Problem 26 - Algebra 1

Question

Find the sum. $$14+(-11)$$

Step-by-Step Solution

Answer

The sum of 14 and -11 is 3

Step 1: Identify the operation

The operation to be performed is \(14 + (-11)\), which is essentially the same as \(14 - 11\). This is because addition of a negative number is the same as subtraction of the absolute value of that number.

Step 2: Perform the operation

Perform the subtraction operation. Subtract 11 from 14.

Step 3: Write down the answer

After performing the subtraction, the result is 3

Key Concepts

Addition of Integers

Adding integers is like mixing two worlds, the positive and the negative. When you add integers, you can think of it as taking steps forwards or backwards on a number line.

• When you have two positive numbers, add them normally.
• When you have two negative numbers, treat both numbers as positive and then put a negative sign in front of the result.

Adding a positive number to a negative number involves thinking about which has the greater absolute value. Essentially, you lose some from the bigger side:- In the example given, adding \(14 + (-11)\) results in taking 11 steps back from 14, resulting in a positive 3.
- This operation can also be seen as subtraction. So you get \(14 - 11 = 3\).
Grasping this can make integer addition much easier! Watch out for those negative signs ruling the addition!

Subtraction of Integers

Subtraction of integers might seem tricky because we often need to flip between adding and subtracting. This operation is about finding the difference between two numbers.
Remember these simple guides:

• If both numbers are positive, subtract normally.
• If both numbers are negative, turn it around. Subtract their absolute values to get the answer, then switch the sign appropriately.

What if there’s a mix? Here's how you do it:- When you subtract a negative number, it actually turns into addition. For instance, \(10 - (-5)\) becomes \(10 + 5\).- In our example, what you're performing is essentially \(14 - 11\), leading us to 3.
Keep the order in mind: switching numbers around changes the result!

Absolute Value

Absolute value is a useful concept that always brings us to the positive side of things. Think of it like looking at the distance a number is from zero on a number line, regardless of its direction.
It is denoted with vertical lines, like this: \(|x|\).

• For positive numbers and zero, the absolute value is the number itself.
• For negative numbers, it is just the positive counterpart of the number.

Using the absolute value helps clarify operations involving negative numbers:- In our solved problem \(||-11||\), the absolute value of -11 is 11.
Absolute values are key to simplifying integer operations, making complex calculations clearer and neater.