Solve Division Problem: (+24) ÷ (-0.4) with Sign Rules

Q: Why is the answer negative when 24 and 0.4 are both numbers I can count?

The sign tells us the direction! (+24) is positive 24, but (-0.4) is negative 0.4. When you divide a positive by a negative, the result is always negative. Think of it like: how many negative 0.4s fit into positive 24?

Q: Can I just ignore the signs and add them at the end?

Never ignore signs! They're part of the numbers. However, you can remember: different signs = negative result, same signs = positive result. So (+) ÷ (-) = (-) means your answer will be negative.

Q: Why did we convert 0.4 to a fraction instead of keeping it as a decimal?

Both ways work! Converting to $ \frac{4}{10} $ makes the division easier to see: $ 24 ÷ \frac{4}{10} = 24 \times \frac{10}{4} $. You could also think: 24 ÷ 0.4 = 240 ÷ 4 = 60.

Q: How can I double-check my answer is correct?

Use multiplication to check division! If (-60) × (-0.4) = +24, then your answer is right. Remember: negative times negative equals positive, which matches our original +24.

Q: What's the easiest way to remember sign rules for division?

Same signs give positive, different signs give negative. Just like multiplication! (+) ÷ (+) = (+)(-) ÷ (-) = (+)(+) ÷ (-) = (-)(-) ÷ (+) = (-)

Division of Signed Numbers with Decimals

Solve the following problem:

$(+24):(-0.4)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:05 Positive divided by negative is always negative

00:16 Convert from decimal to fraction

00:23 Write division as multiplication by reciprocal

00:27 Switch between numerator and denominator

00:34 Make sure to multiply numerator by numerator and denominator by denominator

00:40 Divide 24 by 4

00:45 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 problem:

$(+24):(-0.4)=$

Step-by-step solution

Given that we are dividing a positive number by a negative number, the result must be a negative number:

$+:-=-$

First, let's convert 0.4 to a simple fraction:

$0.4=\frac{4}{10}$

Now we have the problem:

$-(24:\frac{4}{10})=$

Let's convert the division to multiplication, remembering to switch the numerator and denominator:

$-(24\times\frac{10}{4})=$

We'll simplify by 4 as follows:

$-(6\times10)=-6\times10=-60$

Final Answer

$-60$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Positive divided by negative always equals negative
Technique: Convert $0.4 = \frac{4}{10}$ then multiply by reciprocal
Check: Verify $-60 \times (-0.4) = +24$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign in the final answer
Don't calculate 24 ÷ 0.4 = 60 and forget the signs! This gives a positive answer when dividing positive by negative should be negative. Always apply sign rules first: (+) ÷ (-) = (-), then calculate the magnitude.

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 24 and 0.4 are both numbers I can count?

The sign tells us the direction! (+24) is positive 24, but (-0.4) is negative 0.4. When you divide a positive by a negative, the result is always negative. Think of it like: how many negative 0.4s fit into positive 24?

Can I just ignore the signs and add them at the end?

Never ignore signs! They're part of the numbers. However, you can remember: different signs = negative result, same signs = positive result. So (+) ÷ (-) = (-) means your answer will be negative.

Why did we convert 0.4 to a fraction instead of keeping it as a decimal?

Both ways work! Converting to $\frac{4}{10}$ makes the division easier to see: $24 ÷ \frac{4}{10} = 24 \times \frac{10}{4}$ . You could also think: 24 ÷ 0.4 = 240 ÷ 4 = 60.

How can I double-check my answer is correct?

Use multiplication to check division! If (-60) × (-0.4) = +24, then your answer is right. Remember: negative times negative equals positive, which matches our original +24.

What's the easiest way to remember sign rules for division?

Same signs give positive, different signs give negative. Just like multiplication!

(+) ÷ (+) = (+)
(-) ÷ (-) = (+)
(+) ÷ (-) = (-)
(-) ÷ (+) = (-)

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