Problem 17 - Prealgebra

Question

Find the value of each expression. $$12 \div 3+21$$

Step-by-Step Solution

Answer

The value of the expression is 25.

Step 1: Division

Start by performing the division operation in the expression. Divide 12 by 3, which simplifies to 4. So the expression becomes 4 + 21.

Step 2: Addition

Now, add the result of the division to 21. Calculate 4 + 21, which equals 25.

Key Concepts

Division

Division is a fundamental arithmetic operation that involves splitting a quantity into equal parts. When you divide, you essentially ask how many times one number (the divisor) fits into another (the dividend). For instance, dividing 12 by 3 answers the question: "How many groups of 3 fit into 12?"

To divide 12 by 3, you calculate:

• Identify the dividend (12) and the divisor (3).
• Determine how many times the divisor fits into the dividend without exceeding it.
• This results in 12 divided by 3 equaling 4, since 3 times 4 equals 12.

Understanding division is crucial for solving arithmetic problems accurately. It is applied in various situations, from dividing a pizza among friends to understanding larger mathematical concepts later on.

Addition

Addition is the process of combining two or more numbers to find their total. It's one of the first arithmetic operations we learn. In our context, after performing the initial division, we have a simple addition to complete: 4 + 21.

Here's how you can think about addition:

• It involves taking two numbers and putting them together to get a larger number.
• For example, with 4 + 21, we start at 4 and count up 21 places to reach 25.
• Ensure that the units are added first, then tens, hundreds, and so on, if dealing with larger numbers, although that is a more advanced concept.

Knowing how to add correctly is essential for everyday calculations, from adding prices while shopping to balancing budgets.

Order of Operations

In arithmetic, the order of operations is a rule we follow to solve expressions correctly. This is essential when multiple operations are involved. The rule is captured in the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Understanding this order helps in solving expressions without mistakes.

For the expression provided, 12 ÷ 3 + 21, our focus is on the multiplication and division before addition and subtraction.

• First, we perform the division: 12 ÷ 3 = 4.
• Next, move on to addition: 4 + 21 = 25.

By adhering to the order of operations, you can ensure that the steps are followed systematically, leading to the correct answer, as operations performed out of order could lead to incorrect results.