Simplifying Rational Algebraic Expressions

Oct 13, 2025 by orovajewels.com 94 views

Simplifying Rational Algebraic Expressions

In this section, we will explore the basics of simplifying rational algebraic expressions. Rational algebraic expressions are a combination of variables and constants, and they can be simplified using various techniques.

Simplify: 222-8 4 8

To simplify the expression 222-8 4 8, we need to follow the order of operations (PEMDAS). First, we need to evaluate the expression inside the parentheses. In this case, there are no parentheses, so we can move on to the next step.

The expression can be rewritten as 222 - (8 * 4) / 8. To simplify this expression, we need to follow the order of operations.

First, we need to multiply 8 and 4, which gives us 32. Then, we need to divide 32 by 8, which gives us 4.

Now, we can rewrite the expression as 222 - 4. To simplify this expression, we need to subtract 4 from 222, which gives us 218.

Therefore, the simplified expression is 218.

Multiply: 34 × 92

To multiply 34 and 92, we need to follow the order of operations. First, we need to multiply 3 and 9, which gives us 27. Then, we need to multiply 4 and 2, which gives us 8.

Now, we can rewrite the expression as 27 * 8. To simplify this expression, we need to multiply 27 and 8, which gives us 216.

Therefore, the product of 34 and 92 is 216.

Divide: 229

To divide 229 by a number, we need to find the quotient. In this case, we are not given a divisor, so we will assume that we are dividing 229 by 1.

The quotient of 229 divided by 1 is 229.

Simplify: +3 X -3 +3 2-16 1-4 3

To simplify the expression +3 X -3 +3 2-16 1-4 3, we need to follow the order of operations. First, we need to evaluate the expressions inside the parentheses.

The expression can be rewritten as (3 + (-3) + 3) * (2 - 16) * (1 - 4) * 3.

To simplify this expression, we need to follow the order of operations.

First, we need to evaluate the expressions inside the parentheses. The expression (3 + (-3) + 3) can be simplified as 3. The expression (2 - 16) can be simplified as -14. The expression (1 - 4) can be simplified as -3.

Now, we can rewrite the expression as 3 * (-14) * (-3) * 3.

To simplify this expression, we need to multiply 3 and -14, which gives us -42. Then, we need to multiply -42 and -3, which gives us 126. Finally, we need to multiply 126 and 3, which gives us 378.

Therefore, the simplified expression is 378.

Add: 2 + //

To add 2 and //, we need to follow the order of operations. First, we need to evaluate the expression inside the parentheses.

The expression can be rewritten as 2 + (//).

To simplify this expression, we need to follow the order of operations.

First, we need to evaluate the expression inside the parentheses. The expression // can be simplified as 0.

Now, we can rewrite the expression as 2 + 0.

To simplify this expression, we need to add 2 and 0, which gives us 2.

Therefore, the sum of 2 and // is 2.

Subtract: -2

To subtract -2 from a number, we need to add 2 to that number.

For example, if we subtract -2 from 5, we get 5 + 2 = 7.

Therefore, the result of subtracting -2 is 2.

Simplify 2-25 +5 9

To simplify the expression 2-25 +5 9, we need to follow the order of operations. First, we need to evaluate the expressions inside the parentheses.

The expression can be rewritten as (2 - 25) + 5 * 9.

To simplify this expression, we need to follow the order of operations.

First, we need to evaluate the expressions inside the parentheses. The expression (2 - 25) can be simplified as -23. The expression 5 * 9 can be simplified as 45.

Now, we can rewrite the expression as -23 + 45.

To simplify this expression, we need to add -23 and 45, which gives us 22.

Therefore, the simplified expression is 22.

Multiply: x 4x2

To multiply x and 4x2, we need to follow the order of operations. First, we need to multiply 4 and x2, which gives us 4x2.

Now, we can rewrite the expression as x * 4x2.

To simplify this expression, we need to multiply x and 4x2, which gives us 4x3.

Therefore, the product of x and 4x2 is 4x3.

Divide: 2²+52 +6 ÷ 2+2 2+2

To divide 2²+52 +6 ÷ 2+2 2+2 by a number, we need to find the quotient. In this case, we are not given a divisor, so we will assume that we are dividing 2²+52 +6 ÷ 2+2 2+2 by 1.

