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PROVE bracket ( ) can be replaced with ×?

Topic Review

Maths Is The Study Of Balance

You will probably think what does this guy mean my maths is the study of balance. Let take a look at weighing scale
Weighing scale
Weighing scale is a good example of left-hand side {LHS} and right-hand side {RHS} in our day to day mathematics. it also explains the value at the LHS is equal to the value at the RHS to make it stay balanced.
we have
  • \( x^a * x^b =  x^{ab} \) example \( 2^2 * 2^3 = 2^{2+3} = 2^5 = 32 \)
  • to bring our answer back to the first step we need to use this \( x^{ab} = x^a * x^b \) example \( 32 = 2^5 = 2^{2+3} = 2^2 * 2^3 \) which tells you ether you use the \( x^a * x^b =  x^{ab} \) or \( x^{ab} = x^a * x^b \) you are still use the rule of indices only in the reverse way

Word Example

I will take you back to you days in school maths

1.  From the days of addition and subtraction we have

     2 + 3 = ?    ans = 5
     3 - 1 = ?     ans = 2

2.  To the days of LHS = RHS

     2 + [  ]  = 5      [  ] = box
     2 + [3] = 5
here we have the LHS and RHS to enable you get the value to be input in the box
formed of question with 5
    5 = 2 + 3   where they replace 3 with box

3.  In the days of multiplication LHS = RHS

     2 * [  ] = 6     or     2[  ] = 6
     2 * [3] = 6     or     2[3] = 6
Form question with 6
     6 = 2 * 3      or replace the box      {where they replace 3 with box}

4.   In the days of unknown and variable LHS = RHS

     6 = 3y   divide both sides by 3
     \( \require{cancel} \frac{ \cancel 6^2}{ \cancel 3_1 } = \frac{ ^1 \cancel 3y}{ \cancel 3_1 } \)
     y = 2
form question with 6
     6 = 3 * 2     where they replace 2 with y

5.   In the days of adding & subtraction from LHS to RHS 

    2x + 2 = 8   subtract -2 from both side
    2x + 2 - 2 = 8 - 2
    2x = 6
   \( \require{cancel}  \frac{ ^1 \cancel 2x}{ \cancel 2_1 } = \frac{ \cancel 6^3}{ \cancel 2_1 } \)
    x = 3

6.  Multiplication and division from LHS to RHS

\begin{align} \require{cancel} 2x \div 2 & = 3 \\ \frac{ ^1 \cancel 2x }{ \cancel 2_1 } & = \frac{ ^3 \cancel 6 }{ \cancel 2_1 } \\ x & = 3 \end{align}
form question with 3
\begin{align} \require{cancel} 3 & = 6 \div 2 \\ & = 2(3) \div 2 \\ & = 2x \div 2 \end{align} same to \begin{align} \require{cancel} 2 \div 2x & = 3 \\ \frac{ ^1 \cancel 2}{  \cancel 2_1x } & = 3 \\ \frac{1}{x} & = 3  \quad \text{ multiply both side by x }  \\ \frac{1}{x}  \times x & = 3 \times x  \quad \text{ divide both side by x } \\ \frac{1}{3} & = \frac{3x}{3} \quad \text{ rearrange }  \\ x & = \frac{1}{3} \end{align}
form question with 3
\begin{align} 3 & = 2 \div 6 \\ 3 & = 2 \div 2 \times 3 \end{align} Note:- you need replace 3 with x to form this question \begin{align} 3 & = 2 \div 2 \times x \\ 3 & = 2 \div 2x \quad \text{ rearrange } \\ 2 & \div 2x = 3 \end{align}

Proving that  bracket ( ) can't be replaced with × it mean multiplication it self

Let look at this question \begin{align} \text{THE SAME OR DIFFERENT} \\ \text{Discover by computing!} \\ 44 \div 2(9 +3) = \text{?} \\ 44 \div (2(9 +3)) = \text{?} \end{align} check HERE to see peoples comment on FACEBOOK

BODMAS
48 \( \div \) 2(9+3)
= 48 \( \div \) 2 × 12
= 24 × 12
= 288

Also
48 \( \div \) (2(9+3))
= 48 \( \div \) (2(12))
= 48 \( \div \) 24
= 2
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Maths Is The Study Of Balance

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