Solve 14:2·5:7+12+25: Order of Operations Challenge

Order of Operations with Mixed Division

14:25:7+12+25=? 14:2\cdot5:7+12+25=\text{?}

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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 multiplication and division before addition and subtraction
00:12 Always solve from left to right
00:20 Write the division operation as a fraction
00:24 Reduce wherever possible
00:30 Always solve the leftmost operation first
00:34 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

14:25:7+12+25=? 14:2\cdot5:7+12+25=\text{?}

2

Step-by-step solution

According to the rules for the order of operations, we will isolate the multiplication and division exercises in parentheses:

(14:25:7)+12+25= (14:2\cdot5:7)+12+25=

We solve the exercise in parentheses from left to right:

14:2=7 14:2=7

7×5=35 7\times5=35

35:7=5 35:7=5

Now we obtain the exercise:

5+12+25= 5+12+25=

We solve the exercise from left to right:

5+12=17 5+12=17

17+25=42 17+25=42

3

Final Answer

42

Key Points to Remember

Essential concepts to master this topic
  • PEMDAS Rule: Multiplication and division are performed from left to right
  • Technique: Work step-by-step: 14÷2=7, 7×5=35, 35÷7=5
  • Check: Final calculation 5+12+25=42 matches the correct answer ✓

Common Mistakes

Avoid these frequent errors
  • Doing all multiplication before all division
    Don't multiply 2×5 first to get 14÷10÷7 = wrong answer! This ignores left-to-right order and gives incorrect results. Always work multiplication and division from left to right in the order they appear.

Practice Quiz

Test your knowledge with interactive questions

\( 8 + 3 \times 2 = \)

FAQ

Everything you need to know about this question

Why can't I just do multiplication first since it comes before division in PEMDAS?

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Multiplication and division have equal priority in PEMDAS! When they appear together, you work from left to right, not multiplication first. Think of MD as one step, working left to right.

What does the colon symbol (:) mean in math?

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The colon (:) means division, just like the ÷ symbol. So 14:2 14:2 is the same as 14÷2 14÷2 or 142 \frac{14}{2} .

Should I use parentheses when solving this?

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You can add parentheses to help organize your work: (14:2×5:7)+12+25 (14:2×5:7)+12+25 . This reminds you to handle multiplication and division first, but remember to work left to right inside those parentheses!

How do I avoid making calculation errors?

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Work slowly and write each step clearly. For this problem: Step 1: 14÷2=7 14÷2=7 , Step 2: 7×5=35 7×5=35 , Step 3: 35÷7=5 35÷7=5 , Step 4: 5+12+25=42 5+12+25=42 .

What if I get a different answer than the choices given?

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Double-check your order of operations! The most common error is not working left to right for multiplication and division. Retrace each step and make sure you followed PEMDAS correctly.

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