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$\frac{2}{5}$ , $\frac{4}{15}$

Step 1

When comparing two fractions, the denominator of the first fraction must be equal to the denominator of the second fraction. In this case, the two denominators are different, which make $\frac{2}{5}$ and $\frac{4}{15}$ unlike fractions. The first step is finding the least common denominator (LCD) for both fractions $\frac{2}{5}$ and $\frac{4}{15}$ .

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Step 1.1

To find the LCD of a set of numbers $(\frac{2}{5}, \frac{4}{15})$ , find the LCM of the denominators.

$LCM (5, 15)$

Step 1.2

Calculate the LCM of first two denominators in the list, $5$ and $15$ .

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Step 1.2.1

Find the values of the numerical part of each term. Select the largest one, which in this case is $15$ . Multiply them together to get the current total. In this case, the current total is $75$ .

Current Total = $75$

Step 1.2.2

Check each value in the numerical part of each term against the current total. Since the current total is evenly divisible, return it. That is the least common denominator of the numerical part of the fraction.

$15$

Step 2

The denominators can be made equal by finding the least common denominator (LCD), which is $15$ in this case. Next, multiply each fraction by a factor of $1$ that will create the LCD in each of the fractions.

$\frac{2}{5} \cdot \frac{3}{3}, \frac{4}{15} \cdot \frac{1}{1}$

Step 3

Multiply both fractions.

$\frac{6}{15}, \frac{4}{15}$

Step 4

The numerator of the first fraction $6$ is greater than the numerator of the second fraction $4$ , which means that the first fraction $\frac{6}{15}$ is greater than the second fraction $\frac{4}{15}$ and that $\frac{2}{5}$ is greater than $\frac{4}{15}$ .

$\frac{2}{5} > \frac{4}{15}$

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