1Cademy - Example of Contrasting Subtraction and Multiplication of $$\frac{5x}{6}$$ and $$\frac{3}{10}$$

Learn Before

LCD Requirement for Fraction Operations

Example

Example of Contrasting Subtraction and Multiplication of $\frac{5x}{6}$ and $\frac{3}{10}$

This example contrasts the procedures for subtracting and multiplying the fractions $\frac{5x}{6}$ and $\frac{3}{10}$ . Identifying the operation determines if a common denominator is necessary.

ⓐ Subtracting $\frac{5x}{6} - \frac{3}{10}$ : Subtraction requires a least common denominator (LCD). The LCD for $6$ and $10$ is $30$ . First, rewrite each fraction as an equivalent fraction with the LCD: $\frac{5x \cdot 5}{6 \cdot 5} = \frac{25x}{30}$ and $\frac{3 \cdot 3}{10 \cdot 3} = \frac{9}{30}$ . Next, subtract the numerators and place the difference over the common denominator: $\frac{25x - 9}{30}$ . There are no common factors between the numerator and denominator, so the expression is simplified.

ⓑ Multiplying $\frac{5x}{6} \cdot \frac{3}{10}$ : Multiplication does not require a common denominator. Multiply the numerators and denominators directly: $\frac{5x \cdot 3}{6 \cdot 10} = \frac{15x}{60}$ . Rewrite to reveal common factors: $\frac{5x \cdot 3}{2 \cdot 3 \cdot 2 \cdot 5}$ . Removing the common factors of $3$ and $5$ from both the numerator and denominator simplifies the expression to $\frac{x}{4}$ .

Updated 2026-05-02

Contributors are:

Who are from:

References

Learn Before

Related

Learn After