Order of Operations with Rational Numbers (7.EEI.3)

Front

What is the Order of Operations in mathematics?

Back

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

Front

How do you simplify the expression 9 - 10 + 11 - 12 + 13 - 14?

Back

To simplify the expression, follow the order of operations from left to right: 9 - 10 = -1, -1 + 11 = 10, 10 - 12 = -2, -2 + 13 = 11, 11 - 14 = -3. The final answer is -3.

Front

What is the result of the expression -81/-9 + -22/11 - 35/7?

Back

First, simplify each term: -81/-9 = 9, -22/11 = -2, -35/7 = -5. Then combine: 9 + (-2) + (-5) = 9 - 2 - 5 = 2.

Front

How do you evaluate the expression -15 ÷ -3 + -4 × 15?

Back

First, perform the division: -15 ÷ -3 = 5. Then perform the multiplication: -4 × 15 = -60. Finally, combine: 5 + (-60) = 5 - 60 = -55.

Front

What is the result of the expression (5 - 10)(7 - 4)?

Back

First, simplify inside the parentheses: 5 - 10 = -5 and 7 - 4 = 3. Then multiply: (-5)(3) = -15.

Front

How do you calculate (-2)^3 + (-3)^4 + (-4)^3?

Back

Calculate each term: (-2)^3 = -8, (-3)^4 = 81, (-4)^3 = -64. Then combine: -8 + 81 - 64 = 9.

Front

What is the significance of parentheses in the Order of Operations?

Back

Parentheses indicate which operations should be performed first in an expression. They can change the outcome of calculations by altering the order in which operations are executed.

Front

What is the difference between rational and irrational numbers?

Back

Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot be expressed as a simple fraction and have non-repeating, non-terminating decimal expansions.

Front

What is the result of adding a negative number to a positive number?

Back

When adding a negative number to a positive number, you effectively subtract the absolute value of the negative number from the positive number.

Front

How do you handle multiple operations in a single expression?

Back

Follow the Order of Operations (PEMDAS): first solve expressions in parentheses, then exponents, followed by multiplication and division from left to right, and finally addition and subtraction from left to right.