Solve: (27-5×3)÷(6×2) + (15×4)÷3 | Order of Operations Challenge

Order of Operations with Mixed Fractions

Complete the following exercise:

27−5⋅36⋅2+15⋅43= \frac{27-5\cdot3}{6\cdot2}+\frac{15\cdot4}{3}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:12 Let's solve this problem together.
00:15 Remember, we multiply and divide before we add and subtract.
00:22 First, calculate the multiplication in the denominator.
00:27 Next, do the last multiplication in the numerator.
00:31 Now, let's solve step by step from left to right.
00:38 Work on sixty divided by three before we add.
00:42 Simplify whatever you can.
00:47 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Complete the following exercise:

27−5⋅36⋅2+15⋅43= \frac{27-5\cdot3}{6\cdot2}+\frac{15\cdot4}{3}=

2

Step-by-step solution

According to the order of arithmetic operations, first we place the multiplication exercises within parentheses:

27−(5⋅3)(6⋅2)+(15⋅4)3= \frac{27-(5\cdot3)}{(6\cdot2)}+\frac{(15\cdot4)}{3}=

We then solve the exercises within parentheses:

5×3=15 5\times3=15

6×2=12 6\times2=12

15×4=60 15\times4=60

Now we obtain the exercise:

27−1512+603= \frac{27-15}{12}+\frac{60}{3}=

We solve the numerator of the fraction:

27−15=12 27-15=12

We obtain:

1212+603= \frac{12}{12}+\frac{60}{3}=

We solve the fractions:

1212=1 \frac{12}{12}=1

60:3=20 60:3=20

Finally we obtain the exercise:

1+20=21 1+20=21

3

Final Answer

21

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Solve multiplication and division before addition and subtraction
  • Technique: Calculate 5×3=15 5\times3=15 and 6×2=12 6\times2=12 first
  • Check: Verify 1212+603=1+20=21 \frac{12}{12}+\frac{60}{3}=1+20=21 ✓

Common Mistakes

Avoid these frequent errors
  • Adding and subtracting before multiplying and dividing
    Don't solve 27-5 first to get 22, then multiply = wrong answer 24! This ignores PEMDAS order and creates incorrect calculations. Always complete all multiplication and division operations before any addition or subtraction.

Practice Quiz

Test your knowledge with interactive questions

\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why can't I just work left to right?

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Mathematical expressions have a specific order called PEMDAS! Working left to right ignores this rule and gives wrong answers. Always follow Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Do I need to solve the fractions separately?

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Yes! Treat each fraction as its own mini-problem. Solve the numerator and denominator separately using PEMDAS, then divide to get the fraction's value.

What if I get confused about which operations to do first?

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Look for multiplication and division signs first - these always come before addition and subtraction. In 27−5×3 27-5\times3 , do 5×3 5\times3 first!

How do I know when I'm done simplifying?

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You're done when you have single numbers to add or subtract. Like getting to 1+20 1+20 - now you can safely add left to right!

Can I use a calculator for this?

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Calculators can help, but make sure you understand the order of operations. Some calculators follow PEMDAS automatically, others don't. Always double-check your steps!

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