Solving Problems with Negative Numbers

Solving Problems with Negative Numbers exercise

• Can you complete the number line?

  Hints

  Remember, negative numbers have a minus sign ($-$) in front of them and are less than zero.

  Use the numbers already filled in to help you.

  $-7$ is less than $-6$ so it will come before $-6$ on the number line.

  Solution

  Here we can see the completed number line.

• Where is Lucy?

  Hints

  Lucy is currently on floor 2 and she is travelling down so the number of the floor will be less than than 2.

  We need to solve 2 - 4 to find the new floor.

  Count down four times from 2 to find the new floor.

  Solution

  Lucy is now on - 2.

  Lucy started on floor 2 and travelled four floors down so we needed to solve 2 - 4. We can see on the number line above if we jump four times backwards from 2, we get to - 2.

• How much money is in Bill's bank account?

  Hints

  To solve this problem we start at $-12$. What are we adding to $-12$?

  We need to solve $-12 + 15$.

  The answer is a positive number.

  Solution

  Bill is in his overdraft and currently has $-£12$ in his bank account. For his birthday, his Grandma gave him $£15$. Now Bill has $\textbf£\textbf3$ in his bank account.

  $-12 + 15 = 3$

• What is the temperature?

  Hints

  If the temperature is warmer, we need to add or count forwards.

  If the temperature is colder we need to subtract or count backwards.

  We know that Tuesday is $5$ degrees warmer than Monday so we need to add $5$ to $-3$.

  $-3$ + $5$ =

  Use the number line to help you count forwards from $-3$.

  Solution

  Monday: $-3$ °C

  Tuesday: $2$ °C

  Wednesday: $-1$ °C

  Thursday: $6$ °C

  Friday: $8$ °C

  Saturday: $2$ °C

  Sunday: $0$ °C

  __________________________________________

  • Tuesday: $-3$ + $5$ = $2$
  • Wednesday: $2$ - $3$ = $-1$
  • Friday: $2$ + $6$ = $8$
  • Sunday: $-1$ + $1$ = $0$

• What do you know about negative numbers?

  Hints

  Here are some negative numbers:

  • $-4$
  • $-7$
  • $-110$
  • $-20,341$

  On this number line we can see the negative numbers to the left of zero which means they are smaller than zero.

  There are two correct answers.

  Solution

  The true statements are:

  • Negative numbers are less than zero.
  • Negative numbers are represented with a minus symbol (-) in front of them.

• Can you solve the problems?

  Hints

  To find the level Axel and Tank are now at, add $43$ to $35$.

  To find the average temperature in summer, add $33$ to $-11$.

  To find how many floors Randall needs to travel past, find the difference between $-5$ and $37$.

  Solution

  Axel and Tank are in their submarine. They explored the ocean at $35$ m below sea level. They have now descended another $43$ m and are at $\textbf7\textbf8$ m below sea level.

  • To solve this problem we need to add $35 + 43 = 78$. We know they are below sea level so we can say they are $78$ m below sea level now.

  ${}$

  In a country, the average temperature in winter is $-11$ degrees and the average temperature in summer is $\textbf2\textbf2$ degrees. The difference between these temperatures is $33$ degrees.

  • To solve this problem, we needed to add $33$ to $-11$ which equals $22$.

  ${}$

  Randall lives on floor $37$ in a skyscraper. The gym is on floor $-5$ so Randall needs to travel down $\textbf4\textbf2$ floors to get there.

  • To solve this problem, we need to find the difference between $37$ and $-5$. To do this, we can solve $37 - -5 = 42$.