Order of Operations and Absolute Value

Signed numbers and absolute value

An airplane starts ascending and after 10
minutes it reaches an altitude of 2600
meters. After an hour, it descends 200
meters. Forty minutes later, it descends
another 500 meters. Finally, 2 hours later, it
ascends 300 meters.

What would the plane’s final attitude be
compared to its initial altitude in this
scenario? (Assume the plane’s initial
altitude is 0 meters).

A submarine starts at sea level and
submerges 220 meters in 25 minutes. After
an hour, it ascends 10 meters. An hour after
that it submerges 35 meters. After 20
minutes, it submerges another 17 meters.

What would the submarine’s final depth be
in this case?

Math Response

A hot air balloon rises for fifteen minutes and it reaches an altitude of 55 meters. After two minutes, it descends 2 meters. Thirty minutes later, it ascends 5 meters. After twenty minutes, it descends 20 meters. For the following hour, the hot air balloon descends 65 meters in order to land.

What is the final height of the balloon compared to its initial one?

(Write only the signed number).

Type answer here

Correct Answer: -27

Deg^°

Rad

Be careful with the way the
problem is written!

A certain day starts with a temperature of
14°C at 5 am. After two hours, the
temperature raises by 2.5°C. Three hours
after that, the temperature raises another 3°
C. However, clouds start rolling in after, and
for the next 5 hours, the temperature drops
5°C. For the following 6 hours it rains and
the temperature drops by another 3.5°C.

How much lower will the temperature by at
the end of this scenario, compared to the
start of the day?

In this case, we don’t
write -3°C because the
question is already telling
us the temperature will be
lower.
s

What is we only
care about the
magnitude of the
number?

Introducing the operation called absolute
value.

The absolute value of a number basically
tells us to ignore its sign and just write it as
a positive number.

More formally, if a number is 0 or greater,
the absolute value doesn’t do anything to it.

If a number is less than 0, the absolute
value turns it into a positive number.

Examples of
absolute value

|5|=5

|-3|=3

|4.8|=

|-9.26|=

|12-15|=