Math Fundamentals

According to the BODMAS rule, if an expression contains brackets ((), {}, []) we have first to solve or simplify the bracket followed by ‘order’ (that means powers and roots, etc.), then division, multiplication, addition and subtraction from left to right so ,
= 8 + 5 - (7 x 0) + (12 -12 ) X 2 - 10
= 13 -0 + (0) X 2 - 10
= 13 - 0 + 0 - 10
= 3

= (-4 / -2 ) + ( 6/3) + ( 8/-2)
As (-) sign divided by (- ) gives you (+) ,so
= (2) + (2) + (-4)
As we know (-) multiply by (+) will become (-) ,so
= 4 - 4
= 0

LHS = - 4 and RHS= 2
As know that all -ve numbers are smaller than zero so -4 is smaller than 2
So statement -4 > 2 is false

LHS =0.5 and RHS= 2
As know that 0.5 is half of number 1 , hence 0.5 is smaller than 2 also
So statement 0.5 > 2 is false

Factors of -7 = -1 X 7 or 1 X - 7

= - 2 + 2 ÷ 4
= - 2 + 2/4
= - 2 + 1/2
Take L.C.M and simplify
= (- 4+ 1)/2
= - 3/2

= - 3 ÷ (1 /0.4)
= - 3 X 0.4
= - 1.2

= - 24 ÷ 0.8 X 1.6 -7
= - 30 X 1.6 - 7
= - 48 -7
= - 55

As we know HCF (a, b) × LCM (a, b) = a × b
After substituting the values we get, 8 × 96 = 24 × b
Solve for b
b = 32

91858248 will be divisble by 12 if it is divisble by its each factors like 2, 3, 4 and 6.
We can easily see that 91858248 is divisble by 4 as last two digit (48) are divisible by 4 .
This numbers also divisible by 3 as sum of all the digits is divisble by 3 (9+1+8+5+8+2+4+8=45)
As it is divisble by 3 and 4 both, so it will be divisble by 2, 4 and 6 also hence number will be divisble by 12.

0.6 = 6/10
if denominator has to be 75 then multiply both the side by 75
so, (6/10) X (75/75)
simplify it further
= 45/75

= 7/8
Solve it further
= 0.875
So, both are equal

The smallest number that is exactly divisble by each of the given numbers is their L.C.M
Find the L.C.M of 8 , 12 ,16 , 24 and 36
8 = 2 x 2 x 2
12 = 2 x 2 x 3
16 =2 x 2 x 2 X 2
24 = 2 x 2 x 2 X 3
36 = 2 x 2 x 3 X 3
Remove common factors and multiple remaining digits so L.C.M is 144.

Step 1: First, we need to simplify the innermost bracket, (1 + 20 - 16 ÷ 4²) ÷ {2² + 12 ÷ 2}
Step 2: Now we have to evaluate exponents, (1 + 20 - 16 ÷ 16) ÷ {4 + 12 ÷ 2}
Step 3: Now, we need to divide 16 by 16 and 12 by 2 inside the brackets, and we get, (1 + 20 - 1) ÷ {4 + 6}
Step 4: Add 1 to 20 and 4 to 6, (21 - 1) ÷ 10
Step 5: Subtract 1 from 21 to solve the bracket, we get, 20 ÷ 10
Step 6: Divide 20 by 10 to get the final answer, we get 2.
So, (1 + 20 - 16 ÷ 4²) ÷ {(5 - 3)² + 12 ÷ 2} = 2

We have to find two numbers that are divisible by 3 and 4 and which are below 30.
so these numbers are 12 and 24
now just add 1 to each so that they leave 1 as reminder when divided.
so 13, 25 are the numbers.