Solve (12+8)/5: Addition and Division in One Fraction

Order of Operations with Fraction Numerators

12+85= \frac{12+8}{5}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's solve this problem step by step.
00:10 First, we'll work on the top part of the fraction, called the numerator.
00:16 Once complete, we'll divide. Here's how it's done.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

12+85= \frac{12+8}{5}=

2

Step-by-step solution

Let's begin by solving the numerator of the fraction, from left to right, according to the order of operations:

12+8=20 12+8=20

We should obtain the following exercise:

205=20:5=4 \frac{20}{5}=20:5=4

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic
  • Rule: Solve operations inside numerator before dividing by denominator
  • Technique: First calculate 12 + 8 = 20, then divide: 20 ÷ 5 = 4
  • Check: Verify by substitution: (12+8)/5 = 20/5 = 4 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing each term separately instead of solving the numerator first
    Don't divide each term separately like 12/5 + 8/5 = 2.4 + 1.6 = 4! While this gives the same answer here, it's wrong method and creates confusion. Always calculate the entire numerator first: 12 + 8 = 20, then divide by the denominator.

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

Do I solve the numerator first or divide first?

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Always solve the numerator first! The fraction bar acts like parentheses, so you must complete all operations in the numerator before dividing by the denominator.

What if there are operations in both numerator and denominator?

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Solve both the numerator and denominator completely first, then divide. For example: 10+64−1=163 \frac{10+6}{4-1} = \frac{16}{3}

Can I just divide each number by 5 separately?

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No! You must follow order of operations. The addition in the numerator happens before the division. Think of it as (12+8) ÷ 5, not 12÷5 + 8÷5.

Why does the order matter if I get the same answer?

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While some problems might give the same result, using the wrong method will fail on other problems. Building correct habits now prevents mistakes later!

How do I remember the order of operations with fractions?

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Think of the fraction bar as invisible parentheses. So 12+85 \frac{12+8}{5} becomes (12+8) ÷ 5. This helps you see what to solve first!

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