$ and $B$ ?
Answer: ______________

Answer key — Negative numbers and absolute value

1.
250integers-absolute-value-01
$\lvert -250 \rvert = \mathbf{250}$ metres below the surface. The sign says below; the absolute value says how far.
2.
(C)
$-2.5,\ -2,\ -\dfrac{3}{2},\ 0,\ \dfrac{1}{2}$
integers-absolute-value-02
Least to greatest: $-2.5 < -2 < -1.5 < 0 < 0.5$ , so $\mathbf{-2.5,\ -2,\ -\tfrac{3}{2},\ 0,\ \tfrac{1}{2}}$ . The first choice lists the negatives by absolute value, smallest first — the most common mistake.
3.
(B)
$-3 > -7$ , so noon was warmer.
integers-absolute-value-03
$-3$ is to the right of $-7$ , so $-3 > -7$ : noon was warmer. The first choice compares the absolute values $7 > 3$ and gets the direction backwards.
4.
5integers-absolute-value-04
$4 + 3 - 2 = \mathbf{5}$ . A student who writes $\lvert -4 \rvert = -4$ gets $-4 + 3 + 2 = 1$ ; absolute value is never negative.
5.
5integers-absolute-value-05
From $-6$ to $-1$ is $5$ steps to the right, so the distance is $\mathbf{5}$ . (Equivalently $\lvert -1 - (-6) \rvert = \lvert 5 \rvert = 5$ ; subtraction of negatives is formalized in Math 7, but counting on the line works now.)