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

Chain Division with Negative Numbers

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

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-4)= \)

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?

+

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?

+

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?

+

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?

+

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

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Signed Numbers (Positive and Negative) questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations