Solve Mixed Operations: 6×15-142-7/14+20÷5 Step-by-Step

Order of Operations with Mixed Fractions

6×15142714+20 ⁣:5= 6\times15-142-\frac{7}{14}+20\colon5=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:01 Solve multiplication and division operations before addition and subtraction
00:15 When presented with addition and subtraction - always solve from left to right
00:39 Reduce the fraction

Step-by-step written solution

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1

Understand the problem

6×15142714+20 ⁣:5= 6\times15-142-\frac{7}{14}+20\colon5=

2

Step-by-step solution

According to the order of operations, first we solve the multiplication and division exercises.

We will put them in parentheses to avoid confusion later in the solution:

(6×15)142714+(20:5)= (6\times15)-142-\frac{7}{14}+(20:5)=

We solve the exercises in parentheses:

90142714+4= 90-142-\frac{7}{14}+4=

We will rewrite the denominator of the fraction as a multiplication exercise:

9014277×2+4= 90-142-\frac{7}{7\times2}+4=

We simplify and obtain:

9014212+4= 90-142-\frac{1}{2}+4=

Now we solve the exercise from left to right:

5212+4= -52-\frac{1}{2}+4=

5212+4=4812 -52\frac{1}{2}+4=-48\frac{1}{2}

3

Final Answer

-48.5

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Always do multiplication and division before addition and subtraction
  • Technique: Simplify 714=12 \frac{7}{14} = \frac{1}{2} by dividing both numerator and denominator by 7
  • Check: Verify: 90 - 142 - 0.5 + 4 = -48.5 ✓

Common Mistakes

Avoid these frequent errors
  • Solving operations from left to right without following PEMDAS
    Don't solve 6×15-142 first = -52, then continue left to right! This ignores multiplication/division priority and gives wrong answers like 70 or 52.5. Always complete all multiplication and division operations first, then work left to right with addition and subtraction.

Practice Quiz

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\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why do I multiply and divide first instead of going left to right?

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The order of operations (PEMDAS) is a mathematical rule that ensures everyone gets the same answer. Multiplication and division have higher priority than addition and subtraction, just like in real-world calculations.

How do I simplify the fraction 7/14?

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Look for the greatest common factor of 7 and 14. Since 7 goes into both numbers: 714=7÷714÷7=12 \frac{7}{14} = \frac{7÷7}{14÷7} = \frac{1}{2}

What does the colon (:) mean in 20÷5?

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The colon (:) is another way to write division. So 20÷5 and 20:5 both mean the same thing - twenty divided by five equals 4.

Why is the final answer negative?

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Because we subtract 142 from 90, which gives us -52. Even after adding 4 and subtracting 0.5, we still have a negative result of -48.5.

Can I convert everything to decimals instead?

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Yes! You can write 12=0.5 \frac{1}{2} = 0.5 , then calculate: 90 - 142 - 0.5 + 4 = -48.5. Both methods give the same answer.

How do I check if -48.5 is correct?

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Substitute back into the original expression: 6×15142714+20÷5 6×15-142-\frac{7}{14}+20÷5
= 90 - 142 - 0.5 + 4 = -48.5 ✓

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