Solve Integer Addition: (+301) + (-51) Step-by-Step

Q: Why do I subtract 51 instead of adding it?

Because adding a negative number is the same as subtracting! The rule $ +(-x) = -x $ means plus negative 51 becomes minus 51.

Q: What if the negative number was bigger than the positive one?

If you had $ (+51) + (-301) $, you'd get $ 51 - 301 = -250 $. The answer would be negative because you're subtracting a larger number from a smaller one.

Q: How can I visualize this on a number line?

Start at 301 on the number line, then move 51 steps to the left (because you're adding a negative). You'll land on 250. Moving left means subtracting!

Q: Do the parentheses around the numbers matter?

The parentheses help show the sign of each number clearly. $ (+301) $ is positive 301, and $ (-51) $ is negative 51. They prevent confusion about which numbers are positive or negative.

Q: Is there a faster way to solve this?

Yes! Once you recognize the pattern, you can immediately rewrite $ (+301) + (-51) $ as $ 301 - 51 $ and solve the subtraction directly.

Integer Addition with Negative Numbers

$(+301)+(-51)=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this together

00:08 First, find the point, 301, on the number line.

00:13 Positive times negative equals a negative. So, we'll subtract.

00:19 To subtract, move left on the number line. This is the negative dire ction.

00:26 Use long subtraction to carefully find the difference.

00:38 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$(+301)+(-51)=\text{ ?}$

Step-by-step solution

First, remember the rule:

$+(-x)=-x$

Place 301 on the number line and move 51 steps to the left:

Rewrite the exercise in the appropriate form and solve it:

$301-51=250$

Final Answer

$250$

Key Points to Remember

Essential concepts to master this topic

Rule: Adding a negative number means subtracting its absolute value
Technique: Rewrite $(+301) + (-51)$ as $301 - 51$
Check: Verify: $301 - 51 = 250$ and $250 + 51 = 301$ ✓

Common Mistakes

Avoid these frequent errors

Treating both numbers as positive and adding them
Don't add 301 + 51 = 352! This ignores the negative sign and gives the wrong answer. The parentheses around (-51) show it's negative. Always recognize that adding a negative number means subtracting.

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 subtract 51 instead of adding it?

Because adding a negative number is the same as subtracting! The rule $+(-x) = -x$ means plus negative 51 becomes minus 51.

What if the negative number was bigger than the positive one?

If you had $(+51) + (-301)$ , you'd get $51 - 301 = -250$ . The answer would be negative because you're subtracting a larger number from a smaller one.

How can I visualize this on a number line?

Start at 301 on the number line, then move 51 steps to the left (because you're adding a negative). You'll land on 250. Moving left means subtracting!

Do the parentheses around the numbers matter?

The parentheses help show the sign of each number clearly. $(+301)$ is positive 301, and $(-51)$ is negative 51. They prevent confusion about which numbers are positive or negative.

Is there a faster way to solve this?

Yes! Once you recognize the pattern, you can immediately rewrite $(+301) + (-51)$ as $301 - 51$ and solve the subtraction directly.

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