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How do you add something to a fraction?

Published in Fraction Addition 2 mins read

Adding something to a fraction depends on what you're adding. We'll cover adding whole numbers and other fractions.

Adding a Whole Number to a Fraction

To add a whole number to a fraction, you can convert the whole number into a fraction with the same denominator as the original fraction. Then, add the numerators. Here's a breakdown:

  1. Convert the whole number to a fraction: Multiply the whole number by the denominator of the fraction. This result becomes the numerator of the new fraction, and the denominator stays the same.
  2. Add the numerators: Add the numerator of the new fraction (converted whole number) to the numerator of the original fraction.
  3. Keep the denominator: The denominator remains the same.

Example:

Let's say you want to add 9 and 2/3.

  • Step 1: Convert the whole number to a fraction: 9 can be written as 9/1. To get a common denominator of 3, multiply both the numerator and denominator of 9/1 by 3. This gives you 27/3. (From the YouTube video excerpt, 9 times 3 gives you 27).
  • Step 2: Add the numerators: Add the numerators of 27/3 and 2/3. 27 + 2 = 29 (From the YouTube video excerpt, "...27 plus 2 gives you 29.").
  • Step 3: Keep the denominator: The denominator remains 3.

Therefore, 9 + 2/3 = 29/3.

Adding a Fraction to a Fraction

To add two fractions, they need to have the same denominator (a "common denominator").

  1. Find a common denominator: Determine the least common multiple (LCM) of the two denominators. This LCM will be the common denominator.
  2. Convert the fractions: Multiply the numerator and denominator of each fraction by the appropriate number to achieve the common denominator.
  3. Add the numerators: Add the numerators of the converted fractions.
  4. Keep the denominator: The denominator remains the same.

Example:

Let's add 1/4 and 2/5.

  • Step 1: Find a common denominator: The least common multiple of 4 and 5 is 20.
  • Step 2: Convert the fractions:
    • For 1/4, multiply the numerator and denominator by 5: (1 5) / (4 5) = 5/20
    • For 2/5, multiply the numerator and denominator by 4: (2 4) / (5 4) = 8/20
  • Step 3: Add the numerators: Add the numerators of 5/20 and 8/20. 5 + 8 = 13.
  • Step 4: Keep the denominator: The denominator remains 20.

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

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