What is the result of the equation 5x5-2+1x2

Result of the Equation

To solve the equation $5 \times 5 - 2 + 1 \times 2$:

1. First, handle the multiplication operations:

   $$5 \times 5 = 25 \quad \text{and} \quad 1 \times 2 = 2$$

2. Substitute these results back into the equation:

   $$25 - 2 + 2$$

3. Next, perform the subtraction and addition from left to right:

   $$25 - 2 = 23$$ $$23 + 2 = 25$$

Thus, the final result is:

Order of Operations (PEMDAS/BODMAS)

To solve mathematical expressions correctly, it's crucial to follow a specific sequence called the order of operations. This sequence ensures that calculations are performed consistently and accurately, avoiding ambiguities. There are two common mnemonics to remember this order:

PEMDAS:

• Parentheses
• Exponents (including roots, such as square roots)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

BODMAS:

• Brackets
• Orders (i.e., powers and roots, same as exponents)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Parentheses/Brackets

Parentheses and brackets indicate operations that should be performed first.

Exponents/Orders

After solving operations inside parentheses or brackets, handle exponents and orders next.

Multiplication and Division

These operations are performed next, moving from left to right across the expression.

Addition and Subtraction

Finally, perform all addition and subtraction operations, again from left to right.

Example Expression

Consider the expression:

1. Parentheses/Brackets: First solve inside the brackets:

2. Replace the original expression with the evaluated bracket:

3. Multiplication:

4. Addition and Subtraction:

Summary

By following PEMDAS/BODMAS, we ensure that our calculations are consistent and correct. The key is to remember the order:

1. Parentheses/Brackets
2. Exponents/Orders
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)

Adherence to this sequence avoids misunderstandings and errors in resolving mathematical expressions.

Explanation

Multiplication and substitution is a technique often used in algebra, particularly for solving systems of linear equations and manipulating algebraic expressions.

Multiplication

Multiplication involves scaling an equation or an expression by a constant factor. Here, the idea is to multiply both sides of an equation by the same non-zero constant to simplify or adjust coefficients. For example, consider the equation:

Multiplying both sides by a constant $k$ gives:

Substitution

Substitution involves replacing a variable with an equivalent expression from another equation. This method is especially useful when dealing with systems of equations. Consider the system of equations:

1. $x + y = 5$
2. $2x - y = 3$

First, we can solve the first equation for $y$:

Next, we substitute this expression for $y$ in the second equation:

Simplifying this equation:

Then, we substitute back to find $y$:

Thus, the solution to the system is:

Key Points

• Multiplication is used to adjust the coefficients of equations.
• Substitution is used to eliminate variables by replacing them with expressions from other equations.
• These methods are often applied in tandem to simplify and solve systems of equations.