Question

numerical expression
order of operations
types of grouping symbols
examples
an expression that contains only numbers and operations.
give three examples of numerical expressions below.
to simplify a numerical expression means to find its value. when there are several operations, there is a certain order they are done in so that everyone gets the same answer. we use the order of operations to find the value of a numerical expression with more than one operation.
the order of operations:

1. parentheses
2. exponents
3. multiplication and division (from left - to - right)
4. addition and subtraction (from left - to - right)

parentheses are used to group operations.
15+(8 - 3)
a fraction bar groups the numerator from the denominator.
\\(\frac{18 + 6}{5-1}\\)
directions: simplify each expression

1. 19 - 3×4
2. (24 + 14)+8
3. 3²·(37 - 8)
4. 25+(6 + 1)²
5. 30 - 28÷4·2
6. (14 - 5)²-48

Explanation:

Step1: Recall order - of - operations (PEMDAS)

First, perform operations inside parentheses, then exponents, then multiplication and division from left - to - right, and finally addition and subtraction from left - to - right.

Step2: Solve 1. \(19−3\times4\)

Multiply first: \(3\times4 = 12\), then subtract: \(19−12=7\).

Step3: Solve 2. \((24 + 14)+8\)

Add inside the parentheses first: \(24+14 = 38\), then add the remaining number: \(38 + 8=46\).

Step4: Solve 3. \(3^{2}\times(37 - 8)\)

First, calculate the exponent: \(3^{2}=9\), then subtract inside the parentheses: \(37−8 = 29\), and then multiply: \(9\times29 = 261\).

Step5: Solve 4. \(25+(6 + 1)^{2}\)

Add inside the parentheses: \(6 + 1=7\), then calculate the exponent: \(7^{2}=49\), and then add: \(25+49 = 74\).

Step6: Solve 5. \(30−28\div4\times2\)

Divide first: \(28\div4 = 7\), then multiply: \(7\times2 = 14\), and then subtract: \(30−14 = 16\).

Step7: Solve 6. \((14 - 5)^{2}-48\)

Subtract inside the parentheses: \(14−5 = 9\), then calculate the exponent: \(9^{2}=81\), and then subtract: \(81−48 = 33\).

Answer:

1. \(7\)
2. \(46\)
3. \(261\)
4. \(74\)
5. \(16\)
6. \(33\)