Simplify The Expression.${ \frac{|10-1|+4}{8+4 \cdot 3} }$ { \frac{|10-1|+4}{8+4 \cdot 3} = \square \}

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Introduction

In mathematics, simplifying expressions is an essential skill that helps us solve problems efficiently. It involves reducing complex expressions to their simplest form, making it easier to understand and work with. In this article, we will simplify the given expression step by step, using basic mathematical operations and properties.

The Given Expression

The given expression is:

∣10−1∣+48+4⋅3\frac{|10-1|+4}{8+4 \cdot 3}

This expression involves absolute value, addition, multiplication, and division. To simplify it, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Step 1: Evaluate the Absolute Value

The absolute value of a number is its distance from zero on the number line. In this case, we have ∣10−1∣|10-1|. To evaluate this, we need to subtract 1 from 10, which gives us 9. Since 9 is a positive number, the absolute value of 9 is simply 9.

|10-1| = |9| = 9

Step 2: Simplify the Numerator

Now that we have evaluated the absolute value, we can simplify the numerator. The numerator is ∣10−1∣+4|10-1|+4, which is equal to 9+49+4. Adding 9 and 4 gives us 13.

|10-1|+4 = 9+4 = 13

Step 3: Simplify the Denominator

The denominator is 8+4â‹…38+4 \cdot 3. To simplify this, we need to multiply 4 and 3, which gives us 12. Then, we add 8 to 12, which gives us 20.

8+4 \cdot 3 = 8+12 = 20

Step 4: Simplify the Expression

Now that we have simplified the numerator and denominator, we can simplify the expression. The expression is 1320\frac{13}{20}.

\frac{|10-1|+4}{8+4 \cdot 3} = \frac{13}{20}

Conclusion

In this article, we simplified the given expression step by step, using basic mathematical operations and properties. We evaluated the absolute value, simplified the numerator and denominator, and finally simplified the expression. The simplified expression is 1320\frac{13}{20}.

Frequently Asked Questions

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

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the absolute value of a number?

A: The absolute value of a number is its distance from zero on the number line. For example, the absolute value of 5 is 5, and the absolute value of -5 is also 5.

Q: How do I simplify an expression?

A: To simplify an expression, you need to follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Final Answer

The final answer is 1320\boxed{\frac{13}{20}}.

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Introduction

In our previous article, we simplified the given expression step by step, using basic mathematical operations and properties. In this article, we will answer some frequently asked questions related to simplifying expressions.

Q&A

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

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the absolute value of a number?

A: The absolute value of a number is its distance from zero on the number line. For example, the absolute value of 5 is 5, and the absolute value of -5 is also 5.

Q: How do I simplify an expression?

A: To simplify an expression, you need to follow the order of operations (PEMDAS). First, evaluate any expressions inside parentheses. Then, evaluate any exponential expressions. Next, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: What is the difference between simplifying and solving an equation?

A: Simplifying an expression means reducing it to its simplest form, while solving an equation means finding the value of the variable that makes the equation true.

Q: Can I simplify an expression with variables?

A: Yes, you can simplify an expression with variables. However, you need to follow the order of operations (PEMDAS) and use the properties of variables, such as the distributive property.

Q: How do I know when to simplify an expression?

A: You should simplify an expression when:

  • You need to evaluate an expression with multiple operations.
  • You need to compare two or more expressions.
  • You need to substitute an expression into another expression.

Q: Can I use a calculator to simplify an expression?

A: Yes, you can use a calculator to simplify an expression. However, it's always a good idea to check your work by hand to make sure you understand the steps involved in simplifying the expression.

Tips and Tricks

Tip 1: Use the order of operations (PEMDAS) to simplify expressions.

  • Evaluate expressions inside parentheses first.
  • Evaluate any exponential expressions next.
  • Evaluate any multiplication and division operations from left to right.
  • Finally, evaluate any addition and subtraction operations from left to right.

Tip 2: Use the properties of variables to simplify expressions.

  • Use the distributive property to simplify expressions with variables.
  • Use the commutative property to simplify expressions with variables.
  • Use the associative property to simplify expressions with variables.

Tip 3: Check your work by hand to make sure you understand the steps involved in simplifying the expression.

Conclusion

In this article, we answered some frequently asked questions related to simplifying expressions. We also provided some tips and tricks to help you simplify expressions more efficiently. Remember to follow the order of operations (PEMDAS) and use the properties of variables to simplify expressions.

Final Answer

The final answer is 1320\boxed{\frac{13}{20}}.