Lesson 2: Finding Equivalent Fractions Using a Common Denominator

Property

A common denominator for two fractions, $\frac{a}{b}$ and $\frac{c}{d}$, can be found visually using two identical area models.
By partitioning the first model (representing $\frac{a}{b}$) with $d$ horizontal lines and the second model (representing $\frac{c}{d}$) with $b$ vertical lines, both models are decomposed into $b \times d$ equal parts.

Examples

Property

The lowest common denominator (LCD) for two fractions is the smallest number that both denominators divide into evenly.
Finding the LCD is the same as finding the lowest common multiple (LCM) of their denominators.

To find the LCD, you can list multiples of the larger number until you find one that is also a multiple of the smaller number.

Examples

• For $\frac{1}{6}$ and $\frac{3}{8}$, we list multiples of 8: 8, 16, 24. Since 6 divides into 24, the LCD is 24.

Property

Convert two fractions to equivalent fractions with their LCD as the common denominator.
Step 1. Find the LCD.
Step 2. For each fraction, determine the number needed to multiply the denominator to get the LCD.
Step 3. Use the Equivalent Fractions Property to multiply both the numerator and denominator by the number you found in Step 2.

Examples

• Convert $\frac{1}{4}$ and $\frac{1}{6}$ to use their LCD, 12. For $\frac{1}{4}$, multiply by $\frac{3}{3}$ to get $\frac{3}{12}$. For $\frac{1}{6}$, multiply by $\frac{2}{2}$ to get $\frac{2}{12}$.

• Convert $\frac{3}{10}$ and $\frac{5}{18}$ to use their LCD, 90. For $\frac{3}{10}$, multiply by $\frac{9}{9}$ to get $\frac{27}{90}$. For $\frac{5}{18}$, multiply by $\frac{5}{5}$ to get $\frac{25}{90}$.