## Key Concepts

**Find the least common denominator (LCD) of two fractions.**- Factor each denominator into its primes.
- List the primes, matching primes in columns when possible.
- Bring down the columns.
- Multiply the factors. The product is the LCM of the denominators.
- The LCM of the denominators is the LCD of the fractions.

**Equivalent Fractions Property**- If [latex]a,b[/latex] , and [latex]c[/latex] are whole numbers where [latex]b\ne 0[/latex] , [latex]c\ne 0[/latex] then[latex]\Large\frac{a}{b}=\Large\frac{a\cdot c}{b\cdot c}[/latex]

and [latex]\Large\frac{a\cdot c}{b\cdot c}=\Large\frac{a}{b}[/latex]

- If [latex]a,b[/latex] , and [latex]c[/latex] are whole numbers where [latex]b\ne 0[/latex] , [latex]c\ne 0[/latex] then[latex]\Large\frac{a}{b}=\Large\frac{a\cdot c}{b\cdot c}[/latex]
**Convert two fractions to equivalent fractions with their LCD as the common denominator.**- Find the LCD.
- For each fraction, determine the number needed to multiply the denominator to get the LCD.
- Use the Equivalent Fractions Property to multiply the numerator and denominator by the number from Step 2.
- Simplify the numerator and denominator.

**Add or subtract fractions with different denominators.**- Find the LCD.
- Convert each fraction to an equivalent form with the LCD as the denominator.
- Add or subtract the fractions.
- Write the result in simplified form.

**Simplify complex fractions.**- Simplify the numerator.
- Simplify the denominator.
- Divide the numerator by the denominator.
- Simplify if possible.

## Glossary

- least common denominator (LCD)
- The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.

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