Welcome to three examples of application problems that involve comparing integers.
For the first example, liquid hydrogen
evaporates at about negative 429
degrees Fahrenheit. Liquid nitrogen
evaporates at about negative 301
degrees Fahrenheit. Which liquid has a
lower evaporating temperature? To answer the
question need to determine which of
these temperatures is lower or less. To
do this, let's plot these values on the
number line. Notice both integers are
negative and therefore both will be to
the left of zero. Let's scale the number
line by hundreds to the left of zero. So
we have negative 100 negative 200
negative 300 negative 400 and negative
500. And now let's plot negative 429, which
is 429 units of the
left of 0, which would be approximately
here.
Next we need to plot negative 301, which is 301 units to the left of 0, which is
approximately here. We're asked which liquid has a lower evaporating temperature.
Looking at the number line, the number on the left is less than the number on the
right. And therefore negative 429 is less
than negative 301. Because the question
is asking which liquid has a lower
evaporating temperature, we're looking
for the liquid that has an evaporating
temperature of negative 429
degrees Fahrenheit, which is liquid
hydrogen.
When comparing numbers on
the number line, the smaller number or least number is always on the left, the
greater number or larger number is
always on the right.  Next on a cold
winter day the temperature in town A was
negative 5 degrees fahrenheit and the
temperature in town B was negative
three degrees Fahrenheit. Which town was
warmer?
Let's plot negative 5 negative and negative 3 on the number line. We'll go ahead and scale the
number line by ones this time. To the  left of zero we have negative 1 negative 2
negative 3 negative 4 and negative 5. So
negative 5 is located five units to the
left of zero, here. Negative 3 is located
three units to the left of 0, which is
here. Now this question asks which town
was warme,r which means me to identify
the greater or larger value. Because negative 3 is to the right of negative 5,
this tells us negative 3 is greater than
negative 5. And because the temperature
of negative 3 corresponds to town B. Town B is warmer than town A. Now for the last
example, after playing nine holes of golf
Jerry's score was four under par or
negative four, Joyce's score was 3 over
par which is positive 3, and Jack's score
was five-under-par which is negative 5.
Who had the lowest score?
Let's pop these three scores on the
number line. We'll go ahead and scale to
the right and left of zero by ones. So to
the right of 0 we have one two three
four five. To the left of zero we have
negative 1 negative 2 negative 3
negative 4 and negative 5. Now plotting
the scores,  negative 4 is 4 units to the
left of 0 which is here.  Positive 3 is
located three times to the right of 0
here. And negative 5 is located five
units to the left of 0 which is here.
We're looking for the lowest score or the
least of these three values,
which is the value that is furthest to
the left, which is negative 5. Negative 5
is the least or lowest score and jack is
the one that was five-under-par or had a
score of negative 5.
So the answer to the question who had the lowest score is Jack.
I hope you found this helpful.
