Solve (5+3-2)/3: Order of Operations with Fractions

Order of Operations with Numerator Expressions

5+3−23= \frac{5+3-2}{3}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's solve this problem together!
00:11 Remember, perform each step, one at a time, from left to right.
00:26 Now, divide both the numerator and the denominator by three.
00:36 And there you have it! That's the solution to the question.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

5+3−23= \frac{5+3-2}{3}=

2

Step-by-step solution

Let's focus on the fraction of the fraction.
According to the order of operations rules, we'll solve from left to right, since it only contains addition and subtraction operations:

5+3=8 5+3=8

8−2=6 8-2=6

Now we'll get the fraction:

63 \frac{6}{3}

We'll reduce the numerator and denominator by 3 and get:

21=2 \frac{2}{1}=2

3

Final Answer

2 2

Key Points to Remember

Essential concepts to master this topic
  • Rule: Simplify numerator completely before dividing by denominator
  • Technique: Calculate 5+3-2=6 first, then divide: 63=2 \frac{6}{3}=2
  • Check: Substitute back: 5+3−23=63=2 \frac{5+3-2}{3} = \frac{6}{3} = 2 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing each term separately by the denominator
    Don't calculate 53+33−23 \frac{5}{3} + \frac{3}{3} - \frac{2}{3} = wrong answer! The fraction bar acts like parentheses around the entire numerator. Always simplify the complete numerator expression first, then divide by the denominator.

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 divide each number in the numerator by 3 separately?

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The fraction bar acts like parentheses around the entire numerator! 5+3−23 \frac{5+3-2}{3} means (5+3−2)÷3 (5+3-2) ÷ 3 , not 53+33−23 \frac{5}{3} + \frac{3}{3} - \frac{2}{3} .

What order do I follow for the addition and subtraction in the numerator?

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Work left to right since addition and subtraction have equal priority! So 5+3−2 5+3-2 becomes 8−2=6 8-2 = 6 .

How do I know when I've simplified the fraction correctly?

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Look for the greatest common factor! Since both 6 and 3 are divisible by 3, 63=6÷33÷3=21=2 \frac{6}{3} = \frac{6÷3}{3÷3} = \frac{2}{1} = 2 .

What if my numerator calculation gives me a negative number?

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No problem! Just divide the negative result by the denominator. For example, if you got -3 in the numerator: −33=−1 \frac{-3}{3} = -1 .

Can I check my answer without redoing the whole problem?

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Yes! Multiply your answer by the denominator - you should get the numerator value. Here: 2×3=6 2 × 3 = 6 , and 5+3−2=6 5+3-2 = 6 ✓

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