Problem 2 - Fundamentals of Mathematics

Question

Determine the value of each of the following. $$5+(7 \cdot 9)$$

Step-by-Step Solution

Answer

68

Step 1: Identify the Components

The expression given is \[ 5 + (7 \cdot 9) \]Here, we see that inside the parentheses, we have a multiplication operation \(7 \cdot 9\) that needs to be addressed first.

Step 2: Solve the Multiplication

Calculate the result of the expression inside the parentheses: \[ 7 \cdot 9 = 63 \]This simplifies the expression to \[ 5 + 63 \]

Step 3: Solve the Addition

Now, add the remaining numbers together:\[ 5 + 63 = 68 \]

Step 4: Conclusion

The final result of the expression \(5 + (7 \cdot 9)\) is 68.

Key Concepts

Multiplication

Understanding multiplication is essential in solving math problems accurately. It involves combining equal groups to find the total number of items present. In the expression \(5 + (7 \cdot 9)\), the multiplication occurs inside the parentheses with \(7 \cdot 9\). This means you have seven groups of nine. Wouldn't it be the same as adding nine, seven times? That’s exactly what multiplication does for us. Here’s how:

• The symbol \( \cdot \) indicates multiplication.
• \(7\) (the multiplicand) tells us how many times to use the number \(9\) (the multiplier).
• Performing \(7 \cdot 9\) gives you \(63\), which simplifies the problem significantly.

Remember, mastering multiplication can speed up your calculations and make solving complex problems much easier.

Addition

Addition is one of the basic operations in mathematics, used to bring numbers together to find their sum. After we have solved the multiplication in the expression \(7 \cdot 9\), we are left with the addition part: \(5 + 63\). Here's what you need to know:

• Addition is represented by the symbol \( + \).
• When you add two numbers, like \(5\) and \(63\), it means combining them into a single new amount.
• For the given expression, \(5 + 63\), the sum is \(68\).

It is vital to understand that addition is used to accumulate values into a larger total. Whether dealing with single digits or complex expressions, addition combines everything together.

Parentheses

When it comes to order of operations, parentheses are a crucial part of mathematical expressions. They indicate which calculations should be performed first. In the expression \(5 + (7 \cdot 9)\), notice that the operation \(7 \cdot 9\) is inside the parentheses. This prioritizes it over addition, highlighting its significance:

• Operations inside parentheses must be dealt with before addressing other operations outside them.
• They clarify which part of the problem needs solving first, ensuring that the subsequent steps provide accurate results.
• Grouping numbers and operations within parentheses also helps manage complex expressions efficiently.

Overall, parentheses are like an organizer in expressions, ensuring you perform operations in the correct order to arrive at the right answer.