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##### What MATHEMATICIANS say answer of 6/2(2+1) =...? ___________________________________________

```    1
```
##### Explanation

Let us solve it by BODMAS

```  6/2(2+1)
= 6/2(3)
```

Here the parentheses still exist so solve it first and don't try to convert it into multiplication sign 'x'. The problem is that people do not finish the parentheses step before jumping to the multiplication/division step and move toward wrong answer.

```= 6/6
= 1
```

The problem is that some solve it as 6/2(2+1)= 6/2(3)= 6/2*3=3*3=9 which is wrong.

Take a look on following images which are taken from different books. How mathematicians define the factor, division and coefficient. How math expert solve 1/2a, 1/ab or expplain it.

##### Factors

This brings us to factors, such as 5ab = b5a = ba5=ab5. Factors can be rearranged in any order because their product result remains the same. (means the quantity doesn’t change).
Because the quantity is the same therefore there is no need of parenthesis. These rules was very clear in past because people were actually taught basics of mathematics but these problems appears in today, when more and more people are relying on calculators, most of the programmings does not follow the above rules, they always tell you that you should use parentheses when entering the data.  ##### Division

Let us also see some division rules.   ##### Coefficient

There is also the coefficient rule that how coefficients are “attached” to their variable to make a single quantity? The above images are taken from following books
1) Bonnycastle's introduction to Algebra by John Bonnycastle, James Ryan, John Francis Jenkins
2) Algebra for high schools and colleges: containing a systematic exposition By James B. Dodd

###### Introduction to Real Analysis by Bartle and Sherbert
```Page  42: written as
(x²-2)/2x
Page  53: written as
1/2n = 1/(2n)
Page 350:  written as
e/2M
Page 363:  written as
1/n(n+1) < 1/n² <= 1/n and
n/(n-2)(n-1)
```

###### Introduction to Real Analysis by William F. Trench
```Page 123:
k(ε/2k) = ε/2
```

###### An Introduction to Real Analysis: Richard Wheeden, Antoni Zygmund 1977
```Page # 31:
2Mε/4(k + 1)M = ε/2(k + 1)
```

###### Introduction to Real Analysis by William F. Trench
```Page # 123:
k(ε/2k) = ε/2
```

###### The Everything Guide to Algebra by Christopher Monahan
```Page # 46 shows: 6x³÷3x=2x²
(That's because "3x" is a single quantity/operand, and is a product of both factors: 3 and x)
He also describes "PEMDAS" in detail.
```

###### Basic Algebra I: Second Edition by Nathan Jacobson
```Page # 116:
a/b + c/d = (ad +bc)/bd
```

###### Introduction to Algebra by Peter Jephson Cameron
```Page # 17
"Since mx/nx = m/n" [Notice how it is NOT m * x / n * x = mx²/n ???]
```

##### Other links for correct solution

###### https://www.onlinemathlearning.com/multiply-divide-expressions.html

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##### BODMAS Short Questions

###### What is BODMAS?

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###### What is order of operation?

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###### Who invented BODMAS?

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###### Solve 3 - 3 × 2 ÷ 6 = ?

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##### BODMAS Questions

###### What is square root of 25?

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###### Solve 10 ÷ 4 of 5 =...?

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###### Solve 2 / 2 - 2 + 2 × 2 =...?

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###### Solve 10-4×0+3÷3 =..?

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###### Solve 7+7÷7+7×7-7 =...?

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###### Solve 3 + 5% =...?

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###### Solve 2e × 100% =...?

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###### If √(0.04)(0.4)a = (0.4)(0.04)√b then a/b ... ?

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###### Solve 5 × (1/5) ÷ (1/5) ÷ (1/5) × 5 =...?

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###### 3 ÷ (5 ÷ 7) = (3 ÷ 5) ÷ 7

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###### Solve 4 - 2 ÷ (1/2) + 3 =...?

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###### Solve 2 - 2 × 2 - 2 ÷ 2 =...?

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###### Solve 3 - 3 × 3 - 3 ÷ 3 =...?

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###### Solve 4 + 4 × 4 - 4 ÷ 4 =...?

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###### Solve -1 + 2 × 0! =...?

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###### Solve -2 + 3! - 1 =...?

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###### Which step is wrong?

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##### SHORTCUT TRICKS (Division)
• Divisible by 2 Shortcut trick
• Divisible by 3 Shortcut trick
• Divisible by 4 Shortcut trick
• Divisible by 5 Shortcut trick
• Divisible by 6 Shortcut trick • Divisible by 7 Shortcut trick • Divisible by 8 Shortcut trick • Divisible by 9 Shortcut trick
• Divisible by 10 Shortcut trick

##### Worksheets (Solved)

###### Integration     