Compare the fractions: 6/8 [] 8/12. Use <, >, or =.
Understand the Problem
The question asks us to compare two fractions, 6/8 and 8/12, and determine which fraction is greater, or if they are equal. To do this, we can either find a common denominator or convert both fractions to decimals.
Answer
$\frac{6}{8} > \frac{8}{12}$
Answer for screen readers
$\frac{6}{8} > \frac{8}{12}$
Steps to Solve
- Simplify the fractions:
Simplify $\frac{6}{8}$ by dividing both numerator and denominator by their greatest common divisor, which is 2. $$ \frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4} $$ Simplify $\frac{8}{12}$ by dividing both numerator and denominator by their greatest common divisor, which is 4. $$ \frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3} $$
- Find a common denominator:
Find the least common multiple (LCM) of the denominators 4 and 3. The LCM of 4 and 3 is 12.
- Convert fractions to equivalent fractions with the common denominator:
Convert $\frac{3}{4}$ to a fraction with denominator 12. $$ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} $$ Convert $\frac{2}{3}$ to a fraction with denominator 12. $$ \frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} $$
- Compare the fractions:
Now we have $\frac{9}{12}$ and $\frac{8}{12}$. Since $9 > 8$, then $\frac{9}{12} > \frac{8}{12}$.
- State the relationship:
Therefore, $\frac{6}{8} > \frac{8}{12}$.
$\frac{6}{8} > \frac{8}{12}$
More Information
The fraction $\frac{6}{8}$, when simplified to $\frac{3}{4}$, represents 75% of a whole. The fraction $\frac{8}{12}$, when simplified to $\frac{2}{3}$, represents approximately 66.67% of a whole.
Tips
A common mistake is not simplifying the fractions before finding a common denominator. While it still leads to the correct answer, it involves working with larger numbers. For example, finding a common denominator between 8 and 12 directly would be 24. You would then convert $\frac{6}{8}$ to $\frac{18}{24}$, and $\frac{8}{12}$ to $\frac{16}{24}$. It's easier to compare the reduced fractions.
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