Solve Decimal Division: 0.5 ÷ 4 Step-by-Step

Fraction Division with Decimal Conversion

Solve the following expression:

0.54= ? \frac{0.5}{4}=\text{ ?}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's start by solving the problem.
00:08 First, change the decimal into a fraction.
00:12 Then, turn the division into multiplication using the reciprocal.
00:17 Remember: multiply the top numbers with the top, and the bottom numbers with the bottom.
00:22 And there you go! That's how we solve this question.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following expression:

0.54= ? \frac{0.5}{4}=\text{ ?}

2

Step-by-step solution

First let's convert the decimal fraction into a simple fraction:

0.54=124 \frac{0.5}{4}=\frac{\frac{1}{2}}{4}

Then we can convert the division operation into a multiplication operation.

Next, we'll multiply 12 \frac{1}{2} by the reciprocal of 4 as follows:

12×14 \frac{1}{2}\times\frac{1}{4}

Finally, we solve the problem as follows:

1×12×4=18 \frac{1\times1}{2\times4}=\frac{1}{8}

3

Final Answer

18 \frac{1}{8}

Key Points to Remember

Essential concepts to master this topic
  • Convert Decimals: Change 0.5 to fraction 12 \frac{1}{2} before dividing
  • Division Method: Multiply 12×14=18 \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} using reciprocal
  • Check Answer: Verify 18=0.125 \frac{1}{8} = 0.125 and 0.5 ÷ 4 = 0.125 ✓

Common Mistakes

Avoid these frequent errors
  • Treating division as multiplication
    Don't calculate 0.5 × 4 = 2.0 instead of dividing! This gives the completely opposite operation. Always remember that division by 4 means multiply by 14 \frac{1}{4} , not by 4.

Practice Quiz

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What part of the whole does the shaded (blue) area represent?

FAQ

Everything you need to know about this question

Why can't I just divide 0.5 by 4 directly?

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You absolutely can! 0.5 ÷ 4 = 0.125. Converting to fractions just makes it easier to see the exact answer as 18 \frac{1}{8} instead of a decimal.

How do I know when to convert decimals to fractions?

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Convert when you want an exact fractional answer or when working with fractions is easier. For this problem, both 18 \frac{1}{8} and 0.125 are correct!

What's the reciprocal rule for division?

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Dividing by a number is the same as multiplying by its reciprocal. So 12÷4=12×14 \frac{1}{2} ÷ 4 = \frac{1}{2} \times \frac{1}{4} because 14 \frac{1}{4} is the reciprocal of 4.

How do I multiply fractions like this?

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Multiply the numerators together and the denominators together: 12×14=1×12×4=18 \frac{1}{2} \times \frac{1}{4} = \frac{1 \times 1}{2 \times 4} = \frac{1}{8}

Can I check my answer by converting back to decimals?

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Absolutely! 18=1÷8=0.125 \frac{1}{8} = 1 ÷ 8 = 0.125 , and we can verify: 0.5 ÷ 4 = 0.125. Both methods give the same answer!

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