The expression 2²+52 +6 ÷ 2+2 2+2 can be rewritten as (2² + 5 * 2) + 6 / (2 + 2) * 2.

To simplify this expression, we need to follow the order of operations.

First, we need to evaluate the expressions inside the parentheses. The expression (2² + 5 * 2) can be simplified as 4 + 10 = 14. The expression 6 / (2 + 2) can be simplified as 6 / 4 = 1.5. The expression 2 * 2 can be simplified as 4.

Now, we can rewrite the expression as 14 + 1.5 * 4.

To simplify this expression, we need to multiply 1.5 and 4, which gives us 6. Then, we need to add 14 and 6, which gives us 20.

Therefore, the quotient of 2²+52 +6 ÷ 2+2 2+2 is 20.

Simplify

To simplify the expression, we need to follow the order of operations. First, we need to evaluate the expressions inside the parentheses.

The expression can be rewritten as (2 - 25) + 5 * 9.

To simplify this expression, we need to follow the order of operations.

First, we need to evaluate the expressions inside the parentheses. The expression (2 - 25) can be simplified as -23. The expression 5 * 9 can be simplified as 45.

Now, we can rewrite the expression as -23 + 45.

To simplify this expression, we need to add -23 and 45, which gives us 22.

Therefore, the simplified expression is 22.

Conclusion

In this section, we have explored the basics of simplifying rational algebraic expressions. We have learned how to simplify expressions using various techniques, including the order of operations and factoring.

We have also learned how to multiply and divide rational algebraic expressions, and how to simplify expressions with variables and constants.

By following the order of operations and using the techniques we have learned, we can simplify even the most complex rational algebraic expressions.

Final Answer

Frequently Asked Questions

In this section, we will answer some of the most frequently asked questions about rational algebraic expressions.

Q: What is a rational algebraic expression?

A: A rational algebraic expression is a combination of variables and constants, and it can be simplified using various techniques.

Q: How do I simplify a rational algebraic expression?

A: To simplify a rational algebraic expression, you need to follow the order of operations (PEMDAS). First, you need to evaluate the expressions inside the parentheses. Then, you need to multiply and divide the terms from left to right.

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

A: The order of operations (PEMDAS) is a set of rules that tells you which operations to perform first when you have multiple operations in an expression. The acronym PEMDAS stands for:

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

Q: How do I multiply rational algebraic expressions?

A: To multiply rational algebraic expressions, you need to multiply the numerators and denominators separately. For example, if you want to multiply 2x and 3x, you would multiply 2 and 3 to get 6, and then multiply x and x to get x².

Q: How do I divide rational algebraic expressions?

A: To divide rational algebraic expressions, you need to invert the divisor and multiply. For example, if you want to divide 2x by 3x, you would invert 3x to get 1/3x, and then multiply 2x by 1/3x to get 2/3.

Q: What is the difference between a rational algebraic expression and a polynomial?

A: A rational algebraic expression is a combination of variables and constants, and it can be simplified using various techniques. A polynomial, on the other hand, is a sum of terms, each of which is a product of a variable and a constant.

Q: How do I simplify a rational algebraic expression with variables and constants?

A: To simplify a rational algebraic expression with variables and constants, you need to follow the order of operations (PEMDAS). First, you need to evaluate the expressions inside the parentheses. Then, you need to multiply and divide the terms from left to right.

Q: What is the final answer to the problem 2-25 +5 9?

A: The final answer to the problem 2-25 +5 9 is 22.

Conclusion

In this section, we have answered some of the most frequently asked questions about rational algebraic expressions. We have learned how to simplify rational algebraic expressions, how to multiply and divide rational algebraic expressions, and how to simplify expressions with variables and constants.

By following the order of operations and using the techniques we have learned, we can simplify even the most complex rational algebraic expressions.

Final Answer

The final answer is 22.

Additional Resources

If you want to learn more about rational algebraic expressions, we recommend checking out the following resources:

Khan Academy: Rational Algebraic Expressions
Mathway: Rational Algebraic Expressions
Wolfram Alpha: Rational Algebraic Expressions

We hope this article has been helpful in answering your questions about rational algebraic expressions. If you have any further questions, please don't hesitate to ask.