MATHS 3 Marks Question

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.]

self

Let’s try to create an expression that gets as close to (-30) as possible using the given cards: (+1, +7, +18, -5, -2, -9).
One possible expression is: (-9) + (-5) + (-2) + (-18) + (+1)
Let’s calculate the value step by step:
1. (-9) + (-5) = -14
2. -14 + (-2) = -16
3. -16 + (-18) = -34
4. -34 + (+1) = -33
Hence, the value of this expression is (-33), which is quite close to (-30).

The numbers to the right of 12 are decreasing as per the following rule:
12 to 6 = -6
6 to 1 = -5
1 to -3 = -4
-3 to -6 = -3
So, further, they should decrease as follows:
-6 – 2 = -8
-8 – 1 = -9
Now, the numbers to the left of 12 should each increase as follows:
12 + 7 = 19
19 + 8 = 27
27, 19, 12, 6, 1, (-3), (-6), -8, -9, -9

Identify the Differences Between Consecutive Terms:
3 to 4: +1
4 to 2: -2
2 to 5: +3
5 to 1: -4
1 to 6: +5
6 to 0: -6
0 to 7: +7
So, now 7 – 8 = -1
-1 + 9 = 8
8 – 10 = -2
Therefore, the required numbers are -1, 8 and -2
3, 4, 2, 5, 1, 6, 0, 7, -1, 8, -2

(a) 1874
(b) 176 BCE
(c) 360 BCE

(a) -6, -5, -4, -3, -2, -1
(b) -3, -2, -1, 0, 1, 2, 3
(c) -14, -13, -12, -11, -10, -9
(d) -29, -28, -27, -26, -25, -24

Here’s the puzzle:

Border sum: 2

There are multiple ways to fill the last grid with a border sum of -4, here are two examples:

The lowest point on land with respect to sea level is the shoreline of the Dead Sea, which is approximately 1,410 feet (430 metres) below sea level. In terms of height, we can write it as approximately -1,410 feet or -430 metres.
But the lowest point on the ocean floor is the Challenger Deep in the Mariana Trench, which is about 36,070 feet or 10,994 metres below sea level. In terms of height, we can write it as -36070 feet or -10994 metres.

A = +1500 m
B = -500 m
C = +300 m
D = -1200 m
E = +1200 m
F = -200 m
G = +100 m

Consider ‘credits’ as positive numbers and ‘debits’ as negative numbers.
Total credits = +256
Total debits = (-1) + (-2) + (-4) + (-8) + (-16) + (-32) + (-64)+ (-128) =-255
Account balance = Total credits + Total debits = (+256) + (-255) = +1
Hence, the account balance is ₹ 1.

Here, Credits = ₹ 30 + ₹ 40 + ₹ 50 = ₹ 120
and Debits = ₹ 40 + ₹ 50 + ₹ 60 = ₹ 150
∴ Balance = Credits – Debits
= ₹ 120 – ₹ 150
= – ₹30
Therefore, your bank account balance is – ₹ 30.

You have – 3 (3 negative tokens). Subtracting + 5 means you need to remove 5 positive tokens.
Add 5 zero pairs to introduce 5 positive tokens that can be removed.
Remove the 5 positive tokens.
After removing these, you are left with 3 original negative tokens and 5 additional negative tokens.
3 original negative tokens + 5 additional negative tokens
= 8 negative tokens
So, the result is – 8 and you needed to add 5 zero pairs to perform the subtraction.
– 3 – (+ 5) = – 8

Floor B is 9 floors lower than Floor 0.
So, the number of Floor B is -9.
Floor C is 6 floors lower than Floor 0.
So, the number of Floor C is -6.
Floor F is 2 floors higher than Floor 0.
So, the number of Floor F is +2.
Floor G is 6 floors higher than Floor 0.
So, the number of Floor G is +6.
Floor H is 11 floors higher than Floor 0.
So, the number of Floor H is +11.

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.

Let’s mark numbers on all the Floors in the Building of Fun.

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

(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

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.

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)