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A common denominator is required before subtracting $\frac{6}{4}$ and $\frac{2}{5}$ because the fractions have different denominators. The rule for subtracting fractions states that $\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$, which only applies when both fractions share the same denominator $c$.

Conditions: The fractions $\frac{6}{4}$ and $\frac{2}{5}$ have unlike denominators (4 and 5).; The operation being performed is subtraction.

A common denominator is required before subtracting $\frac{6}{4}$ and $\frac{2}{5}$ because the fractions have different denominators. The rule for subtracting fractions states that $\frac{a}{c} - \frac{b}{c} = \frac{a-b}{c}$, which only applies when both fractions share the same denominator $c$.

Conditions: The fractions $\frac{6}{4}$ and $\frac{2}{5}$ have unlike denominators (4 and 5).; The operation being performed is subtraction.

Multiplying a fraction by $\frac{5}{5}$ or $\frac{4}{4}$ keeps it equivalent because each of these factors equals 1. Any nonzero number divided by itself equals 1, and multiplying any quantity by 1 does not change its value.

Conditions: The factor used is a fraction whose numerator and denominator are equal and nonzero.; The original fraction is being rewritten to obtain a specific common denominator.

Multiplying a fraction by $\frac{5}{5}$ or $\frac{4}{4}$ keeps it equivalent because each of these factors equals 1. Any nonzero number divided by itself equals 1, and multiplying any quantity by 1 does not change its value.

Conditions: The factor used is a fraction whose numerator and denominator are equal and nonzero.; The original fraction is being rewritten to obtain a specific common denominator.