How To Evaluate Algebraic Expressions

Summary

This video provides a clear, step-by-step guide on how to evaluate algebraic expressions. It demonstrates substituting given values for variables, applying the order of operations (PEMDAS/BODMAS), and performing calculations carefully. Through multiple examples, including linear, quadratic, and fractional expressions, viewers learn to solve problems accurately and check their work using a calculator. The tutorial also applies these skills to real-world scenarios, such as calculating the height of a ball thrown into the air. By following these methods, learners gain confidence in handling algebraic expressions and understanding their practical applications in everyday problems.

Takeaways

• 😀 To evaluate an algebraic expression, first identify the expression and the given values for the variables.
• 😀 Substitute the given numerical values into the algebraic expression before performing any operations.
• 😀 Follow the order of operations (PEMDAS): Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
• 😀 Carefully handle negative numbers and powers when performing calculations.
• 😀 Multiplication and exponents should always be performed before addition or subtraction.
• 😀 Fractions resulting from expressions can be left as improper fractions, converted to mixed numbers, or expressed as decimals.
• 😀 Always simplify calculations step by step to avoid mistakes.
• 😀 Using a calculator to verify the substituted expression helps ensure the accuracy of your answer.
• 😀 Real-world applications, like calculating the height of a thrown ball, can be solved using the same process of substitution and simplification.
• 😀 Multiple formats of answers are valid: improper fractions, mixed fractions, and decimal values depending on context.
• 😀 When dealing with parentheses in expressions, always resolve them first before applying exponents or other operations.
• 😀 Practice with various types of expressions strengthens understanding and accuracy in evaluating algebraic expressions.

Q & A

What is the first step in evaluating an algebraic expression?

The first step is to substitute the given values for each variable in the expression.

Why is it important to follow the order of operations (PEMDAS) when evaluating expressions?

Following PEMDAS ensures that calculations are done in the correct sequence, preventing errors with parentheses, exponents, multiplication/division, and addition/subtraction.

How do you evaluate the expression 3x + 2y - 5z when x = 2, y = 3, and z = -5?

Substitute the values: 3(2) + 2(3) - 5(-5) = 6 + 6 + 25 = 37.

What is the value of x^2 + 3x - 4 when x = 4?

Substitute x: 4^2 + 3(4) - 4 = 16 + 12 - 4 = 24.

When evaluating expressions with parentheses, which operations should you perform first?

Operations inside the parentheses should be performed first before dealing with exponents or other operations.

How would you simplify the fraction (3x + 4)/(2x - 3y) when x = 5 and y = 2?

Substitute the values: (3(5)+4)/(2(5)-3(2)) = 19/4, which can be written as the mixed fraction 4 3/4 or decimal 4.75.

In the expression 2x^2 - 5y + 3 with x = 2 and y = 3, what common mistake should you avoid?

Avoid calculating multiplication incorrectly; specifically, 5*3 should be 15, not 13, before combining terms.

How do you evaluate x^2 - 5(x - y)^3 when x = 6 and y = 3?

First, evaluate inside parentheses: (6-3)=3, then cube it: 3^3=27, then multiply by 5: 5*27=135, finally subtract from 6^2=36: 36-135=-99.

How can you verify your answers after evaluating an algebraic expression?

Plug the substituted values and the full expression into a calculator to ensure the calculated result matches the manual solution.

Using the height formula h = 6 + 45t - 16t^2, what is the height of a ball after 2 seconds?

Substitute t = 2: h = 6 + 45(2) - 16(2^2) = 6 + 90 - 64 = 32 feet.

Why might someone convert a fraction result to a mixed number or decimal?

Converting makes the answer easier to interpret and apply in real-world contexts, such as measurements or comparisons.

What are the three forms you can express the fraction 27/4?

27/4 can be expressed as an improper fraction (27/4), a mixed number (6 3/4), or a decimal (6.75).