Solve Chain Division: -81:-27·6:-2 Step by Step

Chain Division with Negative Numbers

81:276:2= -81:-27\cdot6:-2=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this problem together.
00:11 First, we can write each division as a fraction.
00:21 Remember, a negative divided by a negative is always positive.
00:32 And a negative divided by a positive is always negative.
00:43 Now, let’s break down eighty-one into factors: twenty-seven and three.
00:51 Next, let's break down six into factors: two and three.
00:59 Let's reduce the fractions as much as we can.
01:08 Positive times negative is always negative, so keep that in mind.
01:16 And that's how we find the solution to this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

81:276:2= -81:-27\cdot6:-2=

2

Step-by-step solution

Let's write the exercise as a multiplication of fractions:

(81:27)×(6:2)= (-81:-27)\times(6:-2)=

8127×62= \frac{-81}{-27}\times\frac{6}{-2}=

Note that in the first fraction we are dividing between two negative numbers, therefore the result must be a positive number.

Note that in the second fraction we are dividing between a positive number and a negative number, therefore the result must be a negative number.

Therefore:

8127×62= \frac{81}{27}\times-\frac{6}{2}=

Let's break down 81 into a multiplication exercise and 6 into a multiplication exercise:

27×327×2×32= \frac{27\times3}{27}\times-\frac{2\times3}{2}=

Let's reduce the 27 and the 2 in the numerator and denominator of the fraction and we get:

3×3= 3\times-3=

Note that we are multiplying between a positive number and a negative number, therefore the result must be a negative number:

9 -9

3

Final Answer

9 -9

Key Points to Remember

Essential concepts to master this topic
  • Order: Follow left-to-right rule for division operations
  • Technique: Convert to fractions: (81:27)×(6:2)=8127×62 (-81:-27) \times (6:-2) = \frac{-81}{-27} \times \frac{6}{-2}
  • Check: Verify sign rules: negative÷negative=positive, positive÷negative=negative ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring the order of operations in chain division
    Don't solve -81:-27·6:-2 by doing -27·6 first = wrong grouping! This changes the entire calculation structure. Always work left-to-right with division operations or group them properly as fractions.

Practice Quiz

Test your knowledge with interactive questions

a is negative number.

b is negative number.

What is the sum of a+b?

FAQ

Everything you need to know about this question

How do I know which operations to do first in chain division?

+

Chain division means multiple division operations in a row. Work left to right or convert to fractions: a:bc:d=ab×cd a:b \cdot c:d = \frac{a}{b} \times \frac{c}{d}

Why did the negative signs change in the solution?

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Sign rules for division: negative ÷ negative = positive and positive ÷ negative = negative. So 8127=+3 \frac{-81}{-27} = +3 and 62=3 \frac{6}{-2} = -3

Can I simplify the fractions before multiplying?

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Yes! Always simplify first to make calculations easier. 8127=3 \frac{81}{27} = 3 and 62=3 \frac{6}{2} = 3 , so you get 3×(3)=9 3 \times (-3) = -9

What's the difference between : and ÷ symbols?

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They mean the same thing! The colon (:) is just another way to write division. Both 81:27 -81:-27 and 81÷(27) -81÷(-27) equal 3.

How do I check if my final answer is correct?

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Work backwards: if 81:276:2=9 -81:-27 \cdot 6:-2 = -9 , then verify each step. 8127=3 \frac{-81}{-27} = 3 , 62=3 \frac{6}{-2} = -3 , and 3×(3)=9 3 \times (-3) = -9

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