Solve Decimal Division: -1.8 ÷ -0.09 Step-by-Step

Decimal Division with Negative Numbers

1.8:0.09= -1.8:-0.09=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 Convert from decimal to fraction
00:12 Here too we'll convert from decimal to fraction
00:25 Multiply by 10 to find a common denominator
00:39 Let's put it in our exercise
00:43 Division is also multiplication by the reciprocal
00:47 Switch between numerator and denominator
00:52 Reduce what we can
00:56 Negative times negative always equals positive
01:07 Break down 180 into factors of 9 and 20
01:10 Reduce what we can
01:13 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

1.8:0.09= -1.8:-0.09=

2

Step-by-step solution

Let's convert 1.8 to a simple fraction:

1.8=1810 -1.8=-\frac{18}{10}

Let's convert 0.09 to a simple fraction:

0.09=9100 -0.09=-\frac{9}{100}

Let's multiply the first fraction we got by 10 to get a common denominator of 100:

1810×1010=180100 -\frac{18}{10}\times\frac{10}{10}=-\frac{180}{100}

Now the exercise we got is:

180100:9100= -\frac{180}{100}:-\frac{9}{100}=

Let's convert the division exercise to a multiplication exercise, and don't forget to swap the numerator and denominator in the second fraction:

180100×1009= -\frac{180}{100}\times-\frac{100}{9}=

Let's reduce the 100 in both fractions and we get:

+1809= +\frac{180}{9}=

Let's break down 180 into a multiplication exercise:

9×209= \frac{9\times20}{9}=

Let's reduce the 9 in both the numerator and denominator of the fraction and we get:

+20 +20

3

Final Answer

+20 +20

Key Points to Remember

Essential concepts to master this topic
  • Sign Rule: Negative divided by negative equals positive
  • Technique: Convert decimals to fractions: -1.8 = -18/10, -0.09 = -9/100
  • Check: Verify 20 × (-0.09) = -1.8 matches original dividend ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting sign rules with negative numbers
    Don't assume negative ÷ negative = negative! This gives -20 instead of +20. When dividing two negatives, the negatives cancel out making the result positive. Always remember: same signs = positive 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 do I get positive 20 when both numbers are negative?

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Great question! When you divide two negative numbers, the result is always positive. Think of it as: negative ÷ negative = positive, just like how (-1) × (-1) = +1.

Can I just ignore the decimals and divide 18 by 9?

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Not quite! You need to account for decimal places. Converting to fractions like 180100÷9100 -\frac{180}{100} ÷ -\frac{9}{100} ensures you handle the decimals correctly.

What if I just move decimal points instead of using fractions?

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You can! Move the decimal point in both numbers the same number of places to make the divisor a whole number: -1.8 ÷ -0.09 becomes -180 ÷ -9 = +20.

How do I check if 20 is the right answer?

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Multiply your answer by the divisor: 20×(0.09)=1.8 20 × (-0.09) = -1.8 . If this equals your original dividend, you're correct!

Why convert to fractions when I can use long division?

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Both methods work! Converting to fractions helps you see the exact values and makes canceling easier. Choose whichever method feels more comfortable to you.

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