Convert Decimal 1.4 to Simplified Fraction Form

Q: How do I know what denominator to use?

Count the decimal places! One decimal place means denominator is 10, two decimal places means 100, and so on. For 1.4, there's one decimal place, so use 10.

Q: What if the fraction doesn't simplify?

Some fractions are already in simplest form! For example, 1.3 becomes $ 1\frac{3}{10} $ and can't be simplified further because 3 and 10 share no common factors.

Q: Can I convert mixed fractions back to check my work?

Absolutely! Convert $ 1\frac{2}{5} $ back: multiply whole number by denominator and add numerator: $ \frac{(1×5)+2}{5} = \frac{7}{5} = 1.4 $ ✓

Q: What's the difference between improper and mixed fractions?

A mixed fraction like $ 1\frac{2}{5} $ shows whole parts separately. An improper fraction like $ \frac{7}{5} $ has numerator ≥ denominator. Both represent the same value!

Decimal to Mixed Fraction with Simplification

Convert into a mixed fraction:

$1.4$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's write this as a simplified fraction.

00:06 Take each number after the decimal point and divide it by its place value.

00:12 Next, find the right denominator for the fraction.

00:16 Don't forget to add 1 as needed.

00:23 Simplify by dividing both the top and bottom by the same amount.

00:37 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Convert into a mixed fraction:

$1.4$

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 4 by 10 and add 1 which represents one whole number, as follows:

$1+\frac{4}{10}$

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:

$1+\frac{4:2}{10:2}=1+\frac{2}{5}=1\frac{2}{5}$

Final Answer

$1\frac{2}{5}$

Key Points to Remember

Essential concepts to master this topic

Place Value: One decimal place means denominator is 10
Technique: Write 1.4 as $1\frac{4}{10}$ , then simplify by dividing by 2
Check: Convert back: $1\frac{2}{5} = 1 + \frac{2}{5} = 1.4$ ✓

Common Mistakes

Avoid these frequent errors

Not simplifying the fraction part
Don't leave $1\frac{4}{10}$ as your final answer = not in simplest form! Teachers expect fully simplified fractions. Always find the GCD of numerator and denominator and divide both by it.

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?

Count the decimal places! One decimal place means denominator is 10, two decimal places means 100, and so on. For 1.4, there's one decimal place, so use 10.

What if the fraction doesn't simplify?

Some fractions are already in simplest form! For example, 1.3 becomes $1\frac{3}{10}$ and can't be simplified further because 3 and 10 share no common factors.

How do I find the GCD to simplify?

List the factors of both numbers and find the largest one they share. For $\frac{4}{10}$ : factors of 4 are 1,2,4 and factors of 10 are 1,2,5,10. The greatest common factor is 2.

Can I convert mixed fractions back to check my work?

Absolutely! Convert $1\frac{2}{5}$ back: multiply whole number by denominator and add numerator: $\frac{(1×5)+2}{5} = \frac{7}{5} = 1.4$ ✓

What's the difference between improper and mixed fractions?

A mixed fraction like $1\frac{2}{5}$ shows whole parts separately. An improper fraction like $\frac{7}{5}$ has numerator ≥ denominator. Both represent the same value!

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