Solve Decimal Division: 0.9 ÷ (-0.15) Step-by-Step

Q: Why is the answer negative when I'm dividing decimals?

The sign rule applies to all division, including decimals! Since we're dividing a positive number (0.9) by a negative number (-0.15), the result must be negative.

Q: Do I have to convert decimals to fractions?

Not always! Converting to fractions like $ \frac{9}{10} ÷ \frac{15}{100} $ can make the division clearer, but you can also divide decimals directly: 0.9 ÷ 0.15 = 6, then apply the negative sign.

Q: How do I remember the sign rules for division?

Use this simple pattern: Same signs = Positive, Different signs = Negative. Since we have (+) ÷ (-), the signs are different, so the answer is negative.

Q: Can I check my answer without doing the whole problem over?

Yes! Multiply your answer by the divisor: $ -6 × (-0.15) = 0.9 $. If you get the original dividend, your answer is correct!

Decimal Division with Negative Numbers

Solve the following expression:

$(+0.9):(-0.15)=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's solve the problem together.

00:12 Remember, when you divide a positive number by a negative number, the result is always negative.

00:23 First, change decimal numbers into fractions for easier manipulation.

00:28 Next, rewrite division as multiplication using a reciprocal. This means flipping the fraction.

00:36 Switch the numerator and the denominator in the fraction.

00:40 Now, let's simplify everything we can. This is called reducing the fractions.

00:46 Remember to multiply the numerators together and multiply the denominators together.

00:55 For example, factor 90 into 3 times 30.

00:59 Keep reducing as much as possible until you cannot simplify anymore.

01:04 And that's how we find the solution to this question. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve the following expression:

$(+0.9):(-0.15)=$

Step-by-step solution

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

$+:-=-$

First, let's convert the numbers in the exercise to simple fractions:

$0.9=-\frac{9}{10}$

$0.15=\frac{15}{100}$

Resulting in the following exercise:

$-(\frac{9}{10}:\frac{15}{100})=$

Let's convert the division to multiplication, don't forget to switch between numerator and denominator:

$-(\frac{9}{10}\times\frac{100}{15})=$

Let's reduce by 10 and obtain the following:

$-(9\times\frac{10}{15})=$

Let's combine into one exercise:

$-(\frac{9\times10}{15})=-\frac{90}{15}$

Let's break down 90 into a multiplication exercise:

$-\frac{3\times30}{15}=$

Let's reduce the numerator and denominator by 15 and obtain:

$-3\times2=-6$

Final Answer

$-6$

Key Points to Remember

Essential concepts to master this topic

Rule: Positive divided by negative equals negative result
Technique: Convert to fractions: 0.9 = 9/10, 0.15 = 15/100
Check: Verify -6 × (-0.15) = 0.9 ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign in the final answer
Don't ignore sign rules and write 6 instead of -6! When dividing positive by negative, the result must be negative. Always apply the sign rule: positive ÷ negative = negative.

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 I'm dividing decimals?

The sign rule applies to all division, including decimals! Since we're dividing a positive number (0.9) by a negative number (-0.15), the result must be negative.

Do I have to convert decimals to fractions?

Not always! Converting to fractions like $\frac{9}{10} ÷ \frac{15}{100}$ can make the division clearer, but you can also divide decimals directly: 0.9 ÷ 0.15 = 6, then apply the negative sign.

How do I remember the sign rules for division?

Use this simple pattern: Same signs = Positive, Different signs = Negative. Since we have (+) ÷ (-), the signs are different, so the answer is negative.

Can I check my answer without doing the whole problem over?

Yes! Multiply your answer by the divisor: $-6 × (-0.15) = 0.9$ . If you get the original dividend, your answer is correct!

What if I get confused with all the fraction steps?

Try the direct method first: divide 0.9 by 0.15 to get 6, then apply the sign rule to get -6. The fraction method is just another way to show the same work!

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