Problem 74 - Algebra 1: Concepts and Skills

Question

NUMERICAL EXPRESSIONS Evaluate the expression. Then simplify the answer. (Lesson 1.3) $$ 9+12-4 $$

Step-by-Step Solution

Answer

The solution to the expression 9 + 12 - 4 equals 17.

Step 1: Addition

The first operation to perform is addition. So, add 9 and 12, which equals 21.

Step 2: Subtraction

The next operation is subtraction. Subtract 4 from the result of the addition operation. So, 21 - 4 equals 17.

Key Concepts

Addition

Addition is the mathematical operation where we combine two or more numbers to get a sum. This process is essential in forming the basis for other numerical operations.

• When performing addition, we start by lining up the numbers based on their place value — units under units, tens under tens, and so on.
• We then add from right to left, carrying over numbers if the sum of a column exceeds 9.

In the context of the expression given, we have the numbers 9 and 12. When we add these two numbers, we align them based on their place value:

• Start with the units: we add 9 (units place) to 12 (which is 10 + 2). This simple addition, 9 + 12, gives us 21.

Adding numbers helps in combining the values and preparing for subsequent operations like subtraction.

Subtraction

Subtraction is another fundamental numerical operation that involves taking one number away from another. It's like counting backward or figuring out the difference between two values.

• We start with two numbers: the minuend (the number we subtract from) and the subtrahend (the number we subtract).
• After setting the numbers correctly based on their place values, subtraction proceeds from right to left, borrowing if necessary.

In our expression, after adding 9 and 12 to get 21, we proceed with subtraction. Here, we subtract 4 from 21:

• The process involves reducing or looking backward by 4 units from 21, resulting in 17.

Subtraction allows us to find out what's left after removing a certain number, providing an essential tool for simplifying expressions.

Simplification

The simplification of a numerical expression is about reducing it to the simplest form by performing all possible operations.

• This process involves evaluating the expression step by step, as seen in our initial steps of addition and subtraction.
• The goal is to achieve a single, concise answer by methodically following the order of operations — like dealing with addition and then subtraction.

In the given exercise, we simplify by first addressing the addition, which gives 21. Following this, we perform subtraction, simplifying further to achieve the answer 17.

• Each operation's result becomes the starting point for the next, ensuring organized and systematic reduction of the expression.

Simplification helps us understand the core of mathematical expressions, removing complexity and making calculations straightforward.