[tex]\boxed{ \ 5(14 - 2)^2 \div 2 = 360 \ }[/tex]
We at present undergo the following operations: addition, subtraction, multiplication, and division. When given an expression sometimes we confuse operations which must take precedence.
In the 1500s the rules of the order of operation were issued. The "order" of these operations states which processes take precedence (as a priority) before which other operations.
The priority of operations is:
Let's implement the rule.
[tex] 5(14 - 2)^2 \div 2 = \ ? [/tex]
Subtract 14 by 2 in parentheses.
[tex] = \ 5(12)^2 \div 2 [/tex]
Squaring 12.
[tex] = \ 5 \times 144 \div 2 [/tex] ... (Equation -1)
Multiply 5 by 144.
[tex] = 720 \div 2 [/tex]
Divide 720 by 2 and we obtain a simplified result.
[tex]\boxed{ \ 5(14 - 2)^2 \div 2 = 360 \ }[/tex]
Or from Equation-1 we divide 144 by 2 first.
[tex] = 5 \times 72 [/tex]
The final results keep the same.
[tex]\boxed{ \ 5(14 - 2)^2 \div 2 = 360 \ }[/tex]
Another example
[tex] 24 \div 4(2 + 1)^2 = \ ?[/tex]
Add 2 by 1 in parentheses.
[tex] = 24 \div 4(3)^2 [/tex]
Squaring 3.
[tex] = 24 \div 4 \times 9 [/tex] ... (Equation-1)
Divide 24 by 4.
[tex] = 6 \times 9 [/tex]
We get a simplified result, i.e. [tex]\boxed{ \ 24 \div 4(2 + 1)^2 = 54 \ }[/tex]
Beware of this. From Equation-1 we are disallowed from multiplying 4 by 9. Remember the priority operation rules that have been stated above.
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The simplified form of [tex]5(14-2)^{2}\div 2[/tex] is [tex]\boxed{\bf 360}[/tex].
Further explanation:
BODMAS is an acronym and it stands for brackets, of, division, multiplication, addition and subtraction. It is the order in which simplification is to be performed.
The expression [tex]a^{2}[/tex] can be expressed as follows:
[tex]\boxed{a^{2}=(a)\cdot (a)}[/tex]
Here, [tex]a[/tex] is a real number.
Given:
The expression is [tex]5(14-2)^{2}\div 2[/tex].
Calculation:
The given expression is [tex]5(14-2)^{2}\div 2[/tex].
The given expression can also be expressed as follows:
[tex]\boxed{\dfrac{5\cdot (14-2)^{2}}{2}}[/tex]
Use the BODMAS rule and then perform all the operations in its order.
First we need to perform the operation of bracket in the given expression.
The operation of brackets can be performed by subtracting the terms inside the bracket.
[tex]\boxed{\dfrac{5\cdot (14-2)^{2}}{2}=\dfrac{5\cdot (12)^{2}}{2}}[/tex]
Now the expression [tex](12)^{2}[/tex] can be expressed as follows:
[tex]\boxed{(12)^{2}=12\cdot 12}[/tex]
Now the second operation is division as it followed by the BODMAS rule, it can be performed as follows:
[tex]\boxed{\dfrac{5\cdot 12\cdot 12}{2}=5\cdot 12 \cdot 6}[/tex]
Third, we will multiply the above terms with each other as followed by BODMAS rule.
[tex]\boxed{5\cdot 12\cdot 6=360}[/tex]
Therefore, the simplified form of the given expression [tex]5(14-2)^{2}\div 2[/tex] is [tex]\boxed{\bf 360}[/tex].
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Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Simplification
Keywords: Real numbers, simplification, BODMAS rule, expression, operations, addition, subtraction, square brackets, curly brackets. division, multiplication, of, order, terms, product, like terms, fractions, sum, difference.
