Compare Fractions and Decimals: Is 4/8 = 0.5?

Fraction-Decimal Comparison with Common Denominators

Choose the appropriate sign:

48?0.5 \frac{4}{8}?0.5

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 First, choose the right sign. Is it a plus or a minus?
00:11 Next, let's change the decimal number into a fraction.
00:20 Now, reduce the fraction. Divide the numerator and the denominator as much as you can.
00:28 We also want to simplify this fraction as much as we can.
00:37 See, the fractions are equal. Great job!
00:41 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Choose the appropriate sign:

48?0.5 \frac{4}{8}?0.5

2

Step-by-step solution

First, let's convert 0.5 to a simple fraction.

Since there is only one digit after the decimal point, the number is divided by 10 as follows:

0.5=510 0.5=\frac{5}{10}

Now we have two simple fractions with different denominators.

To compare them, note that the smallest common denominator between them is 2.

We'll divide each one to reach the common denominator as follows:

48:44=12 \frac{4}{8}:\frac{4}{4}=\frac{1}{2}

510:55=12 \frac{5}{10}:\frac{5}{5}=\frac{1}{2}

Now we can compare the two fractions and see that:

12=12 \frac{1}{2}=\frac{1}{2}

3

Final Answer

= =

Key Points to Remember

Essential concepts to master this topic
  • Conversion Rule: Convert decimal 0.5 to fraction form 510 \frac{5}{10}
  • Simplification Technique: Reduce both fractions to common denominator: 48=12 \frac{4}{8} = \frac{1}{2}
  • Verification: Check both simplified forms equal 12 \frac{1}{2} so 48=0.5 \frac{4}{8} = 0.5 ✓

Common Mistakes

Avoid these frequent errors
  • Comparing fractions without finding common denominators
    Don't compare 48 \frac{4}{8} and 510 \frac{5}{10} directly by looking at numerators = wrong comparison! Different denominators make direct comparison impossible. Always simplify both fractions to their lowest terms or find a common denominator first.

Practice Quiz

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Which decimal number is greater?

FAQ

Everything you need to know about this question

How do I convert 0.5 to a fraction?

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Since 0.5 has one digit after the decimal, put 5 over 10: 0.5=510 0.5 = \frac{5}{10} . Then simplify by dividing both numerator and denominator by 5 to get 12 \frac{1}{2} .

Why can't I just compare 4 and 5 in the numerators?

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Because the denominators are different! 48 \frac{4}{8} and 510 \frac{5}{10} represent different-sized pieces. You must simplify both fractions first or find a common denominator to compare properly.

What's the easiest way to simplify fractions?

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Find the GCD (Greatest Common Divisor) of numerator and denominator, then divide both by it. For 48 \frac{4}{8} : GCD of 4 and 8 is 4, so 4÷48÷4=12 \frac{4÷4}{8÷4} = \frac{1}{2} .

How do I know if my comparison is correct?

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Convert both numbers to the same form (both fractions or both decimals). For example: 48=0.5 \frac{4}{8} = 0.5 and 0.5=0.5 0.5 = 0.5 , so they're equal!

Can I use cross-multiplication to compare?

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Not directly for comparison with decimals. First convert the decimal to a fraction, then cross-multiply: 48 \frac{4}{8} vs 510 \frac{5}{10} gives 4×10 = 40 and 8×5 = 40, so they're equal!

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