Convert 2.6 to a Simplified Fraction: Step-by-Step Solution

Decimal to Mixed Fraction with Simplification

Convert into a mixed fraction:

2.6 2.6

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Write as a reduced and simplified fraction
00:03 Divide each digit after the decimal point by the division amount it represents
00:08 Place the appropriate denominator
00:11 Remember to add 2
00:17 Reduce as much as possible, make sure to divide both numerator and denominator
00:32 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Convert into a mixed fraction:

2.6 2.6

2

Step-by-step solution

Let's write the decimal fraction as a mixed fraction.

Since there is one digit after the decimal point, we divide 6 by 10 and add 2, as follows:

2+610 2+\frac{6}{10}

Now let's divide the simple fraction by the highest number that can divide both the numerator and denominator, in this case the number is 2:

2+6:210:2=2+35=235 2+\frac{6:2}{10:2}=2+\frac{3}{5}=2\frac{3}{5}

3

Final Answer

235 2\frac{3}{5}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Place decimal digits over power of 10 based on place value
  • Technique: Convert 2.6=2610 2.6 = 2\frac{6}{10} then simplify using GCD
  • Check: Convert back: 235=2.6 2\frac{3}{5} = 2.6

Common Mistakes

Avoid these frequent errors
  • Forgetting to simplify the fractional part
    Don't leave 2610 2\frac{6}{10} as final answer = incomplete solution! The fraction 6/10 can be reduced further by dividing both numerator and denominator by their GCD of 2. Always simplify fractions to lowest terms: 610=35 \frac{6}{10} = \frac{3}{5} .

Practice Quiz

Test your knowledge with interactive questions

Reduce the following fraction:

\( 0.30 \)

FAQ

Everything you need to know about this question

How do I know what denominator to use for the decimal part?

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Count the decimal places! For 2.6, there's 1 decimal place, so use 10. For 2 decimal places (like 2.65), use 100. The pattern is: 1 place = 10, 2 places = 100, 3 places = 1000, etc.

Why do I need to simplify the fraction?

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Simplifying gives the simplest form of the fraction, which is the standard way to express answers. 610 \frac{6}{10} and 35 \frac{3}{5} are equal, but 35 \frac{3}{5} is preferred because it uses smaller numbers.

How do I find the greatest common divisor (GCD)?

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List the factors of both numbers and find the largest one they share. For 6 and 10: factors of 6 are 1, 2, 3, 6 and factors of 10 are 1, 2, 5, 10. The largest common factor is 2.

What if the decimal has more than one digit after the decimal point?

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The same process works! For example, 3.25 becomes 325100 3\frac{25}{100} , then simplify by dividing both 25 and 100 by their GCD of 25 to get 314 3\frac{1}{4} .

Can I check my answer by converting back to decimal?

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Absolutely! Convert 235 2\frac{3}{5} back: divide 3 ÷ 5 = 0.6, then add 2 + 0.6 = 2.6. This matches the original decimal, so your answer is correct!

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