Copy And Complete The Following By Writing The Missing Numbers:a. 2 \times(5+9)=(2 \times 5)+\left(2 \times \_\right ]b. 7 × ( 5 + 10 ) = ( 7 × 5 ) + ( 7 × _ 7 \times(5+10)=(7 \times 5)+(7 \times \_ 7 × ( 5 + 10 ) = ( 7 × 5 ) + ( 7 × _ ]c. 5 × ( 50 + 6 ) = ( 5 × 50 ) + ( 5 × 6 5 \times(50+6)=(5 \times 50)+(5 \times 6 5 × ( 50 + 6 ) = ( 5 × 50 ) + ( 5 × 6 ]d. $8

Mastering the Order of Operations: A Guide to Simplifying Algebraic Expressions

In mathematics, the order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. This is crucial in simplifying algebraic expressions and ensuring that calculations are accurate. In this article, we will explore the order of operations and use it to simplify four algebraic expressions.

Understanding the Order of Operations

The order of operations is a mnemonic device that helps us remember the order in which operations should be performed. The acronym PEMDAS is commonly used to remember the order of operations:

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.

Simplifying Algebraic Expressions

Now that we have a good understanding of the order of operations, let's use it to simplify four algebraic expressions.

a. $2 \times(5+9)=(2 \times 5)+\left(2 \times \_\right)$

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

$5+9=14$

Now, we can rewrite the expression as:

$2 \times 14=(2 \times 5)+\left(2 \times \_\right)$

Next, we need to evaluate the multiplication operation:

$2 \times 14=28$

Now, we can rewrite the expression as:

$28=(2 \times 5)+\left(2 \times \_\right)$

To find the missing value, we need to evaluate the expression inside the parentheses:

$2 \times 5=10$

Now, we can rewrite the expression as:

$28=10+\left(2 \times \_\right)$

To find the missing value, we need to isolate it on one side of the equation. We can do this by subtracting 10 from both sides:

$28-10=\left(2 \times \_\right)$

Simplifying the left side of the equation, we get:

$18=\left(2 \times \_\right)$

Now, we can divide both sides of the equation by 2 to find the missing value:

$\frac{18}{2}=\_$

Simplifying the left side of the equation, we get:

$9=\_$

Therefore, the missing value is 9.

b. $7 \times(5+10)=(7 \times 5)+(7 \times \_$

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

$5+10=15$

Now, we can rewrite the expression as:

$7 \times 15=(7 \times 5)+(7 \times \_$

Next, we need to evaluate the multiplication operation:

$7 \times 15=105$

Now, we can rewrite the expression as:

$105=(7 \times 5)+(7 \times \_$

To find the missing value, we need to evaluate the expression inside the parentheses:

$7 \times 5=35$

Now, we can rewrite the expression as:

$105=35+(7 \times \_$

To find the missing value, we need to isolate it on one side of the equation. We can do this by subtracting 35 from both sides:

$105-35=\left(7 \times \_\right)$

Simplifying the left side of the equation, we get:

$70=\left(7 \times \_\right)$

Now, we can divide both sides of the equation by 7 to find the missing value:

$\frac{70}{7}=\_$

Simplifying the left side of the equation, we get:

$10=\_$

Therefore, the missing value is 10.

c. $5 \times(50+6)=(5 \times 50)+(5 \times 6$

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

$50+6=56$

Now, we can rewrite the expression as:

$5 \times 56=(5 \times 50)+(5 \times 6$

Next, we need to evaluate the multiplication operation:

$5 \times 56=280$

Now, we can rewrite the expression as:

$280=(5 \times 50)+(5 \times 6$

To find the missing value, we need to evaluate the expression inside the parentheses:

$5 \times 50=250$

Now, we can rewrite the expression as:

$280=250+(5 \times 6$

To find the missing value, we need to isolate it on one side of the equation. We can do this by subtracting 250 from both sides:

$280-250=\left(5 \times 6\right)$

Simplifying the left side of the equation, we get:

$30=\left(5 \times 6\right)$

Now, we can divide both sides of the equation by 5 to find the missing value:

$\frac{30}{5}=\_$

Simplifying the left side of the equation, we get:

$6=\_$

Therefore, the missing value is 6.

d. $8 \times(3+2)=(8 \times 3)+(8 \times \_$

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

$3+2=5$

Now, we can rewrite the expression as:

$8 \times 5=(8 \times 3)+(8 \times \_$

Next, we need to evaluate the multiplication operation:

$8 \times 5=40$

Now, we can rewrite the expression as:

$40=(8 \times 3)+(8 \times \_$

To find the missing value, we need to evaluate the expression inside the parentheses:

$8 \times 3=24$

Now, we can rewrite the expression as:

$40=24+(8 \times \_$

To find the missing value, we need to isolate it on one side of the equation. We can do this by subtracting 24 from both sides:

$40-24=\left(8 \times \_\right)$

Simplifying the left side of the equation, we get:

$16=\left(8 \times \_\right)$

Now, we can divide both sides of the equation by 8 to find the missing value:

$\frac{16}{8}=\_$

Simplifying the left side of the equation, we get:

$2=\_$

Therefore, the missing value is 2.

In conclusion, the order of operations is a crucial concept in mathematics that helps us simplify algebraic expressions. By following the order of operations, we can evaluate expressions and find the missing values. In this article, we used the order of operations to simplify four algebraic expressions and found the missing values.
Mastering the Order of Operations: A Guide to Simplifying Algebraic Expressions

Q&A: Frequently Asked Questions About the Order of Operations

In our previous article, we explored the order of operations and used it to simplify four algebraic expressions. However, we know that there are many more questions and concerns about the order of operations. In this article, we will address some of the most frequently asked questions about the order of operations.

Q: What is the order of operations?

A: The order of operations is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS is commonly used to remember the order of operations:

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: Why is the order of operations important?

A: The order of operations is important because it ensures that mathematical expressions are evaluated correctly. Without the order of operations, mathematical expressions can be ambiguous and lead to incorrect results.

Q: How do I remember the order of operations?

A: There are several ways to remember the order of operations. One way is to use the acronym PEMDAS. Another way is to use a mnemonic device, such as "Please Excuse My Dear Aunt Sally."

Q: What is the difference between multiplication and division?

A: Multiplication and division are both arithmetic operations that involve combining numbers. However, multiplication involves combining numbers by adding a number a certain number of times, while division involves finding the number that, when multiplied by another number, gives a certain result.

Q: How do I evaluate expressions with multiple operations?

A: To evaluate expressions with multiple operations, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, 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 order of operations for fractions?

A: The order of operations for fractions is the same as for whole numbers. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I use the order of operations for decimals?

A: Yes, you can use the order of operations for decimals. The order of operations for decimals is the same as for whole numbers. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I simplify expressions with variables?

A: To simplify expressions with variables, you need to follow the order of operations. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, 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 order of operations for negative numbers?

A: The order of operations for negative numbers is the same as for positive numbers. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

Q: Can I use the order of operations for complex numbers?

A: Yes, you can use the order of operations for complex numbers. The order of operations for complex numbers is the same as for real numbers. First, evaluate any expressions inside parentheses. Next, evaluate any exponential expressions. Then, evaluate any multiplication and division operations from left to right. Finally, evaluate any addition and subtraction operations from left to right.

In conclusion, the order of operations is a crucial concept in mathematics that helps us simplify algebraic expressions. By following the order of operations, we can evaluate expressions and find the missing values. We hope that this Q&A article has helped to clarify any questions or concerns you may have had about the order of operations.