Problem 49 - Elementary Algebra

Question

Rewrite the problem in a simpler form. $$ 6-(-14) $$

Step-by-Step Solution

Answer

Answer: 20

Step 1: Identify the operation and numbers involved

In the given expression, we are asked to perform subtraction between two numbers: 6 and -14.

Step 2: Apply the rule for subtracting negative numbers

When subtracting a negative number, we can change the subtraction operation to addition and change the sign of the number being subtracted. So, the expression becomes: $$ 6-(-14) = 6+14 $$

Step 3: Perform the addition

Now that we have converted the expression into an addition problem, we can simply add the two numbers: $$ 6+14 = 20 $$

Step 4: Write the simplified form

The simplified form of the given expression is 20.

Key Concepts

Subtracting Negative Numbers

Subtracting negative numbers can be a slightly confusing concept at first, but it's quite logical when broken down. When you see a subtraction sign followed by a negative number, such as in the expression \(6 - (-14)\), you can reframe the operation:

• Think of "subtracting a negative" as "adding a positive".
• This is because subtracting a negative number is equivalent to adding its positive counterpart.

In the given example, \(6 - (-14)\) becomes \(6 + 14\). By transforming the subtraction into an addition, you simplify the operation, making it easier to solve.

Addition of Integers

Adding integers is one of the foundational operations in arithmetic. To add integers, you align them according to their signs and perform the addition:

• If both numbers are positive, as with the 6 and 14 in our example, you simply add their absolute values: \(6 + 14\).
• If the integers had different signs, you would subtract the smaller absolute value from the larger one and keep the sign of the number with the larger absolute value.

In our problem, both numbers are positive because after changing \(-(-14)\) to \(+14\), they are directly added, resulting in \(20\).
Remember, the key with addition of integers is to watch the signs closely and apply the basic operations correctly.

Arithmetic Simplification

Arithmetic simplification involves reducing expressions to their simplest form. It often requires performing various operations on numbers step by step.

• Start by observing the initial expression and identify the basic operations involved.
• Apply the necessary arithmetic rules to transform the expression into a more manageable format.
• Finally, carry out the arithmetic operations to arrive at the simplest form.

For \(6 - (-14)\), simplification occurs as follows: first, apply the subtraction rule for negative numbers to transform it to \(6 + 14\). Then, perform the addition to get their sum, which is \(20\).
This process highlights how simplification helps in solving arithmetic expressions straightforwardly and efficiently.