Problem 30 - Algebra A Combined Function

Question

Perform each indicated operation. $$ 5^{2}-11+3(-5) $$

Step-by-Step Solution

Answer

The result is -1.

Step 1: Evaluate Exponents

The expression begins with simplifying the term with the exponent. Evaluate \(5^2\):\[5^2 = 25\]

Step 2: Simplify Multiplication

Next, simplify the multiplication part of the expression. Calculate \(3(-5)\):\[3(-5) = -15\]

Step 3: Combine the Terms

Now that we have evaluated the exponent and the multiplication, substitute these values back into the expression and simplify:\[25 - 11 - 15\]

Step 4: Perform Subtraction

Perform the subtraction operations from left to right:First, calculate \(25 - 11\):\[25 - 11 = 14\]Then calculate \(14 - 15\):\[14 - 15 = -1\]

Key Concepts

Exponents

Exponents are a way to express repeated multiplication of a number by itself. When you see a number like \(5^2\), this is read as "five squared" and it represents the number 5 multiplied by itself a total of two times. So, \(5^2 = 5 \times 5 = 25\). Think of an exponent as a small number above a regular number, signaling how many times you multiply the base number by itself. When tackling algebra problems, always solve exponents first according to the order of operations. This is important because it drastically simplifies the problem early, making subsequent steps easier.

Multiplication

Multiplication is one of the most common operations in math, essential for simplifying expressions and solving equations. In algebra, multiplication is often indicated by parentheses or the multiplication symbol \(\times\). For example, in the expression \(3(-5)\), the number 3 is being multiplied by -5. Calculating this gives \(3 \times (-5) = -15\). **Negative Numbers in Multiplication**: When you are multiplying a positive number by a negative number, like \(3(-5)\) in this exercise, the result is always negative. Understanding the rules of multiplication with negative numbers helps to avoid common mistakes. Simply multiply the absolute values of the numbers and give the product a negative sign.

Subtraction

Subtraction involves taking one number away from another. It's a straightforward concept, but in algebra, you'll often see it combined with other operations. Let’s look at the expression: \(25 - 11 - 15\). To solve this, handle the subtraction from left to right. First, subtract 11 from 25 to get 14. Then, subtract 15 from 14 to reach the final solution: \(14 - 15 = -1\). **Order Matters**: Remember, subtraction is not commutative, which means changing the order will affect the result. Always perform subtraction in the order given in the problem to ensure accuracy.