Solve (0.5 + 2)/5: Adding Mixed Numbers in a Fraction

Fraction Simplification with Decimal Numerators

0.5+25= \frac{0.5+2}{5}=

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

0.5+25= \frac{0.5+2}{5}=

2

Step-by-step solution

The first step is to resolve the problem in the numerator of the fraction:

0.5+2=2.5 0.5+2=2.5

Resulting in the following:

2.55 \frac{2.5}{5}

We then proceed to reduce the numerator and denominator by 2.5 in order to obtain the below fraction:

12 \frac{1}{2}

3

Final Answer

12 \frac{1}{2}

Key Points to Remember

Essential concepts to master this topic
  • Order of Operations: Always solve the numerator before dividing by denominator
  • Technique: Convert 2.55 \frac{2.5}{5} by dividing 2.5 ÷ 5 = 0.5
  • Check: Verify 12=0.5 \frac{1}{2} = 0.5 matches our decimal result ✓

Common Mistakes

Avoid these frequent errors
  • Dividing each number in numerator separately by denominator
    Don't calculate 0.55+25 \frac{0.5}{5} + \frac{2}{5} = 0.1 + 0.4 = 0.5! This ignores order of operations and gives the right answer by accident. Always solve the numerator first: 0.5 + 2 = 2.5, then divide by 5.

Practice Quiz

Test your knowledge with interactive questions

\( 100+5-100+5 \)

FAQ

Everything you need to know about this question

Why do I add 0.5 + 2 before dividing by 5?

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Order of operations (PEMDAS) tells us to solve what's in the numerator first! The fraction bar acts like parentheses, so we must calculate 0.5 + 2 = 2.5 before dividing by 5.

How do I convert 2.5/5 to a simple fraction?

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Divide directly: 2.5÷5=0.5 2.5 ÷ 5 = 0.5 . Since 0.5=12 0.5 = \frac{1}{2} , your final answer is 12 \frac{1}{2} !

Can I work with the decimal 0.5 or should I convert it first?

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Either way works! You can add 0.5 + 2 = 2.5 then divide, OR convert 0.5=12 0.5 = \frac{1}{2} first and add 12+2=52 \frac{1}{2} + 2 = \frac{5}{2} . Both give the same result.

Why isn't the answer one of the larger mixed numbers?

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Those answers come from misreading the problem! Students often think it's asking for (0.5+2)×5 (0.5 + 2) × 5 or mixing up operations. Always check: we're dividing a small number (2.5) by 5, so the result must be less than 1.

How can I double-check my work?

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Convert your answer back to decimal: 12=0.5 \frac{1}{2} = 0.5 . Then verify: 0.5+25=2.55=0.5 \frac{0.5 + 2}{5} = \frac{2.5}{5} = 0.5

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