Solve 14 + (-19): Adding Positive and Negative Integers on a Number Line

Q: Why do I move left when adding a negative number?

Adding a negative number is the same as subtracting! So $ 14 + (-19) $ equals $ 14 - 19 $. Since subtraction means "take away," you move left on the number line.

Q: How do I know how many steps to move?

Look at the absolute value of the negative number. For $ +(-19) $, ignore the negative sign and move 19 steps. The negative sign just tells you which direction to go!

Q: Can I just ignore the parentheses around -19?

Never ignore the parentheses! They show that -19 is being added, not subtracted. Without parentheses, $ 14 - 19 $ looks different but means the same thing as $ 14 + (-19) $.

Q: How can I check my answer without the number line?

Use basic subtraction: $ 14 - 19 = -5 $. Or think of it as "What number plus 19 equals 14?" Since $ -5 + 19 = 14 $, your answer is correct!

Integer Addition with Number Line Movement

Solve the following expression using the number line below:

$14+(-19)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 According to the exercise, we'll start from point 14 on the positive side (right)

00:06 The number is directed and negative

00:10 The negative direction on the axis is to the left, so we'll take 19 to the left

00:31 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following expression using the number line below:

$14+(-19)=$

Step-by-step solution

Let's begin by locating the number 14 on the number line.

Let's proceed to handle the operation in the exercise, given that the operation is $+(-19)$

Since minus 19 is less than 0, we will move nineteen steps to the left from the number 14, where each step represents one whole number as follows:

We can see that the number we reached is minus 5.

Final Answer

$-5$

Key Points to Remember

Essential concepts to master this topic

Starting Point: Begin at the first number on the number line
Direction Rule: Adding negative numbers means moving left: 14 + (-19) = move 19 steps left
Final Position: Count your ending position carefully: 14 - 19 = -5 ✓

Common Mistakes

Avoid these frequent errors

Moving in the wrong direction when adding negatives
Don't move right when adding negative numbers like +(-19) = wrong positive result! Adding a negative is the same as subtracting, so you must move left on the number line. Always remember: adding negatives means moving left, adding positives means moving right.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

Why do I move left when adding a negative number?

Adding a negative number is the same as subtracting! So $14 + (-19)$ equals $14 - 19$ . Since subtraction means "take away," you move left on the number line.

How do I know how many steps to move?

Look at the absolute value of the negative number. For $+(-19)$ , ignore the negative sign and move 19 steps. The negative sign just tells you which direction to go!

What if I end up with a negative answer?

That's completely normal! When you start with a positive number but subtract (or add a negative) a larger number, you'll always get a negative result. $14 + (-19) = -5$ makes perfect sense.

Can I just ignore the parentheses around -19?

Never ignore the parentheses! They show that -19 is being added, not subtracted. Without parentheses, $14 - 19$ looks different but means the same thing as $14 + (-19)$ .

How can I check my answer without the number line?

Use basic subtraction: $14 - 19 = -5$ . Or think of it as "What number plus 19 equals 14?" Since $-5 + 19 = 14$ , your answer is correct!

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