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------------------------------------------------ Simplify the following expression:

[tex]\[ \frac{2}{5} \div \frac{14}{15} \][/tex]

Sure! Let's solve the problem step by step:

We need to divide the fraction [tex]\( \frac{2}{5} \)[/tex] by the fraction [tex]\( \frac{14}{15} \)[/tex].

1. Understand the Division of Fractions:
When you divide by a fraction, it's the same as multiplying by its reciprocal. So, we need to find the reciprocal of [tex]\( \frac{14}{15} \)[/tex].

2. Reciprocal of [tex]\( \frac{14}{15} \)[/tex]:
The reciprocal of [tex]\( \frac{14}{15} \)[/tex] is [tex]\( \frac{15}{14} \)[/tex].

3. Convert Division to Multiplication:
Therefore, [tex]\( \frac{2}{5} \div \frac{14}{15} \)[/tex] can be written as [tex]\( \frac{2}{5} \times \frac{15}{14} \)[/tex].

4. Multiply the Fractions:
To multiply fractions, multiply the numerators together and multiply the denominators together:
[tex]\[
\frac{2 \times 15}{5 \times 14} = \frac{30}{70}
\][/tex]

5. Simplify the Fraction:
Next, we need to simplify [tex]\( \frac{30}{70} \)[/tex]. Find their greatest common divisor (GCD). The GCD of 30 and 70 is 10.

6. Divide the Numerator and Denominator by the GCD:
[tex]\[
\frac{30 \div 10}{70 \div 10} = \frac{3}{7}
\][/tex]

Therefore, the simplified result of [tex]\( \frac{2}{5} \div \frac{14}{15} \)[/tex] is [tex]\( \frac{3}{7} \)[/tex].