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How to Add Fractions with Different Denominators in 5th Grade?

Published in Fractions Arithmetic 2 mins read

To add fractions with different denominators (the bottom number), you need to find a common denominator first! Here's how:

Steps to Add Fractions with Different Denominators

  1. Find the Least Common Multiple (LCM) of the Denominators: The LCM is the smallest number that both denominators divide into evenly. Think of multiples of each denominator until you find a number they share. This will be your common denominator.

    • Example: If you're adding 1/2 and 1/3, the denominators are 2 and 3.
      • Multiples of 2: 2, 4, 6, 8, 10...
      • Multiples of 3: 3, 6, 9, 12...
      • The LCM (and common denominator) is 6.

  2. Convert the Fractions: Change each fraction so it has the common denominator you just found. To do this, multiply both the numerator (top number) and the denominator of each fraction by the same number. This doesn't change the value of the fraction, just how it looks.

    • Example (continuing from above):
      • For 1/2, you need to multiply the denominator (2) by 3 to get 6. So, multiply both the numerator and denominator by 3: (1 x 3) / (2 x 3) = 3/6
      • For 1/3, you need to multiply the denominator (3) by 2 to get 6. So, multiply both the numerator and denominator by 2: (1 x 2) / (3 x 2) = 2/6

  3. Add the Numerators: Now that the fractions have the same denominator, you can add the numerators. Keep the denominator the same.

    • Example: 3/6 + 2/6 = (3 + 2) / 6 = 5/6

  4. Simplify (if possible): See if you can simplify the fraction. Can you divide both the numerator and the denominator by the same number? If so, do it to get the fraction in its simplest form.

    • Example: 5/6 is already in its simplest form because 5 and 6 don't have any common factors other than 1.

Example Problem

Let's add 1/4 + 2/5:

  1. Find the LCM of 4 and 5:

    • Multiples of 4: 4, 8, 12, 16, 20...
    • Multiples of 5: 5, 10, 15, 20...
    • The LCM is 20.

  2. Convert the fractions:

    • 1/4 = (1 x 5) / (4 x 5) = 5/20
    • 2/5 = (2 x 4) / (5 x 4) = 8/20

  3. Add the numerators:

    • 5/20 + 8/20 = (5 + 8) / 20 = 13/20

  4. Simplify: 13/20 is already simplified.

Therefore, 1/4 + 2/5 = 13/20.

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