Solve the Fraction: 9/(42+7) - Division with Compound Denominator

Order of Operations with Compound Denominators

942+7= \frac{9}{42+7}=

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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 Convert the fraction into a division exercise using parentheses
00:06 Always solve the parentheses first and then continue
00:09 Rewrite the division exercise as a fraction once again
00:12 Here is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

942+7= \frac{9}{42+7}=

2

Step-by-step solution

To solve the expression 942+7 \frac{9}{42+7} , we need to follow the order of operations, commonly known by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). In this question, we focus on Parentheses and Addition.

Step-by-Step Solution:

  • First, we identify the operation inside the parentheses: 42+742 + 7.
  • According to the order of operations, we must solve what is inside the parentheses before dealing with any division. So, we perform the addition first.
  • Calculate 42+742 + 7 to get 4949.
  • We then substitute 4949 back into the original expression in the place of 42+742 + 7.
  • This gives us a simplified expression: 949\frac{9}{49}.
  • Since 99 and 4949 do not have any common factors aside from 11, this fraction cannot be simplified further.

Therefore, the final answer is 949 \frac{9}{49} .

3

Final Answer

949 \frac{9}{49}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Always solve parentheses first before dividing in fractions
  • Technique: Calculate 42 + 7 = 49 before dividing 9 by denominator
  • Check: Verify 9/49 cannot simplify further by finding GCD(9,49) = 1 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing before solving the parentheses
    Don't calculate 9/42 + 9/7 = 3/14 + 9/7 = wrong answer! This ignores order of operations and changes the entire expression. Always solve what's in parentheses first: 42 + 7 = 49, then divide 9/49.

Practice Quiz

Test your knowledge with interactive questions

Solve the following problem:

\( 187\times(8-5)= \)

FAQ

Everything you need to know about this question

Why can't I just divide 9 by 42 and then add 7?

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Because the parentheses tell you to add first! The expression 942+7 \frac{9}{42+7} means 9 divided by the entire sum of 42 + 7, not 9/42 plus something else.

How do I know if 9/49 can be simplified?

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Check if 9 and 49 share any common factors. Since 9 = 3×3 and 49 = 7×7, they don't share any factors except 1, so 949 \frac{9}{49} is already in simplest form.

What if I calculated 42 + 7 wrong?

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Double-check your addition! 42+7=49 42 + 7 = 49 . If you got a different sum like 48 or 50, you'd get the wrong final answer. Always verify your arithmetic step by step.

Is there a faster way to solve this?

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Not really! Order of operations exists for a reason. You must do the addition in parentheses first. Trying shortcuts will lead to wrong answers every time.

Can this fraction become a mixed number?

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No, because 9 < 49. Since the numerator is smaller than the denominator, 949 \frac{9}{49} is a proper fraction less than 1 and cannot be written as a mixed number.

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