Simplify The Expression. Show All Of Your Work:$\[ 4^2 - 12 + 6 \div 3 \cdot 5 = \\]

Feb 28, 2025 by ADMIN 85 views

Simplify the Expression: A Step-by-Step Guide

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Introduction

In mathematics, simplifying expressions is a crucial skill that helps us solve problems efficiently and accurately. It involves breaking down complex expressions into simpler ones, making it easier to understand and work with. In this article, we will simplify the given expression step by step, using the order of operations (PEMDAS) to ensure that we get the correct result.

The Expression

The given expression is:

${ 4^2 - 12 + 6 \div 3 \cdot 5 = }$

Step 1: Evaluate the Exponent

The first step is to evaluate the exponent. In this case, we have $4^2$ , which means $4$ raised to the power of $2$ . To evaluate this, we multiply $4$ by itself $2$ times:

${ 4^2 = 4 \times 4 = 16 }$

Step 2: Rewrite the Expression

Now that we have evaluated the exponent, we can rewrite the expression with the result:

${ 16 - 12 + 6 \div 3 \cdot 5 = }$

Step 3: Evaluate the Division

Next, we need to evaluate the division. In this case, we have $6 \div 3$ , which means we need to divide $6$ by $3$ . To do this, we perform the division:

${ 6 \div 3 = 2 }$

Step 4: Rewrite the Expression Again

Now that we have evaluated the division, we can rewrite the expression with the result:

${ 16 - 12 + 2 \cdot 5 = }$

Step 5: Evaluate the Multiplication

Next, we need to evaluate the multiplication. In this case, we have $2 \cdot 5$ , which means we need to multiply $2$ by $5$ . To do this, we perform the multiplication:

${ 2 \cdot 5 = 10 }$

Step 6: Rewrite the Expression Once More

Now that we have evaluated the multiplication, we can rewrite the expression with the result:

${ 16 - 12 + 10 = }$

Step 7: Evaluate the Subtraction and Addition

Finally, we need to evaluate the subtraction and addition. In this case, we have $16 - 12 + 10$ , which means we need to subtract $12$ from $16$ and then add $10$ to the result. To do this, we perform the operations:

${ 16 - 12 = 4 }$ ${ 4 + 10 = 14 }$

Conclusion

And that's it! We have simplified the expression step by step, using the order of operations (PEMDAS) to ensure that we get the correct result. The final answer is:

${ 14 }$

Tips and Tricks

Always follow the order of operations (PEMDAS) when simplifying expressions.
Evaluate exponents first, then divisions, then multiplications, and finally additions and subtractions.
Use parentheses to group numbers and operations when necessary.
Simplify expressions step by step, rather than trying to simplify them all at once.

Practice Problems

Simplify the expression: $3^2 - 8 + 4 \div 2 \cdot 3$
Simplify the expression: $2^3 - 12 + 6 \div 3 \cdot 4$
Simplify the expression: $5^2 - 15 + 3 \div 3 \cdot 2$

Resources

Khan Academy: Simplifying Expressions
Mathway: Simplifying Expressions
IXL: Simplifying Expressions

FAQs

Q: What is the order of operations (PEMDAS)? A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying expressions. The acronym PEMDAS stands for:
- P: Parentheses
- E: Exponents
- M: Multiplication
- D: Division
- A: Addition
- S: Subtraction
Q: Why is it important to simplify expressions? A: Simplifying expressions is important because it helps us solve problems efficiently and accurately. It also helps us to understand the underlying math concepts and to identify patterns and relationships between numbers and operations.

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Introduction

In our previous article, we simplified the expression $4^2 - 12 + 6 \div 3 \cdot 5$ step by step, using the order of operations (PEMDAS) to ensure that we get the correct result. In this article, we will answer some frequently asked questions (FAQs) about simplifying expressions.

Q&A

Q: What is the order of operations (PEMDAS)?

A: The order of operations (PEMDAS) is a set of rules that tells us which operations to perform first when simplifying expressions. The acronym PEMDAS stands for: + P: Parentheses + E: Exponents + M: Multiplication + D: Division + A: Addition + S: Subtraction

Q: Why is it important to simplify expressions?

A: Simplifying expressions is important because it helps us solve problems efficiently and accurately. It also helps us to understand the underlying math concepts and to identify patterns and relationships between numbers and operations.

Q: How do I know which operation to perform first?

A: To determine which operation to perform first, follow the order of operations (PEMDAS). If there are parentheses, evaluate the expression inside the parentheses first. If there are no parentheses, evaluate any exponents next. Then, perform any multiplications and divisions from left to right. Finally, perform any additions and subtractions from left to right.

Q: What if I have multiple operations with the same precedence?

A: If you have multiple operations with the same precedence, perform them from left to right. For example, if you have the expression $3 + 4 \cdot 5$ , you would first perform the multiplication $4 \cdot 5$ , and then perform the addition $3 + 20$ .

Q: Can I simplify expressions with fractions?

A: Yes, you can simplify expressions with fractions. To simplify a fraction, first simplify the numerator and denominator separately. Then, divide the numerator by the denominator to get the simplified fraction.

Q: How do I simplify expressions with variables?

A: To simplify expressions with variables, first simplify the expression inside the parentheses. Then, evaluate any exponents. Next, perform any multiplications and divisions from left to right. Finally, perform any additions and subtractions from left to right.

Q: What if I have a negative number in an expression?

A: If you have a negative number in an expression, treat it as a positive number and change the sign of the result. For example, if you have the expression $-3 + 4$ , you would first perform the addition $-3 + 4$ , and then change the sign of the result to get $1$ .

Tips and Tricks

Always follow the order of operations (PEMDAS) when simplifying expressions.
Evaluate exponents first, then divisions, then multiplications, and finally additions and subtractions.
Use parentheses to group numbers and operations when necessary.
Simplify expressions step by step, rather than trying to simplify them all at once.

Practice Problems

Simplify the expression: $3^2 - 8 + 4 \div 2 \cdot 3$
Simplify the expression: $2^3 - 12 + 6 \div 3 \cdot 4$
Simplify the expression: $5^2 - 15 + 3 \div 3 \cdot 2$

Resources

Khan Academy: Simplifying Expressions
Mathway: Simplifying Expressions
IXL: Simplifying Expressions

Conclusion

Simplifying expressions is an essential skill in mathematics that helps us solve problems efficiently and accurately. By following the order of operations (PEMDAS) and using parentheses to group numbers and operations, we can simplify expressions step by step. Remember to always evaluate exponents first, then divisions, then multiplications, and finally additions and subtractions. With practice and patience, you will become proficient in simplifying expressions and solving math problems with ease.