New Concept
Comparing fractions by converting them to decimals provides a reliable method when fractions have unrelated denominators. In Grade 6 Saxon Math Course 1, students divide each fraction's numerator by its denominator to get a decimal, then compare the decimals. For 5/8 versus 7/11: 5/8 = 0.625 and 7/11 ≈ 0.636, so 7/11 > 5/8. This method avoids finding a common denominator and works for any two fractions, making it a practical universal comparison strategy.
Key Concepts
Property To compare fractions, one method is to convert the fractions into their decimal forms first.
Examples To compare $\frac{3}{5}$ and $\frac{5}{8}$, convert them: $\frac{3}{5} = 0.6$ and $\frac{5}{8} = 0.625$. Since $0.600 < 0.625$, we have $\frac{3}{5} < \frac{5}{8}$. To compare $\frac{1}{4}$ and $\frac{3}{10}$, convert them: $\frac{1}{4} = 0.25$ and $\frac{3}{10} = 0.30$. Since $0.25 < 0.30$, we have $\frac{1}{4} < \frac{3}{10}$. To compare $\frac{3}{20}$ and $\frac{1}{8}$, convert them: $\frac{3}{20} = 0.15$ and $\frac{1}{8} = 0.125$. Since $0.150 0.125$, we have $\frac{3}{20} \frac{1}{8}$.
Explanation Think of fractions as secret codes. It's hard to tell if $\frac{3}{5}$ is bigger than $\frac{5}{8}$ just by looking. But when you decode them into decimals by dividing the top by the bottom, you get $0.6$ and $0.625$. Suddenly, the secret is out, and it's easy to see which number is the true heavyweight champion!
Common Questions
How do you compare fractions by converting to decimals?
Divide each numerator by its denominator, then compare the resulting decimal values.
Compare 5/8 and 7/11.
5/8 = 0.625; 7/11 ≈ 0.6364. Since 0.6364 > 0.625, we have 7/11 > 5/8.
Compare 3/7 and 5/12.
3/7 ≈ 0.4286; 5/12 ≈ 0.4167. So 3/7 > 5/12.
When is the decimal method better than finding a common denominator?
When denominators are large primes or unrelated numbers, finding LCD is cumbersome. Converting to decimals (especially with a calculator) is faster.
What is a limitation of the decimal comparison method?
Repeating decimals (like 1/3 = 0.333...) may need rounding for comparison, which could introduce small errors. For exact comparison, common denominators are more precise.