Complete the Decimal Equation: 2.4 = ___

Decimal to Mixed Number Conversion

2.4= 2.4=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Convert to fraction
00:03 Break down the number into whole number and remainder
00:08 Convert the remainder to fraction
00:17 Convert whole number to whole fraction
00:27 Add with common denominator
00:35 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

2.4= 2.4=

2

Step-by-step solution

To convert the decimal 2.42.4 to a mixed number, we need to follow these steps:

  • Step 1: Identify the whole number part and the decimal part. Here, the whole number is 22 and the decimal part is 0.40.4.
  • Step 2: Convert the decimal part 0.40.4 to a fraction. To do this, recognize that 0.40.4 can be written as 410\frac{4}{10} since there is one digit after the decimal point, which implies the denominator is 1010.
  • Step 3: Simplify the fraction 410\frac{4}{10}. Divide the numerator and the denominator by their greatest common divisor, which is 22. Thus, 410=25\frac{4}{10} = \frac{2}{5}.
  • Step 4: Combine the whole number and the simplified fraction to form the mixed number. The whole number 22 and the fraction 25\frac{2}{5} together give 2252\frac{2}{5}.

Therefore, the decimal 2.42.4 is equivalent to the mixed number 2252\frac{2}{5}.

3

Final Answer

225 2\frac{2}{5}

Key Points to Remember

Essential concepts to master this topic
  • Decimal Structure: Whole number is 2, decimal part is 0.4
  • Fraction Form: 0.4 = 4/10, then simplify to 2/5
  • Final Check: Convert back: 2⅖ = 2 + ⅖ = 2.4 ✓

Common Mistakes

Avoid these frequent errors
  • Not simplifying the fraction in lowest terms
    Don't write 2.4 as 2410 2\frac{4}{10} and stop there = incorrect answer! The fraction isn't in simplest form. Always divide both numerator and denominator by their GCD to get 225 2\frac{2}{5} .

Practice Quiz

Test your knowledge with interactive questions

Convert into fraction form:

\( 0.38= \)

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 digits after the decimal point. One digit means denominator 10, two digits means 100, three digits means 1000, and so on. Since 0.4 has one digit, use 10.

Why do I need to simplify the fraction?

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Fractions should always be in lowest terms for the final answer. 410 \frac{4}{10} and 25 \frac{2}{5} are equal, but 25 \frac{2}{5} is the simplified form that's expected.

What if the decimal has more digits, like 2.47?

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Use the same process! The decimal 2.47 becomes 247100 2\frac{47}{100} because there are two digits after the decimal point. Check if the fraction can be simplified.

How can I check if my mixed number is correct?

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Convert your mixed number back to a decimal. For 225 2\frac{2}{5} : divide 2 ÷ 5 = 0.4, then add the whole number: 2 + 0.4 = 2.4 ✓

What's the difference between an improper fraction and a mixed number?

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A mixed number like 225 2\frac{2}{5} shows the whole part separately. An improper fraction like 125 \frac{12}{5} has the numerator larger than denominator. Both equal 2.4!

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