Question

main ideas/questions notes/examples
numerical
expression • an expression that contains only
and

• give three examples of numerical expressions below:

order of
operations to simplify a numerical expression means to find its value. when there are
several operations, there is a certain order they are done in to make sure
everyone gets the same answer. we use the order of operations to find the
value of a numerical expression with more than one operation.

types of
grouping symbols parentheses are used
to group operations.
15+(8 - 3) a fraction bar groups the
numerator from the denominator.
(18 + 6)/(5 - 1)
directions: simplify each expression.
examples 1. 19-3×4 2. (24 + 16)÷8

1. 3²·(37 - 8) 4. 25+(6 + 1)²
2. 30-28÷4·2 6. (14 - 5)²-48

Explanation:

Step1: Recall order - of - operations (PEMDAS: Parentheses, Exponents, Multiplication and Division from left - to - right, Addition and Subtraction from left - to - right)

1. For \(19 - 3\times4\):

• First, perform multiplication: \(3\times4 = 12\).
• Then, perform subtraction: \(19-12 = 7\).

1. For \((24 + 16)\div8\):

• First, perform the operation inside the parentheses: \(24 + 16=40\).
• Then, perform division: \(40\div8 = 5\).

1. For \(3^{2}\cdot(37 - 8)\):

• First, calculate the exponent: \(3^{2}=9\).
• Then, perform the operation inside the parentheses: \(37 - 8 = 29\).
• Finally, perform multiplication: \(9\times29 = 261\).

1. For \(25+(6 + 1)^{2}\):

• First, perform the operation inside the parentheses: \(6 + 1=7\).
• Then, calculate the exponent: \(7^{2}=49\).
• Finally, perform addition: \(25 + 49=74\).

1. For \(30-28\div4\cdot2\):

• First, perform division: \(28\div4 = 7\).
• Then, perform multiplication: \(7\times2 = 14\).
• Finally, perform subtraction: \(30-14 = 16\).

1. For \((14 - 5)^{2}-48\):

• First, perform the operation inside the parentheses: \(14 - 5 = 9\).
• Then, calculate the exponent: \(9^{2}=81\).
• Finally, perform subtraction: \(81-48 = 33\).

Answer:

1. \(7\)
2. \(5\)
3. \(261\)
4. \(74\)
5. \(16\)
6. \(33\)