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:
- 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.
- Add the numerators: Add the numerator of the new fraction (converted whole number) to the numerator of the original fraction.
- 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").
- Find a common denominator: Determine the least common multiple (LCM) of the two denominators. This LCM will be the common denominator.
- Convert the fractions: Multiply the numerator and denominator of each fraction by the appropriate number to achieve the common denominator.
- Add the numerators: Add the numerators of the converted fractions.
- 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.