Compare Fractions and Decimals: Find the Correct Sign for 1/2 ? 0.25

Q: Should I convert the fraction to decimal or decimal to fraction?

Either way works! Converting fractions to decimals is often easier since you just divide. For $ \frac{1}{2} $, divide 1 ÷ 2 = 0.5, then compare 0.5 and 0.25.

Q: What if the division doesn't come out evenly?

That's fine! Some fractions become repeating decimals like $ \frac{1}{3} = 0.333... $. Use enough decimal places to make an accurate comparison.

Q: How do I know which decimal is bigger?

Compare place by place from left to right. In 0.5 vs 0.25: both have 0 in ones place, but 0.5 has 5 tenths while 0.25 has 2 tenths, so 0.5 is larger.

Q: Can I use a number line to help?

Absolutely! Place both numbers on a number line. 0.5 is halfway between 0 and 1, while 0.25 is one-quarter of the way. The number farther right is larger.

Q: What if I converted 0.25 to a fraction instead?

Great approach! 0.25 = $ \frac{25}{100} = \frac{1}{4} $. Then compare $ \frac{1}{2} $ and $ \frac{1}{4} $ using common denominators: $ \frac{2}{4} > \frac{1}{4} $.

Fraction-Decimal Comparison with Mixed Forms

Choose the appropriate sign (?):

$\frac{1}{2}?0.25$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 First, let's pick the right sign for the problem.

00:09 Next, expand the fraction so the bottom number becomes 10.

00:14 Remember to multiply both the top and bottom by the same number.

00:22 Now, change the fraction into a decimal.

00:27 Write the top number as a whole number.

00:30 If the bottom number is 10, move the decimal point one place left.

00:35 Swap the fraction with your decimal answer.

00:40 Choose the correct sign again.

00:43 And that's how we solve this question!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Choose the appropriate sign (?):

$\frac{1}{2}?0.25$

Step-by-step solution

To compare $\frac{1}{2}$ with 0.25, we will first convert the fraction to a decimal.

Step 1: Convert $\frac{1}{2}$ to a decimal:

To do this, divide 1 by 2:

1 \div 2 = 0.5

Thus, $\frac{1}{2}$ is equivalent to 0.5 when expressed as a decimal.

Step 2: Compare the decimal values:

Now, we clearly see that 0.5 (from $\frac{1}{2}$ ) is greater than 0.25.

Therefore, the appropriate sign for the expression $\frac{1}{2} ? 0.25$ is $\gt$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Convert fractions to decimals by dividing numerator by denominator
Technique: $\frac{1}{2} = 1 \div 2 = 0.5$ for direct comparison
Check: Verify 0.5 > 0.25 by comparing place values left to right ✓

Common Mistakes

Avoid these frequent errors

Comparing fraction and decimal without converting
Don't try to compare $\frac{1}{2}$ and 0.25 directly without conversion = wrong conclusions! You can't properly judge size when numbers are in different forms. Always convert to the same form (both fractions or both decimals) before comparing.

Practice Quiz

Test your knowledge with interactive questions

Write the following fraction as a decimal:

$\frac{5}{100}=$

FAQ

Everything you need to know about this question

Should I convert the fraction to decimal or decimal to fraction?

Either way works! Converting fractions to decimals is often easier since you just divide. For $\frac{1}{2}$ , divide 1 ÷ 2 = 0.5, then compare 0.5 and 0.25.

What if the division doesn't come out evenly?

That's fine! Some fractions become repeating decimals like $\frac{1}{3} = 0.333...$ . Use enough decimal places to make an accurate comparison.

How do I know which decimal is bigger?

Compare place by place from left to right. In 0.5 vs 0.25: both have 0 in ones place, but 0.5 has 5 tenths while 0.25 has 2 tenths, so 0.5 is larger.

Can I use a number line to help?

Absolutely! Place both numbers on a number line. 0.5 is halfway between 0 and 1, while 0.25 is one-quarter of the way. The number farther right is larger.

What if I converted 0.25 to a fraction instead?

Great approach! 0.25 = $\frac{25}{100} = \frac{1}{4}$ . Then compare $\frac{1}{2}$ and $\frac{1}{4}$ using common denominators: $\frac{2}{4} > \frac{1}{4}$ .

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