Module 4 · Fractions · Lesson 15 of 39

Adding and subtracting fractions

Same denominators combine directly; different ones need a common denominator.

In this lesson · about 16 minutes

  • Add and subtract fractions with the same denominator
  • Find the least common denominator
  • Simplify the answer

Same denominator

Add or subtract the numerators and keep the denominator: 57 + 37 = 5 + 37 = 87.

Different denominators

First rewrite both fractions with a common denominator. The best one is the LCM of the denominators, called the least common denominator (LCD). Multiply the top and bottom of each fraction by whatever turns its denominator into the LCD.

35 + 13: the LCD is 15, so 3 · 35 · 3 + 1 · 53 · 5 = 915 + 515 = 1415.

Worked example

Add 5/24 + 3/40

Large denominators: use prime factorizations to find the LCD.

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