Question

Use the inequality symbols\(<\) or \(>\) to compare the following fractions. $$\frac{5}{12} \text { and } \frac{1}{3}$$

Short answer

Question: Compare the fractions 5/12 and 1/3. Answer: 5/12 > 1/3

Step-by-step solution

Find a common denominator

To compare the fractions, we first need to find a common denominator, which is a multiple of both denominators. In this case, the denominators are 12 and 3. The least common multiple (LCM) of 12 and 3 is 12.

Convert each fraction to an equivalent fraction with the common denominator

Next, we must convert each fraction to an equivalent fraction with the common denominator, 12. Since the first fraction already has a denominator of 12, we don't need to change it. For the second fraction, its denominator should be multiplied by 4 to reach the common denominator: $$\frac{1}{3} \times \frac{4}{4} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}$$

Compare the numerators of the equivalent fractions

Now that both fractions have the same denominator, we can compare the numerators to determine their relationship. In this case: $$\frac{5}{12} \text { and } \frac{4}{12}$$ The numerator of 5/12 (5) is greater than the numerator of 4/12 (4).

Write the inequality

Since the numerator of 5/12 is greater, we can write the inequality as: $$\frac{5}{12} > \frac{4}{12}$$ And we remember that 4/12 is the equivalent of 1/3, so we can write the final inequality as: $$\frac{5}{12} > \frac{1}{3}$$