Integers Test - 3

Jatin scored 32.

Correct answer = 10.

Let x be the number of questions which Jatin answered incorrectly.

According to the question,

10 × 6 + x × (-3) = 33
60 - 3x = 33
-3x = 33 - 60
-3x = -27
x = 9
Vinay scored 6.

Correct answer = 9

Let y be the number of questions incorrectly answered by Vinay.
According to the question,
9 × 6 + y × (-3) = 6
54 - 3y = 6
3y = 54 - 6
y = 16

Total of integers = -15 + 6 + ( - 11) + ( - 16) + 10 + 9 + 18

= -15 -11 -16 + 6 + 10 + 9 + 18

= -42 + 43

= 1

The temperature at 5 p.m = 24^oC
Reduction every hour = 2^oC

Total drop in temperature in 6 hours = 2 x 6 = 12^oC
Therefore, temperature at 11 p.m. = 24 - 6 × 2 = 24 - 12 = 12^oC

The correct answer is: 1 - c, 2 - a, 3 - d, 4 - b

1. The commutative property says it doesn't matter which order you add or multiply two numbers in: a x b = b x a

2. Any two negative numbers, e.g. -2 x -3 = 6, will give a positive number as a result.

3. The distributive property tells you what happens if you add two numbers and multiply the sum by another number.
This formula is a x (b + c) = a x b + a x c.

4. -5 x -5 x -5 = -125, so the answer is negative.

(i) When even number of negative integers are multiplied the result is always positive.
(ii) When an equation is multiplied by same number then there is no effect on the equation.

This is also true for adding and subtracting the same number from both the sides.

(iii) Associative Property: When three or more numbers are added, the sum is the same regardless of the grouping of the addends. For example, (2 + 3) + 4 = 2 + (3 + 4)
(iv) Addition and subtraction can be done using number line.

(i) 11 × (-5) + 24 ÷ 6 _____ 22 ÷ 2 + 5 × (-3)
= -55 + 4 _____11 - 15
= -51 < -4

(ii) 25 × 3 - 2 × 15 _____ 12 × 3 - 27 ÷ 3
= 75 - 30 _______ 36 - 9
= 45 >27

(iii) (78 ÷ 3) × 5 × 0 ______ 12 × 0 × 3 × 6
= 0