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Simplify: [(-17) + 4 ÷ 2] ÷ [8 ÷ (-4) + 4] = ?​

Sagot :

SalmonWorldTopper

[tex]\large{\underline{\underline{\textsf{\textbf{\purple{Solution \: : - }}}}}}[/tex]

[tex]\begin{gathered} \\ \\ \quad\dashrightarrow{\sf \bigg[ \bigg( - 17 \bigg) + 4 \div 2 \bigg] \div \bigg[8 \div \bigg( - 8 \bigg) + 4 \bigg]} \\ \\ \end{gathered}[/tex]

[tex]\red \divideontimes[/tex] According to the "BODMAS rule" firstly performing "division".

[tex]\begin{gathered} \\ \\ \quad\dashrightarrow{\sf \bigg[ \bigg( - 17 \bigg) + \dfrac{4}{2} \bigg] \div \bigg[ \dfrac{8}{ - 8} + 4 \bigg]} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\quad\dashrightarrow{\sf \bigg[ \bigg( - 17 \bigg) + \cancel{\dfrac{4}{2}} \bigg] \div \bigg[ \: \cancel{\dfrac{8}{ - 8}} + 4 \bigg]} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\quad\dashrightarrow{\sf \bigg[ \bigg( - 17 \bigg) + 2 \bigg] \div \bigg[ - 1 + 4 \bigg]} \\ \\ \end{gathered}[/tex]

[tex]\red \divideontimes[/tex] Now, performing "addition and opening round brackets".

[tex]\begin{gathered} \\ \\\quad\dashrightarrow{\sf \bigg[ - 17 + 2 \bigg] \div \bigg[ - 1 + 4 \bigg]} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\quad\dashrightarrow{\sf \bigg[ \: - 15 \: \: \bigg] \div \bigg[ \: \: 3\: \: \bigg]} \\ \\ \end{gathered}[/tex]

[tex]\red \divideontimes[/tex] Now, opening "square brackets".

[tex]\begin{gathered} \\ \\ \quad\dashrightarrow{\sf { - 15 \div 3}} \\ \\ \end{gathered}[/tex]

[tex]\red \divideontimes[/tex] Now, "dividing 15 by 3".

[tex]\begin{gathered}\\ \\ \quad\dashrightarrow{\sf {\dfrac{ - 15}{3} }} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\quad\dashrightarrow{\sf { \cancel{\dfrac{ - 15}{3}}}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\quad\dashrightarrow{\underline{\underline{ \sf{\red{ - 5}}}}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered}\bigstar{\underline{\boxed{\bf{\purple{Answer = - 5}}}}} \\ \\ \end{gathered}[/tex]

∴ The Answer is -5.

[tex]\begin{gathered}\end{gathered}[/tex]

[tex]\large{\underline{\underline{\textsf{\textbf{\purple{Learn More \: : - }}}}}}[/tex]

[tex]\underline{\underline{\pmb{\mathbb{\red{BODMAS \: :}}}}}[/tex]

BODMAS rule is an acronym used to remember the order of operations to be followed while solving expressions in mathematics.

It stands for :-

  • ↠ B - Brackets,
  • ↠ O - Order of powers or roots,
  • ↠ D - Division,
  • ↠ M - Multiplication 
  • ↠ A - Addition,
  • ↠ S - Subtraction.

It means that expressions having multiple operators need to be simplified from left to right in this order only.

[tex]\rule{200}2[/tex]

[tex]\underline{\underline{\pmb{\mathbb{\red{BODMAS \: RULE \: :}}}}}[/tex]

First, we solve brackets, then powers or roots, then division or multiplication (whatever comes first from the left side of the expression), and then at last subtraction or addition.

  • ↠ Addition (+)
  • ↠ Subtraction (-)
  • ↠ Multiplication (×)
  • ↠ Division (÷)
  • ↠ Brackets ( )

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rlesandisusanya

Answer:

-7.5

Step-by-step explanation:

[tex] |( - 17) + 4 \div 2| \div |8 \div ( - 4) + 4| \\ | - 17 + 2| \div | - 2 + 4| \\ - 15 \div2 \\ - 7.5[/tex]

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