The Other Side of Zero | IT

Question 8

Connect the inverses by drawing lines.

Solution

Understand the Question

The additive inverse (or opposite) of a number is the number that, when added to it, gives a sum of $0$ .
For any integer $a$ , its additive inverse is $-a$ because: $a + (-a) = 0$
To connect the inverses, each positive integer is paired with the negative integer of the same magnitude, and vice versa.

Step 1 · Find the Inverse of $+5$

The additive inverse of $+5$ is $-5$ because: $+5 + (-5) = 0$ Diagram 1

Therefore, $+5$ connects to $-5$ .

Step 2 · Find the Inverse of $-7$

The additive inverse of $-7$ is $+7$ because: $-7 + (+7) = 0$ Diagram 2

Therefore, $-7$ connects to $+7$ .

Step 3 · Find the Inverse of $-8$

The additive inverse of $-8$ is $+8$ because: $-8 + (+8) = 0$ Diagram 3

Therefore, $-8$ connects to $+8$ .

Step 4 · Find the Inverse of $+9$

The additive inverse of $+9$ is $-9$ because: $+9 + (-9) = 0$ Diagram 4

Therefore, $+9$ connects to $-9$ .

Answer

The connected pairs of inverses are:

$+5$ connects to $-5$
$-7$ connects to $+7$
$-8$ connects to $+8$
$+9$ connects to $-9$

Common Mistakes

Confusing Additive with Multiplicative Inverse: The additive inverse changes the sign (e.g., $+5 \to -5$ , sum $= 0$ ), whereas the multiplicative inverse is the reciprocal (e.g., $5 \to \dfrac{1}{5}$ , product $= 1$ ).
Connecting Numbers with the Same Sign: Pairing $+5$ with $+5$ instead of inverting its sign to $-5$ .

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?

Q10

Should we write $-3 < -4$ or $-4 < -3$ ?

Q11

Evaluate $15 - 5$ , $100 - 10$ and $74 - 34$ from this perspective.

Q12

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?

Q13

Take a look at the 'infinite lift' above. Does it remind you of a number line? In what ways?

Q14

Use unmarked number lines to evaluate these expressions:

Q15

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 _______.

Q16

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 _______.

Q17

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?

Q18

Your bank balance was $-\text{₹}20$ . You make $\text{₹}200$ at your business the next day.

Q. What is your balance now?