Question

Simplify each expression using the order of operations. 3+(7−5)2×6= 25(4+4)×2= 8−6÷2+3×5= 7×3−15÷5= 8+2(1+12÷2)2=

Answer 1

Using the order of operation which states

`\begin{gathered} B\Rightarrow Bracket \\ O\Rightarrow Orders \\ D\Rightarrow Division \\ M\Rightarrow Multilication \\ A\Rightarrow Addition \\ S\Rightarrow Subtraction \end{gathered}`

Expressions in brackets/parentheses are evaluted first, followed by expressions involving orders, division, multiplication, addition and subtraction in that order.

Thus,

1)

`\begin{gathered} 3+(7-5)2*6\text{ = ?} \\ \text{Evaluate expressions in parentheses. thus,} \\ 3+(2)2*6 \\ \text{Evaluate expressions involving multiplication,} \\ 3+24 \\ \text{Add up the expressions,} \\ 3+24\text{ = 27} \end{gathered}`

thus, 3+(7−5)2×6 = 27

2)

`\begin{gathered} 25\mleft(4+4\mright)*2=\text{?} \\ \text{Evaluate expressions in parentheses. thus,} \\ 25(8)*2 \\ \Rightarrow400 \end{gathered}`

thus, 25(4+4)×2 = 400

3)

`\begin{gathered} 8-6/2+3*5\text{ = ?} \\ \text{Evaluate expressions involving division. thus,} \\ 8-3+3*5 \\ \text{Evaluate expressions involving multipliation. thus,} \\ 8-3+15 \\ \text{Evaluate expressions involving addition. thus,} \\ 8+12 \\ \text{Add up the terms,} \\ 8+12\text{ = 20} \end{gathered}`

thus, 8−6÷2+3×5 = 20

4)

`\begin{gathered} 7*3-15/5=\text{ ?} \\ \text{Evaluate expressions involving division. thus,} \\ 7*3-3 \\ \text{Evaluate expressions involving multiplication. thus,} \\ 21-3 \\ \text{Subtract the terms,} \\ 21-3\text{ = }18 \end{gathered}`

thus, 7×3−15÷5 = 18

5)

`\begin{gathered} 8+2\mleft(1+12/2\mright)2=\text{ ?} \\ \text{Evaluate the terms in parentheses. thus,} \\ 8+2*\: 7*\: 2 \\ \text{Evaluate the terms involving multiplication. thus,} \\ 8+28 \\ \text{Add up the terms,} \\ 8+28\text{ = }36 \end{gathered}`

thus, 8+2(1+12÷2)2 = 36.