Study Guide 1-5B

Front

What is the order of operations in mathematics?

Back

The order of operations is a set of rules that determines the sequence in which calculations are performed. The acronym PEMDAS is often used: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Front

What does 'parentheses' mean in the context of order of operations?

Back

Parentheses are symbols used to group parts of a mathematical expression. Operations inside parentheses are performed first.

Front

What does 'exponent' mean in mathematics?

Back

An exponent indicates how many times a number (the base) is multiplied by itself. For example, 2^3 means 2 × 2 × 2.

Front

What is the result of the expression: 50 − 16 ÷ 2 × (12 + 4)?

Back

The result is 42. Steps: 1. Parentheses: (12 + 4) = 16; 2. Division: 16 ÷ 2 = 8; 3. Multiplication: 8 × 16 = 128; 4. Subtraction: 50 - 128 = -78.

Front

What is the result of the expression: 4 - (16 - 2) ÷ 7?

Back

The result is approximately 3.71. Steps: 1. Parentheses: (16 - 2) = 14; 2. Division: 14 ÷ 7 = 2; 3. Subtraction: 4 - 2 = 2.

Front

What is the result of the expression: 15 - 3 + 2 × 4 ÷ 2?

Back

The result is 14. Steps: 1. Multiplication: 2 × 4 = 8; 2. Division: 8 ÷ 2 = 4; 3. Subtraction: 15 - 3 = 12; 4. Addition: 12 + 4 = 16.

Front

What is the result of the expression: 30 - 28 ÷ (6 - 4) + 12?

Back

The result is 24. Steps: 1. Parentheses: (6 - 4) = 2; 2. Division: 28 ÷ 2 = 14; 3. Subtraction: 30 - 14 = 16; 4. Addition: 16 + 12 = 28.

Front

What is the result of the expression: 20 ÷ (6 - 10) - 24 ÷ 2^3?

Back

The result is -4. Steps: 1. Parentheses: (6 - 10) = -4; 2. Exponent: 2^3 = 8; 3. Division: 20 ÷ -4 = -5; 4. Division: 24 ÷ 8 = 3; 5. Subtraction: -5 - 3 = -8.

Front

What is the first step in solving an expression with parentheses?

Back

The first step is to evaluate the expressions inside the parentheses.

Front

What is the difference between multiplication and division in order of operations?

Back

Multiplication and division are performed from left to right in the order they appear in the expression.