To subtract three fractions, you need to find a common denominator, convert the fractions to equivalent fractions with the common denominator, and then subtract the numerators while keeping the common denominator.
Here's a step-by-step guide based on the provided reference:
-
Find a Common Denominator: Identify the least common multiple (LCM) of the denominators of the three fractions. This will be your common denominator.
-
Convert to Equivalent Fractions: Convert each fraction into an equivalent fraction with the common denominator. You do this by multiplying both the numerator and the denominator of each fraction by the same number, ensuring the denominator equals the common denominator.
- For example, from the reference (0:08-1:22), to subtract fractions with denominators of 6, 2, and 3, the common denominator is 6. The fractions become x/6 - y/6 - z/6. So, any fractions that don't have 6 as the denominator need to be converted.
-
Subtract the Numerators: Once all fractions have the same denominator, subtract the numerators from left to right. The reference (0:08-1:22) shows an example like: 5/6 - 3/6 - 2/6. Subtract the numerators: 5 - 3 - 2.
-
Simplify: If possible, simplify the resulting fraction to its lowest terms.
Example:
Let's say you want to subtract the following fractions: 5/6 - 1/2 - 1/3
-
Find the Common Denominator: The least common multiple of 6, 2, and 3 is 6.
-
Convert to Equivalent Fractions:
- 5/6 remains as 5/6
- 1/2 becomes (1*3)/(2*3) = 3/6
- 1/3 becomes (1*2)/(3*2) = 2/6
-
Subtract the Numerators:
- 5/6 - 3/6 - 2/6 = (5 - 3 - 2)/6 = 0/6
-
Simplify:
- 0/6 = 0
Therefore, 5/6 - 1/2 - 1/3 = 0.
