Problem 7 - Fundamentals of Mathematics

Question

Determine the value of each of the following. \((17+8)+(9+20)\)

Step-by-Step Solution

Answer

The value of the expression \((17+8)+(9+20)\) is 54.

Step 1: Solve the Inner Parentheses

First, solve the expressions inside the parentheses separately. For the first parentheses, add 17 and 8: \[ 17 + 8 = 25 \]For the second parentheses, add 9 and 20: \[ 9 + 20 = 29 \]

Step 2: Add the Results from Step 1

Now, add the results obtained from each set of parentheses: \[ 25 + 29 = 54 \]

Key Concepts

Addition

Addition is one of the most basic yet essential operations in mathematics. It combines two or more numbers into a single sum. Understanding how addition works helps in tackling more complex math problems.

In the exercise, "Determine the value of each of the following: \((17+8)+(9+20)\)," addition is used to combine values to find a total sum. First, calculate each separate group of numbers inside the parentheses. This requires you to add the numbers 17 and 8 together to begin with:

• The equation becomes \(17 + 8 = 25\).

Then, perform the same operation on the second set of numbers, 9 and 20:

• Here, it results in \(9 + 20 = 29\).

Finally, add these results together:

• Add 25 and 29, which equals 54.

Through these simple steps, addition helps you find combined sums and eventually solve the entire expression.

Parentheses

Parentheses are critical symbols used in mathematics to determine the order of operations. They indicate which parts of an arithmetic expression should be solved first. Ignoring them can lead to incorrect results. In the given problem, parentheses clarify which operations need to be prioritized.

The expression given is \((17+8)+(9+20)\). Here, parentheses group numbers together to specify that the values inside each set should be calculated first. This ensures the order of operations is maintained, starting by solving these grouped values before moving to any operation outside the parentheses.

You begin by addressing the first parentheses: Add the numbers 17 and 8. Once solved, proceed to the second parentheses by adding 9 and 20. These steps ensure each part is correctly completed before combining the results. This reliance on parentheses is why they're so crucial in solving arithmetic expressions.

Arithmetic Expressions

Arithmetic expressions are combinations of numbers and operations, such as addition, subtraction, multiplication, and division, arranged to form a problem. Solving them often requires an understanding of specific rules, known as the order of operations.

In the question \((17+8)+(9+20)\), the arithmetic expression consists of addition operations inside parentheses to be evaluated separately. Each part of the expression needs to be solved with respect to order of operations guidelines:

• First, solve any operations within parentheses.
• Next, proceed to other operations outside them.

By recognizing the individual parts of the arithmetic expression and computing them step-by-step, you achieve a logical and correct result. The final step involves adding the intermediate values obtained from evaluating the expressions inside the parentheses, leading to the overall outcome of 54.