Question

summer math - week 2

order of operations:
its important to follow the order of operations when evaluating an expression. otherwise, you might get the wrong answer! you can remember the order of operations using the acronym pemdas:

1. parentheses, and other grouping symbols
2. exponents
3. multiplication and division, from left to right
4. addition and subtraction, from left to right

if your problem doesnt have one of these steps, move on to the next step!

lets try an example. use the order of operations to evaluate \\(4 \times 6 + 2^2 - (4 + 3)\\).
\\(4 \times 6 + 2^2 - (4 + 3)\\) first, simplify whats inside the parentheses: \\(4 + 3 = 7\\).
\\(4 \times 6 + 2^2 - 7\\) then, evaluate the exponent: \\(2^2 = 4\\).
\\(4 \times 6 + 4 - 7\\) next, multiply: \\(4 \times 6 = 24\\).
\\(24 + 4 - 7\\) then, add: \\(24 + 4 = 28\\).
\\(28 - 7 = 21\\) finally, subtract \\(28 - 7\\) to get the answer, 21.

evaluate each expression using the order of operations.

1. \\(9 + 7 \times 8\\)
2. \\(46 + 19 - 4^2\\)
3. \\(16 \div 4 + 7\\)
4. \\(10^2 \times 2 + 40 \div 8\\)
5. \\(8 \times 12 \div (30 - 6)\\)
6. \\(64 - (8 + 12) \times 3\\)
7. \\(21 \div (3 + 4) \times 6\\)
8. \\((9 - 5) \times 7 - 2 \times 8\\)
9. \\(48 \div 6 \times 2^2 - (3 + 5)\\)

Explanation:

Identify the expressions to evaluate

We need to evaluate nine arithmetic expressions using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Evaluate the first row of expressions

• Expression 1: \(9 + 7 \times 8\)

Perform multiplication first: \(7 \times 8 = 56\).
Then perform addition: \(9 + 56 = 65\).

• Expression 2: \(46 + 19 - 4^2\)

Evaluate the exponent first: \(4^2 = 16\).
The expression becomes \(46 + 19 - 16\).
Perform addition and subtraction from left to right:
\(46 + 19 = 65\),
\(65 - 16 = 49\).

• Expression 3: \(16 \div 4 + 7\)

Perform division first: \(16 \div 4 = 4\).
Then perform addition: \(4 + 7 = 11\).

Evaluate the second row of expressions

• Expression 4: \(10^2 \times 2 + 40 \div 8\)

Evaluate the exponent first: \(10^2 = 100\).
The expression becomes \(100 \times 2 + 40 \div 8\).
Perform multiplication and division from left to right:
\(100 \times 2 = 200\),
\(40 \div 8 = 5\).
The expression becomes \(200 + 5\).
Perform addition: \(200 + 5 = 205\).

• Expression 5: \(8 \times 12 \div (30 - 6)\)

Evaluate parentheses first: \(30 - 6 = 24\).
The expression becomes \(8 \times 12 \div 24\).
Perform multiplication and division from left to right:
\(8 \times 12 = 96\),
\(96 \div 24 = 4\).

• Expression 6: \(64 - (8 + 12) \times 3\)

Evaluate parentheses first: \(8 + 12 = 20\).
The expression becomes \(64 - 20 \times 3\).
Perform multiplication next: \(20 \times 3 = 60\).
Then perform subtraction: \(64 - 60 = 4\).

Evaluate the third row of expressions

• Expression 7: \(21 \div (3 + 4) \times 6\)

Evaluate parentheses first: \(3 + 4 = 7\).
The expression becomes \(21 \div 7 \times 6\).
Perform division and multiplication from left to right:
\(21 \div 7 = 3\),
\(3 \times 6 = 18\).

• Expression 8: \((9 - 5) \times 7 - 2 \times 8\)

Evaluate parentheses first: \(9 - 5 = 4\).
The expression becomes \(4 \times 7 - 2 \times 8\).
Perform multiplications:
\(4 \times 7 = 28\),
\(2 \times 8 = 16\).
The expression becomes \(28 - 16\).
Perform subtraction: \(28 - 16 = 12\).

• Expression 9: \(48 \div 6 \times 2^2 - (3 + 5)\)

Evaluate parentheses first: \(3 + 5 = 8\).
Evaluate exponent next: \(2^2 = 4\).
The expression becomes \(48 \div 6 \times 4 - 8\).
Perform division and multiplication from left to right:
\(48 \div 6 = 8\),
\(8 \times 4 = 32\).
The expression becomes \(32 - 8\).
Perform subtraction: \(32 - 8 = 24\).

Answer:

No.	Problem	Answer
2	\(46 + 19 - 4^2\)	\(49\)
3	\(16 \div 4 + 7\)	\(11\)
4	\(10^2 \times 2 + 40 \div 8\)	\(205\)
5	\(8 \times 12 \div (30 - 6)\)	\(4\)
6	\(64 - (8 + 12) \times 3\)	\(4\)
7	\(21 \div (3 + 4) \times 6\)	\(18\)
8	\((9 - 5) \times 7 - 2 \times 8\)	\(12\)
9	\(48 \div 6 \times 2^2 - (3 + 5)\)	\(24\)