Question

it was -5 °c in copenhagen and -12 °c in oslo. which city was colder?

a. a fish is 12 meters below the surface of the ocean. what is its elevation?

b. a sea bird is 28 meters above the surface of the ocean. what is its elevation?

c. if the bird is directly above the fish, how far apart are they?

compare the numbers in each statement using >, =, or <.

a. 3 ___ -3

b. 12 ___ 24

c. -12 ___ -24

d. 5 ___ -(-5)

e. 7.2 ___ 7

f. -7.2 ___ -7

g. -1.5 ___ $\frac{-3}{2}$

h. $\frac{-4}{5}$ ___ $\frac{-5}{4}$

i. $\frac{-3}{5}$ ___ $\frac{-6}{10}$

j. $\frac{-2}{3}$ ___ $\frac{1}{3}$

Explanation:

Step1: Compare city temperatures

$-12 < -5$, so Oslo is colder.

Step2: Find fish elevation

Surface = 0, below = negative: $0 - 12 = -12$

Step3: Find bird elevation

Surface = 0, above = positive: $0 + 28 = 28$

Step4: Calculate distance between them

$28 - (-12) = 28 + 12 = 40$

Step5: Compare positive/negative numbers

Positive > negative: $3 > -3$

Step6: Compare positive integers

Smaller < larger: $12 < 24$

Step7: Compare negative integers

Closer to 0 > farther: $-12 > -24$

Step8: Simplify and compare

$-(-5)=5$, so $5 = 5$

Step9: Compare decimal and integer

$7.2 > 7$

Step10: Compare negative decimals

Farther from 0 < closer: $-7.2 < -7$

Step11: Convert fraction to decimal

$\frac{-3}{2}=-1.5$, so $-1.5 = -1.5$

Step12: Compare negative fractions

$\frac{-4}{5}=-0.8$, $\frac{-5}{4}=-1.2$, so $-0.8 > -1.2$

Step13: Simplify fraction

$\frac{-6}{10}=\frac{-3}{5}$, so $\frac{-3}{5} = \frac{-3}{5}$

Step14: Compare negative and positive

Negative < positive: $\frac{-2}{3} < \frac{1}{3}$

Answer:

Oslo was colder.
a. -12 meters
b. 28 meters
c. 40 meters
a. $3 > -3$
b. $12 < 24$
c. $-12 > -24$
d. $5 = -(-5)$
e. $7.2 > 7$
f. $-7.2 < -7$
g. $-1.5 = \frac{-3}{2}$
h. $\frac{-4}{5} > \frac{-5}{4}$
i. $\frac{-3}{5} = \frac{-6}{10}$
j. $\frac{-2}{3} < \frac{1}{3}$