Question 14
Use unmarked number lines to evaluate these expressions:
We use a number line for each problem.
Step 1 — Adding a negative number
We start at -125 on the number line. We need to add -30. Adding a negative number means moving left. So, we move 30 steps to the left. We land on -155.
Step 2 — Subtracting a negative number
We start at +105 on the number line. We need to subtract -55. Subtracting a negative number is like adding a positive number. So, this becomes +105 + 55. We move 55 steps to the right. We land on +160.
Step 3 — Subtracting a negative number
We start at +80 on the number line. We need to subtract -150. Subtracting a negative number is like adding a positive number. So, this becomes +80 + 150. We move 150 steps to the right. We land on +230.
Step 4 — Subtracting a negative from a negative
We start at -99 on the number line. We need to subtract -200. Subtracting a negative number is like adding a positive number. So, this becomes -99 + 200. We move 200 steps to the right. First, we move 99 steps right to reach 0. Then, we move 101 more steps right (). We land on +101.
Answer
a. - 125 + (- 30) = - 155 b. + 105 - (- 55) = + 160 c. + 80 - (- 150) = + 230 d. - 99 - (- 200) = + 101
More questions in IT
Can there be a number less than 0? Can you think of any ways to have less than 0 of something?
Observe that some of the floors in the 'Building of Fun' are below the ground. What are the shops that you find on these floors? What is there on the ground floor?
In Bela's Building of Fun, a lift is used to go up and down between the floors. It has two buttons: '+' to go up and '-' to go down. Pressing '+' once goes up one floor (+1), and pressing '-' once goes down one floor (-1).
Q. What do you press to go four floors up? What do you press to go three floors down?
Number all the floors in the Building of Fun.
Start from the Food Court and press +2 in the lift. Where will you reach?
If Basant now presses +4 and then presses -4 in the lift, where will he reach?
Write the inverses of these numbers: +4, -4, -3, 0, +2, -1.
Connect the inverses by drawing lines.
Comparing numbers using floors
Who is on the lowest floor?
Should we write -3 < -4 or -4 < -3?
Evaluate 15 – 5, 100 – 10 and 74 – 34 from this perspective.
In the other exercises that you did above, did you notice that subtracting a negative number was the same as adding the corresponding positive number?
Take a look at the 'infinite lift' above. Does it remind you of a number line? In what ways?
Use unmarked number lines to evaluate these expressions:
Suppose you open a bank account at your local bank with the ₹100 that you had been saving over the last month. Your bank balance therefore, starts at ₹100. Then you make ₹60 at your job the next day and you deposit it in your account. This is shown in your bank passbook as a 'credit'.
Q. Your new bank balance is _______.
Suppose you open a bank account with a starting balance of ₹100 and deposit ₹60 (making the balance ₹160). The next day you pay your electric bill of ₹30 using your bank account. This is shown in your bank passbook as a 'debit'.
Q. Your bank balance is now _______.
Suppose you open a bank account with a starting balance of ₹100, deposit ₹60 (making the balance ₹160), and pay an electric bill of ₹30 (making the balance ₹130). The next day you make a major purchase for your business of ₹150. Again this is shown as a debit.
Q. What is your bank balance now? _______
Is this possible?
Your bank balance was -₹20. You make ₹200 at your business the next day.
Q. What is your balance now?