Math 7 · Unit 3, Lesson 1: Adding Signed Numbers · Tile 5 of 5
Distance and Real-World Problems
How far apart, and how much it changed
Write it down. Do every change on paper, one line per step. Changing signs in your head is the number one reason for missed problems. If you changed something, it should be on the paper.
Distance between two numbers
To find the distance, subtract and take the absolute value.
The order does not matter: |−6 − 9| = |−15| = 15.
In money: going from owing $6 to having $9 takes $15. $6 to pay off the debt, then $9 more.
The distance between two numbers on the number line is the absolute value of their difference.
Subtract the two numbers, then drop the negative sign if there is one. Distance is never negative.
Change = end − start
The temperature went from −8°F to 5°F. How much did it change?
To find the change, subtract the starting value from the ending value.
Change is where you ended up minus where you started. If the answer is positive, it went up. If it's negative, it went down.
Words that tell you the sign
Positive: have, earn, gain, deposit, above, rise, warmer.
Negative: owe, spend, lose, withdraw, below, fall, colder.
And 0 means something too: breaking even, sea level, or a balance of $0.
Interpret the answer in context.
Say what your answer means in the story. A net worth of negative 6 dollars and 25 cents means you owe 6 dollars and 25 cents.
NC standard: NC.7.NS.1.