The Other Side of Zero — Question 46

Rules for Addition:
1. The sum of two positives is positive.
3 + 4 = 7
2. The sum of two negatives is negative.
(-4) + (-6) = -10
3. To add a positive number and a negative number, subtract the smaller number (without the sign) from the greater number (without the sign), and place the sign of the greater number to obtain the result.
(-3) + 4 = 1
4. The sum of a number and its inverse is zero.
(-4) + 4 = 0
5. The sum of any number and zero is the same number.
(-7) + 0 = -7
Rules for Subtraction:
1. If a smaller positive is subtracted from a larger positive, the result is positive.
9 – 8 = 1
2. If a larger positive is subtracted from a smaller positive, the result is negative.
7 – 8 = -1
3. Subtracting a negative number is the same as adding the corresponding positive number.
3 – (-5) = 3 + 5 = 8
4. Subtracting a number from itself gives zero.
9 – 9 = 0
5. Subtracting zero from a number gives the same number.
8 – 0 = 8
Intext Questions
Can there be a number less than 0? Can you think of any way to have less than 0 of something?
(Page No. 243)
Solution:
Negative Numbers: Less than zero.
Yes, there can be numbers less than 0. These numbers are called negative numbers.
[While it might seem impossible to have less than nothing, but negative numbers are used in many real-world situations.]
10.1 Bela’s Building of Fun
What do you press to go four floors up? What do you press to go three floors down?
(Page No. 243)
Solution:
If you press the ‘+’ button once then you will go up one floor and if you press the ‘-‘ button once then you will go down 1 floor.
Hence to go four floors up you must press the ‘+’ button four times which we write as + + + + or +4.
Now to go three floors down you must press the button three times which we write as – – – or -3.
Number all the Floors in the Building of Fun.
(Page 244)
Solution:
Let’s mark numbers on all the Floors in the Building of Fun.
In addition to Keep Track of Movement
Start from the Food Court and press +2 in the lift Where will you reach? _________
(Page No. 245)
Solution:
Here, Target floor = Starting floor + Movement
∴ The starting floor is +1 (Food Court) and the number of button presses is +2.
Therefore, floor = starting floor + movement
= (+1) + (+2)
= +3 (Book Store)
Back to Zero!
Write the inverses of these numbers:
(Page No. 246)
+4, -4, -3, 0, +2, -1
Solution:
The additive inverse of +4 = -(+4) = -4.
The additive inverse of -4 = -(-4) = +4.
The additive inverse of -3 = -(-3) = +3.
The additive inverse of zero (0) is zero itself.
The additive inverse of +2 = -(+2) = -2.
The additive inverse of -1 = -(-1) = +1.
Connect the inverses by drawing lines.
(Page No. 246)
Solution:
Comparing Numbers using Floors
(Page No. 246)
Who is on the lowest floor?
1. Jay is in the Art Centre. So, he is on Floor +2.
2. Asin is in the Sports Centre. So, she is on Floor ______.
3. Binnu is in the Cinema Centre. So, she is on Floor ______.
4. Aman is in the toy shop. So, he is on ______.
Solution:
1. Jay is in the Art Centre. So, he is on Floor+2.
2. Asin is in the Sports Centre. So, she is on Floor +5.
3. Binnu is in the Cinema Centre. So, she is on Floor -3.
4. Aman is in the toy shop. So, he is on Floor -1.
Evaluate 15 – 5, 100 – 10, and 74 – 34 from this perspective.
(Page No. 248)
Solution:
(a) There are 15 pens in the shop. I take away 5 pens. How many pens are left in the shop?
Then 15 – 5 = 10
(b) There are loo books on the shelf. I take away 10 books. How many are left on the shelf?
Then 100 – 10 = 90
(c) There are 74 books on the shelf. I take away 34 books. How many are left on the shelf?
Then 74 – 34 = 40
Adding, Subtracting, and Comparing any Numbers
Try evaluating the following expressions by similarly drawing or imagining a suitable lift:
(Page No. 251)
(a) -125 + (-30)
(b) +105 – (-55)
(c) +105 + (+55)
(d) +80 – (-150)
(e) +80 + (+150)
(f) -99 – (-200)
(g) -99 + (+200)
(h) +1500 – (-1500)
Solution:
(a) -125 + (-30) = -125 – 30 = -155
(b) +105 – (-55) = 105 + 55 = +160
(c) +105 + (+55) = 105 + 55 = +160
(d) +80 – (-150) = 80 + 150 = +230
(e) +80 + (+150) = 80 + 150 = +230
(f) -99 – (-200) = -99 + 200 = +101
(g) -99 + (+200) = -99 + 200 = +101
(h) +1500 – (-1500) = +1500 + 1500 = 3,000
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?
(Page No. 252)
Solution:
Subtracting a number is the same as adding it’s opposite. So subtracting a positive number is like adding a negative number – you move to the left on the number line. Subtracting a negative number is like adding a positive number – you move to the right on the number line.
For example: Subtract -2 – (-3)
Start at -2 and move 3 units to the right.
So, -2 – (-3) = +1
Take a look at the ‘infinite lift’ above. Does it remind you of a number line? In what ways?
(Page No. 252)
Solution:
A number line is a way of representing numbers visually on a straight line. For instance, the number line has arrows at the end to represent this, idea of having no bounds. The symbol used to represent infinity is ∞.
Using the Unmarked Number Line to Add and Subtract
Use unmarked number lines to evaluate these expressions:
(Page No. 255)
(a) -125 + (-30) = _________
(b) +105 – (-55) = _________
(c) +80 – (-150) = _________
(d) -99 – (-200) = _________
Solution:
(a) -125 + (-30)
Adding two negative numbers on the number line
∴ -125 + (-30) = – 125 – 30 = -155
(b) +105 – (-55)
Subtracting a negative number is the same as adding the positive counterpart.
∴ +105 – (-55) = 105 + 55 = 160
(c) +80 – (-150)
Subtracting a negative number is the same as adding the positive counterpart.
∴ +80 – (-150) = 80 + 150 = 230
(d) -99 – (-200)
Subtracting a negative number is the same as adding the positive counterpart.
∴ -99 – (-200) = -99 + 200 = 101