Solve -5×-49÷14×-10: Multiple Operations with Negative Numbers

Order of Operations with Negative Number Multiplication

Solve the following problem:

549:1410= -5\cdot-49:14\cdot-10=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:05 Let's write division as a fraction
00:15 Negative times negative always equals positive
00:33 Let's factor 49 into factors 7 and 7, and 14 into factors 7 and 2
00:47 Let's reduce what we can
00:56 Let's factor 10 into factors 5 and 2
01:00 Let's reduce what we can
01:08 Positive times negative always equals negative
01:18 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

Solve the following problem:

549:1410= -5\cdot-49:14\cdot-10=

2

Step-by-step solution

Let's write the exercise in the following way:

5×4914×10= \frac{-5\times-49}{14}\times-10=

Note that in the numerator of the fraction we are multiplying two negative numbers, therefore the result must be a positive number:

5×4914×10= \frac{5\times49}{14}\times-10=

Break down 49 and 14 into multiplication exercises:

5×7×77×2×10= \frac{5\times7\times7}{7\times2}\times-10=

Reduce the 7 in the numerator and denominator of the fraction and proceed to break down the 10 into a multiplication exercise:

5×72×5×2= \frac{5\times7}{2}\times-5\times2=

Reduce the 2 and note that we are multiplying a positive number by a negative number, therefore the result must be negative:

5×7×5= -5\times7\times5=

Let's solve the exercise from left to right.

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

5×7=35 -5\times7=-35

We obtain the following:

35×5= -35\times5=

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

175 -175

3

Final Answer

175 -175

Key Points to Remember

Essential concepts to master this topic
  • Sign Rules: Negative times negative equals positive always
  • Division Priority: Treat 49÷14 -49÷14 as 4914=3.5 \frac{-49}{14} = -3.5 first
  • Verify: (5)×(3.5)×(10)=175 (-5) × (-3.5) × (-10) = -175

Common Mistakes

Avoid these frequent errors
  • Treating division symbol as multiplication
    Don't calculate -5×-49×14×-10 = 34,300! The ÷ symbol means division, not multiplication, so -49÷14 = -3.5. Always recognize that ÷ creates a fraction and changes the calculation completely.

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 does negative times negative equal positive?

+

Think of it like directions: if you're facing backwards (-) and walking backwards (-), you end up moving forward (+)! The rule negative × negative = positive always works.

How do I know when to divide vs multiply?

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The ÷ symbol means division! So 49÷14 -49÷14 becomes 4914=3.5 \frac{-49}{14} = -3.5 . Then you multiply: (5)×(3.5)×(10) (-5) × (-3.5) × (-10) .

Can I work from left to right with these operations?

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Yes! Since we only have multiplication and division (same priority level), work left to right: (5)×(49)÷14×(10) (-5) × (-49) ÷ 14 × (-10) becomes 245÷14×(10) 245 ÷ 14 × (-10) then 17.5×(10)=175 17.5 × (-10) = -175 .

What if I get confused with all the negative signs?

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Count the negative signs! With three negatives total, the final answer must be negative. Use the rule: odd number of negatives = negative result.

Is there an easier way to handle the division?

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Yes! Simplify 4914=7×77×2=72=3.5 \frac{49}{14} = \frac{7×7}{7×2} = \frac{7}{2} = 3.5 first. Then your calculation becomes (5)×(3.5)×(10)=175 (-5) × (-3.5) × (-10) = -175 .

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