2.1: Which One Doesn’t Belong: Arrows
Which pair of arrows doesn't belong?
Let's add signed numbers.
Which pair of arrows doesn't belong?
Complete the table and draw a number line diagram for each situation.
start ($^\circ\text{C}$) | change ($^\circ\text{C}$) | final ($^\circ \text{C}$) | addition equation | |
---|---|---|---|---|
a | +40 | 10 degrees warmer | +50 | $40 + 10 = 50$ |
b | +40 | 5 degrees colder | ||
c | +40 | 30 degrees colder | ||
d | +40 | 40 degrees colder | ||
e | +40 | 50 degrees colder |
Complete the table and draw a number line diagram for each situation.
start ($^\circ\text{C}$) | change ($^\circ\text{C}$) | final ($^\circ\text{C}$) | addition equation | |
---|---|---|---|---|
a | -20 | 30 degrees warmer | ||
b | -20 | 35 degrees warmer | ||
c | -20 | 15 degrees warmer | ||
d | -20 | 15 degrees colder |
For the numbers $a$ and $b$ represented in the figure, which expression is equal to $|a+b|$?
$|a|+|b|$
$|a|-|b|$
$|b|-|a|$
If it is $42^\circ$ outside and the temperature increases by $7^\circ$, then we can add the initial temperature and the change in temperature to find the final temperature.
$42 + 7 = 49$
If the temperature decreases by $7^\circ$, we can either subtract $42-7$ to find the final temperature, or we can think of the change as $\text-7^\circ$. Again, we can add to find the final temperature.
$42 + (\text-7) = 35$
In general, we can represent a change in temperature with a positive number if it increases and a negative number if it decreases. Then we can find the final temperature by adding the initial temperature and the change. If it is $3^\circ$ and the temperature decreases by $7^\circ$, then we can add to find the final temperature.
$3+ (\text-7) = \text-4$
We can represent signed numbers with arrows on a number line. We can represent positive numbers with arrows that start at 0 and points to the right. For example, this arrow represents +10 because it is 10 units long and it points to the right.
We can represent negative numbers with arrows that start at 0 and point to the left. For example, this arrow represents -4 because it is 4 units long and it points to the left.
To represent addition, we put the arrows “tip to tail.” So this diagram represents $3+5$:
And this represents $3 + (\text-5)$: