Solve Division Problem: (+3) ÷ (-0.05) with Signed Numbers

Q: Why is the answer negative when 3 is positive?

The sign rule for division states that when you divide numbers with different signs, the result is always negative. Since (+3) and (-0.05) have different signs, the answer must be negative.

Q: How do I divide by a decimal like -0.05?

Convert the decimal to a fraction first! $ -0.05 = -\frac{5}{100} = -\frac{1}{20} $. Then dividing by a fraction means multiplying by its reciprocal: $ 3 ÷ (-\frac{1}{20}) = 3 × (-20) = -60 $.

Q: Can I just ignore the signs and add them back later?

No! Always keep track of signs throughout your calculation. The sign rules must be applied during the division process, not added as an afterthought.

Q: What's the difference between (+3) ÷ (-0.05) and (-3) ÷ (+0.05)?

Both give the same result: -60! In division, what matters is whether the signs are the same (positive result) or different (negative result). Both cases have different signs.

Q: How can I check if -60 is correct?

Use multiplication to verify: $ (-60) × (-0.05) $. Since both numbers are negative, the result is positive: $ (-60) × (-0.05) = +3 $ ✓

Division of Signed Numbers with Decimals

$(+3):(-0.05)=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Positive divided by negative is always negative

00:16 Convert from decimal to fraction

00:20 Write division as multiplication by reciprocal

00:25 Switch between numerator and denominator

00:30 Calculate the quotient

00:34 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

$(+3):(-0.05)=\text{ ?}$

Step-by-step solution

Firstly we need to realise that since we are dividing two negative numbers, the result must be a positive number.

$+:-=-$

Next, let's convert 0.05 into a simple fraction:

$-0.05=-\frac{5}{100}$

We are left with:

$-(3:\frac{5}{100})=$

Then let's convert the division into multiplication, remembering to switch the numerator and denominator:

$-(3\times\frac{100}{5})=$

Finally we can continue solving to find the answer:

$-(3\times20)=-60$

Final Answer

$-60$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive divided by negative always gives negative result
Technique: Convert $-0.05 = -\frac{5}{100} = -\frac{1}{20}$ for easier division
Check: Verify $(-60) \times (-0.05) = +3$ ✓

Common Mistakes

Avoid these frequent errors

Incorrectly applying sign rules for division
Don't think positive ÷ negative = positive because "division makes things smaller"! This ignores sign rules and gives +60 instead of -60. Always remember: different signs in division always produce a negative result.

Practice Quiz

Test your knowledge with interactive questions

What will be the sign of the result of the next exercise?

$(-2)\cdot(-4)=$

FAQ

Everything you need to know about this question

Why is the answer negative when 3 is positive?

The sign rule for division states that when you divide numbers with different signs, the result is always negative. Since (+3) and (-0.05) have different signs, the answer must be negative.

How do I divide by a decimal like -0.05?

Convert the decimal to a fraction first! $-0.05 = -\frac{5}{100} = -\frac{1}{20}$ . Then dividing by a fraction means multiplying by its reciprocal: $3 ÷ (-\frac{1}{20}) = 3 × (-20) = -60$ .

Can I just ignore the signs and add them back later?

No! Always keep track of signs throughout your calculation. The sign rules must be applied during the division process, not added as an afterthought.

What's the difference between (+3) ÷ (-0.05) and (-3) ÷ (+0.05)?

Both give the same result: -60! In division, what matters is whether the signs are the same (positive result) or different (negative result). Both cases have different signs.

How can I check if -60 is correct?

Use multiplication to verify: $(-60) × (-0.05)$ . Since both numbers are negative, the result is positive: $(-60) × (-0.05) = +3$ ✓

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