Solve Complex Fraction: [(15×8+15)÷27+45]×8÷20÷(-5)

Order of Operations with Negative Division

Solve the following equation:

[(15×8+15) ⁣:27+45]×8 ⁣:205= \frac{\lbrack(15\times8+15)\colon27+45\rbrack\times8\colon20}{-5}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve the following expression
00:03 Always solve parentheses first, even nested parentheses
00:07 Multiplication and division precede addition and subtraction
00:28 Continue to calculate the parentheses
00:47 Continue to solve the expression according to the proper order of operations, from left to right
01:07 Break down 50 into factors 10 and 5
01:20 Reduce wherever possible
01:26 Continue to solve the expression according to the proper order of operations, from left to right
01:31 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

[(15×8+15) ⁣:27+45]×8 ⁣:205= \frac{\lbrack(15\times8+15)\colon27+45\rbrack\times8\colon20}{-5}=

2

Step-by-step solution

Initially, we address the first parentheses in the numerator of the fraction:

(15×8+15)= (15\times8+15)=

According to the rules, we first must solve the multiplication exercise and then the addition:

120+15=135 120+15=135

We obtain the following exercise:

(135:27+45)×8:205= \frac{(135:27+45)\times8:20}{-5}=

We will again address the parentheses in the numerator of the fraction. First by solving the division and then addition exercise.

5+45=50 5+45=50

We are left with the following exercise:

50×8:205= \frac{50\times8:20}{-5}=

We divide 50 into a multiplication exercise:

5×10×8:205= \frac{5\times10\times8:20}{-5}=

We then simplify:

10×8:20= -10\times8:20=

Lastly we solve from left to right:

80:20=4 -80:20=-4

3

Final Answer

4-

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS: Solve parentheses, multiplication, division from left to right
  • Technique: Break down complex expressions: 15×8+15 = 120+15 = 135
  • Check: Verify final division: -80÷20 = -4 matches negative quotient ✓

Common Mistakes

Avoid these frequent errors
  • Ignoring order of operations in parentheses
    Don't solve 15+8×15 instead of 15×8+15 = wrong order gives 255 instead of 135! Multiplication must come before addition even inside parentheses. Always follow PEMDAS strictly: multiply first, then add.

Practice Quiz

Test your knowledge with interactive questions

\( 20\div(4+1)-3= \)

FAQ

Everything you need to know about this question

Why do I get a positive answer when dividing by -5?

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Remember that dividing by a negative number changes the sign! When you have 205 \frac{20}{-5} , the positive 20 divided by negative 5 equals negative 4, not positive 4.

Do I solve the brackets first or the parentheses?

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Work from the innermost to outermost: parentheses ( ) first, then brackets [ ]. So solve (15×8+15) (15\times8+15) before dealing with the entire bracket expression.

Can I simplify the fraction before doing all the operations?

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It's better to complete all operations in the numerator first, then divide by the denominator. Trying to simplify too early can lead to mistakes and missed steps.

What if I forget the negative sign in the final step?

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Always pay close attention to negative signs! Write them clearly and double-check your final division. A positive result when the answer should be negative is a very common error.

How do I know when to use the colon (:) vs division symbol?

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The colon (:) means the same as ÷ \div - it's just another way to write division. Treat 135:27 135:27 exactly like 135÷27 135\div27 .

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