Problem 52 - Elementary Algebra

Question

For exercises 1-80, evaluate. $$ 3+5(11-5) \div 3 $$

Step-by-Step Solution

Answer

The final answer is 13.

Step 1: Parentheses

First, solve the expression inside the parentheses. Evaluate \(11 - 5\).

Step 2: Simplify Parentheses

Calculate \(11 - 5\) which equals 6. So, the expression becomes \(3 + 5(6) \div 3\).

Step 3: Multiplication

Next, perform the multiplication. Calculate \(5 \times 6\).

Step 4: Simplify Multiplication

Calculate \(5 \times 6\) which equals 30. So, the expression now is \(3 + 30 \div 3\).

Step 5: Division

Then, carry out the division. Calculate \(30 \div 3\).

Step 6: Simplify Division

Calculate \(30 \div 3\) which equals 10. So, the expression now is \(3 + 10\).

Step 7: Addition

Finally, perform the addition. Calculate \(3 + 10\).

Step 8: Final Answer

Calculate \(3 + 10\) which equals 13.

Key Concepts

parentheses in math

When solving math expressions, parentheses are always handled first. Parentheses help to group parts of an expression that need to be calculated together. In our exercise, we start with the expression inside the parentheses:

• Step 1: Identify the parentheses in the expression: \( 11 - 5 \)
• Step 2: Evaluate the expression inside the parentheses. So, calculate \( 11 - 5 \) to get 6.

This simplifies our original expression to: 3 + 5(6) ÷ 3.

multiplication in algebra

After parentheses, we handle multiplication and division from left to right. In our simplified expression, we now need to carry out the multiplication: \( 5(6) \).Multiplication in algebra is the process of combining numbers. Here’s what you do:

• Step 1: Identify the multiplication part of the expression: \( 5 \times 6 \)
• Step 2: Calculate \( 5 \times 6 \) which equals 30.

This changes our expression to: 3 + 30 ÷ 3.

division operations

Next, we perform the division in our expression. Just like with multiplication, we handle division from left to right: \( 30 ÷ 3 \).Division involves splitting a number into equal parts. Here’s the process:

• Step 1: Identify the division part: \( 30 ÷ 3 \)
• Step 2: Calculate \( 30 ÷ 3 \) to get 10.

So, the expression becomes: 3 + 10.

addition in math expressions

Finally, we perform the addition. Addition is combining two numbers to get a sum. In our remaining expression, we have: \( 3 + 10 \). Here’s how we do it:

• Step 1: Identify the addition part: \( 3 + 10 \)
• Step 2: Calculate \( 3 + 10 \) which equals 13.

So the final value of the expression is: 13.

step by step solutions in algebra

In algebra, following a step-by-step approach ensures you get the right answer. The order of operations is crucial. Always start with parentheses, followed by multiplication and division (left to right), and complete with addition and subtraction. Recapping our steps:

• Step 1: Solve inside parentheses: \( 11 - 5 \)
• Step 2: Simplify to get: \( 3 + 5(6) ÷ 3 \)
• Step 3: Perform multiplication to get: \( 3 + 30 ÷ 3 \)
• Step 4: Perform the division to get: \( 3 + 10 \)
• Step 5: Perform the addition to get the final answer: 13.

This structured process helps avoid mistakes and simplifies solving complex math problems.