Problem 33 - Elementary and Intermediate Algebra

Question

Simplify. $$ 9 \div 3+16 \div 8 $$

Step-by-Step Solution

Answer

5

Step 1: Divide 9 by 3

First, perform the division of 9 by 3. This calculation gives: \[ 9 \div 3 = 3 \]

Step 2: Divide 16 by 8

Next, divide 16 by 8. This calculation gives: \[ 16 \div 8 = 2 \]

Step 3: Add the results from Step 1 and Step 2

Finally, add the results of the previous two calculations together: \[ 3 + 2 = 5 \]

Key Concepts

Understanding Division

Division is one of the four basic arithmetic operations. It involves splitting a number (called the dividend) into a specified number of parts (denoted by the divisor). The result is called the quotient. In simple terms, division tells us how many times a number is contained within another number. For example, in the expression \(9 \div 3\), 9 is the dividend, 3 is the divisor, and the result 3 is the quotient.

Division is visually akin to distributing items into groups. If you have 9 apples and want to distribute them equally into 3 baskets, each basket will get 3 apples. Therefore, \(9 \div 3 = 3\).

• Dividend (what you are splitting): 9
• Divisor (into how many parts): 3
• Quotient (the result): 3 for each part

Understanding this concept is crucial for correctly solving arithmetic expressions that involve division. Let's now look more closely at addition.

Exploring Addition

Addition is the process of finding the total or sum by combining two or more numbers. It is another core arithmetic operation. In our example, after performing the division operations, we need to add the results.

Here is a quick refresher: Addition takes two or more addends and combines them into a single total. If we add the results of \(9 \div 3\) and \(16 \div 8\), we get \(3 + 2\). In this expression: \ 3\ and \2\ are the addends, and \5\ is the sum.

• First addend: 3 (result from the first division)
• Second addend: 2 (result from the second division)
• Sum: 5

Addition is a fundamental operation that combines separate values into a single, total value. Mastering addition is essential for solving more complex arithmetic problems.

Applying Step-by-Step Solutions

Solving arithmetic problems step-by-step is a powerful method to ensure accuracy and comprehension. Let's walk through the solution of the given problem step-by-step:

• Step 1: Divide the first pair of numbers. In this case, \(9 \div 3\). The result is 3.
• Step 2: Next, divide the second pair of numbers, \(16 \div 8\). The result is 2.
• Step 3: Finally, add the results from these two division operations: \ 3 + 2\. The final result is 5.

By breaking the problem into smaller, manageable steps, we simplify the process and make it easier to understand and solve. This approach can be applied to various arithmetic problems, enhancing both skills and confidence. Remember, tackling complex problems step-by-step can help avoid mistakes and make mathematics far more approachable.