Evaluate , and from this perspective.

Understand the Question Subtraction represents the operation of taking away a certain number of items from a total collection to find out how many remain. We can evaluate each difference directly or by breaking numbers into their tens and ones place values. Part (i) Evaluate Step 1 · Subtract 5 from 15 Taking away from Answer > (i) Part (ii) Evaluate Step 1 · Subtract 10 from 100 Taking away from Answer > (ii) Part (iii) Evaluate Step 1 · Subtract 34 from 74 by Place Value Separating into tens and ones Answer > (iii) Common Mistakes Place Value Alignment: Forgetting to group tens and ones properly when decomposing numbers like and . Order of Subtraction: Subtraction is not commutative; .

The Other Side of Zero | IT

Question 11

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

Solution

Understand the Question

Subtraction represents the operation of taking away a certain number of items from a total collection to find out how many remain.
We can evaluate each difference directly or by breaking numbers into their tens and ones place values.

(i) Evaluate $15 - 5$

Step 1 · Subtract 5 from 15

Diagram 1

Taking away $5$ from $15$ $15 - 5 = 10$

Answer

(i) $10$

(ii) Evaluate $100 - 10$

Step 1 · Subtract 10 from 100

Diagram 2

Taking away $10$ from $100$ $100 - 10 = 90$

Answer

(ii) $90$

(iii) Evaluate $74 - 34$

Step 1 · Subtract 34 from 74 by Place Value

Diagram 3

Separating into tens and ones

\begin{aligned} 74 - 34 &= (70 + 4) - (30 + 4) \\[0.6em] &= (70 - 30) + (4 - 4) \\[0.6em] &= 40 + 0 \\[0.6em] &= 40 \end{aligned}

Answer

(iii) $40$

Common Mistakes

Place Value Alignment: Forgetting to group tens and ones properly when decomposing numbers like $74$ and $34$ .
Order of Subtraction: Subtraction is not commutative; $15 - 5 \neq 5 - 15$ .

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?