Adding and Subtracting Fractions

Adding and Subtracting common denominators with common denominators

Keep the denominator the same.
Add the numerators.
Simplify the result if possible (divide numerator & denominator by their GCD).
If the numerator ≥ denominator, convert to a mixed number (whole part = numerator ÷ denominator, remainder over denominator).

Keep the denominator the same.
Subtract the numerators (top minus top).
If the fractional numerator would be negative, borrow 1 from the whole-number part (if you have a mixed number) or convert first fraction into an improper fraction and subtract.
Simplify result if possible.

Used to find equivalent fractions with a common denominator

Find the Least Common Denominator (LCD) — a number both denominators divide into.
Fast way: use the LCM of the denominators (or multiply denominators if you can’t easily find the LCM).
Rewrite each fraction as an equivalent fraction with the LCD.
For each fraction, divide the LCD by its denominator to get a multiplier, then multiply both numerator and denominator by that multiplier.
Add the new numerators (keep the common denominator).
Simplify the resulting fraction by dividing numerator and denominator by their greatest common Factor (GCF).
If the result is an improper fraction (numerator ≥ denominator), convert to a mixed number.

Find the Least Common Denominator (LCD).
Compute the LCM of the denominators (or multiply denominators if LCM isn’t easy).
Convert each fraction to an equivalent fraction with the LCD:
For each fraction, divide the LCD by its denominator → that gives the multiplier.
Multiply numerator and denominator by that multiplier.
Subtract the numerators, keeping the common denominator.
Simplify the resulting fraction by dividing numerator and denominator by their GCD.
If improper, convert to a mixed number (divide numerator by denominator; quotient = whole number, remainder over denominator).
If a negative fractional part occurs in mixed-number subtraction, borrow 1 from the whole-number part

This method helps you see the factors of each number so you can find the Greatest Common Factor (GCF) easily.

Draw a T-chart.
- Write the numerator (top number) on the left.
- Write the denominator (bottom number) on the right.
List all factors of each number under its side of the T.
- Factors are numbers that divide evenly into your number.
Circle the greatest number that appears on both sides — that’s the GCF.
Divide both numerator and denominator by the GCF.
Write your simplified fraction (and check that you can’t divide anymore).

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