Problem on Order of Operations

In mathematics and computer programming, an expression or string of symbols is intended to represent a numerical value; a properly-formed expression may be evaluated in an unambiguous way. But in practice, an expression with multiple terms and operators may be written without parentheses, in which case the intended value of the expression is determined by convention. When a term in the expression is both preceded and followed by an operator such as minus or times, a convention is needed to clarify which operator should be applied first; this rule is known as a precedence rule, or more informally order of operation. From the earliest use of mathematical notation[citation needed], multiplication took precedence over addition, whichever side of a number it appeared on. Thus 3 + 4 × 5 = 5 × 4 + 3 = 23. When numeric and algebraic operations were first introduced, in the 16th and 17th centuries, exponents took precedence over both addition and multiplication, and could be placed only as a superscript to the right of their base. Thus 3 + 5 2 = 28 and 3 × 5 2 = 75. To change the order of operations calculator , a vinculum (an over line or underline) was originally used. Today one uses parentheses (). Thus, if one wants to force addition to precede multiplication, one writes (3 + 4) × 5 = 35.

Let's see an example from algebra answers

Question:-

solve 24-(24+4+2)+2 x (4 x 2)

by using PEMDAS rule

Answer:-

In PEMDAS

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

let's solve the given equation step by step
in the same order ...

24-(30)+2 x (16)

24-32+30

combine the same terms

24+32-30

56 - 30

26 is the answer.

Equation of the line which is passing through two points

Question :-

Find the equation of the line which is passing through two points (-3,7)(5,-1)

Answer:-

We have to use the point formula to find the equation of the line which is similar to midpoint formula

y-y1     x-x1
------ = ------
y2-y1     x2-x1

We have 2 points

( -3 , 7 )  and ( 5 , -1 )
  x1  y1          x2  y2

So the equation is

y-7      x-(-3)
------ = ------
-1-7      5-(-3)

y-7      x+3
------ = ------
-8        8

We can further simplify it by cross multiplication.that comes under indices maths

similarly we can find all points having an x-coordinate of 2 whose distance from the point 2 1 is 5

Maximum and Minimum value of a function

Maximum and minimum value of a function can be determined by simplifying the function with given intervals of time.

Function is a concept which expresses the idea that one quantity completely determines another quantity. Here is one such problem for your practice and understand how the value of function varies with respect to given interval of time.

Question : Find the maximum and minimum value of the function y = x³ - x on the interval [-3,3]

On substituting the value of x as -3 and 3, maxima and minima of function are found.

Solution :

When x = -3

y = x³ - x

= (-3)³ - (-3)

= -27 + 3

= - 24

And when x = 3

y = (3)³ - 3

= 27 - 3

= 24

Hence maximum value of function is 24 and minimum is - 24

Problem on Mixed fractions

Topic:-Mixed fractions

A fraction is a number that can represent part of a whole.
The earliest fractions were reciprocals of integers, symbols representing one half, one third, one quarter, and so on.A much later development were the common or vulgar fractions which are still used today, and which consist of a numerator and a denominator.

In this algebra help ,we are giving an example of mixed fraction problem.
Topic:- Mixed Fractions
Question:-

 
 
  3      10
8--- - 4---- = ? 
  5      15


Answer:-

  3      10
8--- - 4---- = ? 
  5      15

(5*8)+3      (15*4)+10
--------  -  ----------
  5              15

 43          70
------  -  ------- 
  5          15

Multiply the numarator and the 
denominator of the first fraction 
with 3 to make equal denomitors 


   43*3         70
 -------  -   ------
   5*3          15

 
    129       70
   -----  -  -----
    15        15

      129-70
    -----------
        15

          59        14
         ----  or 3------
          15        15

For more help on this ,you can reply me.