Solve Division Problem: -66.6 ÷ -0.6 Step by Step

Q: Why do two negatives make a positive in division?

Think of it this way: dividing by a negative is like asking "how many times does this negative number go into another negative?" Since both numbers point in the same direction (negative), the result is positive!

Q: Do I have to convert decimals to fractions?

Not always! You can divide decimals directly: $ -66.6 ÷ -0.6 = 66.6 ÷ 0.6 = 111 $. Converting to fractions just makes the process clearer and helps avoid decimal errors.

Q: How do I know when to multiply by the reciprocal?

Division by a fraction always becomes multiplication by its reciprocal. So $ a ÷ \frac{b}{c} = a \times \frac{c}{b} $. Flip the second fraction and multiply!

Q: What if I get confused about which numbers to cancel?

Look for common factors in numerator and denominator. In $ \frac{666}{6} $, both 666 and 6 are divisible by 6, so $ \frac{666÷6}{6÷6} = \frac{111}{1} = 111 $.

Q: Can I just move the decimal point instead?

Yes! Since $ -66.6 ÷ -0.6 $, you can think: "0.6 goes into 66.6 how many times?" Move decimal in 0.6 one place right to get 6, then move decimal in 66.6 one place right to get 666. So $ 666 ÷ 6 = 111 $!

Division of Negative Decimals with Fraction Conversion

$-66.6:-0.6=\text{ ?}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Convert from decimal to fraction

00:16 Here too we'll convert from decimal to fraction

00:26 We'll substitute these fractions in our exercise

00:36 Division is also multiplication by the reciprocal

00:40 Let's swap the numerator and denominator

00:44 Let's reduce what we can

00:47 Negative times negative always equals positive

00:55 Let's factor the number 666 into factors 6 and 111

00:59 Let's reduce what we can

01:02 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$-66.6:-0.6=\text{ ?}$

Step-by-step solution

Let's convert 66.6 into a simple fraction:

$-66.6\times\frac{10}{10}=-\frac{666}{10}$

Let's then convert 0.6 into a simple fraction:

$-0.6=-\frac{6}{10}$

Now the exercise we have is:

$-\frac{666}{10}:-\frac{6}{10}=$

Let's next convert the division exercise into a multiplication exercise, remembering to switch the numerator and denominator in the second fraction:

$-\frac{666}{10}\times-\frac{10}{6}=$

Let's now reduce the 10 in both fractions to get:

$+\frac{666}{6}=$

next, we'll factor 666 into a multiplication exercise:

$\frac{6\times111}{6}=$

Finally, we reduce the 6 in the numerator and denominator of the fraction to get:

$+111$

Final Answer

$+111$

Key Points to Remember

Essential concepts to master this topic

Sign Rule: Negative divided by negative equals positive result
Technique: Convert $-66.6 \div -0.6$ to $-\frac{666}{10} \times -\frac{10}{6}$
Check: Multiply answer by divisor: $111 \times (-0.6) = -66.6$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting the negative sign rules
Don't assume negative ÷ negative = negative result = wrong answer like -111! Two negatives make a positive in division. Always remember: negative ÷ negative = positive, so the answer is +111.

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 do two negatives make a positive in division?

Think of it this way: dividing by a negative is like asking "how many times does this negative number go into another negative?" Since both numbers point in the same direction (negative), the result is positive!

Do I have to convert decimals to fractions?

Not always! You can divide decimals directly: $-66.6 ÷ -0.6 = 66.6 ÷ 0.6 = 111$ . Converting to fractions just makes the process clearer and helps avoid decimal errors.

How do I know when to multiply by the reciprocal?

Division by a fraction always becomes multiplication by its reciprocal. So $a ÷ \frac{b}{c} = a \times \frac{c}{b}$ . Flip the second fraction and multiply!

What if I get confused about which numbers to cancel?

Look for common factors in numerator and denominator. In $\frac{666}{6}$ , both 666 and 6 are divisible by 6, so $\frac{666÷6}{6÷6} = \frac{111}{1} = 111$ .

Can I just move the decimal point instead?

Yes! Since $-66.6 ÷ -0.6$ , you can think: "0.6 goes into 66.6 how many times?" Move decimal in 0.6 one place right to get 6, then move decimal in 66.6 one place right to get 666. So $666 ÷ 6 = 111$ !

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