Solve: Adding Negative 0.85 and Positive 2.25 in Decimal Operations

Q: Why do I subtract when the problem shows addition?

When you add numbers with opposite signs, you're really finding the difference between their distances from zero. Think of it as: which number "wins" and by how much?

Q: How do I know which sign the answer should have?

The answer takes the sign of the number with the larger absolute value. Since 2.25 > 0.85, and 2.25 is positive, the answer is positive!

Q: Can I use the number line for all decimal addition?

Absolutely! The number line is a great visual tool. Positive numbers move right, negative numbers move left. Your final position is the answer.

Q: Why does the explanation use 2.25 - 0.85?

This uses the commutative property! Since we're finding the difference between absolute values, we can rearrange to subtract the smaller from the larger: easier mental math!

Decimal Addition with Opposite Sign Numbers

$(-0.85)+(+2.25)=$ ?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Find the point (-0.85) on the axis

00:08 To add, we'll move to the right (positive) on the axis

00:17 We'll use the commutative law and arrange the exercise

00:22 We'll use long subtraction for calculation

00:38 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

$(-0.85)+(+2.25)=$ ?

Step-by-step solution

First, locate -0.85 on the number line and note that we are moving 2.25 steps to the right:

Then use the commutative property:

$2.25-0.85=$

Finally, solve vertically:

$2.25\\-0.85\\=1.40$

Final Answer

$1.4$

Key Points to Remember

Essential concepts to master this topic

Rule: Adding opposite signs means subtract smaller from larger absolute value
Technique: Use number line movement: start at -0.85, move right +2.25
Check: Verify that 2.25 - 0.85 = 1.40 by vertical subtraction ✓

Common Mistakes

Avoid these frequent errors

Adding the absolute values instead of subtracting
Don't add 0.85 + 2.25 = 3.10! When signs are opposite, you must subtract the smaller absolute value from the larger. Always think: different signs means subtract, then use the sign of the larger number.

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 when the problem shows addition?

When you add numbers with opposite signs, you're really finding the difference between their distances from zero. Think of it as: which number "wins" and by how much?

How do I know which sign the answer should have?

The answer takes the sign of the number with the larger absolute value. Since 2.25 > 0.85, and 2.25 is positive, the answer is positive!

Can I use the number line for all decimal addition?

Absolutely! The number line is a great visual tool. Positive numbers move right, negative numbers move left. Your final position is the answer.

What if both decimals were negative?

If both numbers are negative, like (-0.85) + (-2.25), you would add their absolute values and keep the negative sign: -3.10.

Why does the explanation use 2.25 - 0.85?

This uses the commutative property! Since we're finding the difference between absolute values, we can rearrange to subtract the smaller from the larger: easier mental math!

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