Compare the fractions: 2/3 ? 10/12.
Understand the Problem
The question asks to compare two fractions, 2/3 and 10/12, and determine the relationship between them using the symbols <, >, or =.
Answer
$\frac{2}{3} < \frac{10}{12}$
Answer for screen readers
$\frac{2}{3} < \frac{10}{12}$
Steps to Solve
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Simplify the fraction $\frac{10}{12}$ Find the greatest common divisor (GCD) of 10 and 12. The GCD is 2. Divide both the numerator and the denominator by 2: $$ \frac{10}{12} = \frac{10 \div 2}{12 \div 2} = \frac{5}{6} $$
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Find a common denominator for $\frac{2}{3}$ and $\frac{5}{6}$. The least common multiple (LCM) of 3 and 6 is 6. Convert $\frac{2}{3}$ to an equivalent fraction with a denominator of 6: $$ \frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6} $$
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Compare the two fractions Now we have $\frac{4}{6}$ and $\frac{5}{6}$. Since they have the same denominator, we can compare their numerators: $4 < 5$, therefore $\frac{4}{6} < \frac{5}{6}$
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State the relationship between the original fractions Since $\frac{4}{6} = \frac{2}{3}$ and $\frac{5}{6} = \frac{10}{12}$, we have: $\frac{2}{3} < \frac{10}{12}$
$\frac{2}{3} < \frac{10}{12}$
More Information
The fraction $\frac{10}{12}$ simplifies to $\frac{5}{6}$, which is larger than $\frac{2}{3}$.
Tips
A common mistake is to try to compare the fractions without finding a common denominator or simplifying. This can lead to an incorrect comparison. Always simplify or find a common denominator before comparing fractions.
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