Subtract and Simplify
2/3 - 1/5 = 1/2
Not quite.
The common denominator 15 (the smallest number divisible by both 3 and 5).
Since 15 divided by 3 is 5, then you multiply the numerator by 5.
Since 15 divided by 5 is 3, then you multiply the numerator by 3.
2/3 - 1/5 = 10/15 - 3/15 = 7/15
To subtract fractions, we need to have a common denominator. Here are the steps to subtract and simplify fractions:
Step 1: Find the least common denominator (LCD)
The least common denominator is the smallest number that both denominators can divide evenly into. In this case, the denominators are 3 and 5. To find the LCD, we can list the multiples of each denominator:
Multiples of 3: 3, 6, 9, 12, ...
Multiples of 5: 5, 10, 15, 20, ...
The first common multiple is 15, so the LCD is 15.
Step 2: Rewrite the fractions with the LCD as the new denominator
To convert the fractions, we need to multiply the numerator and denominator of each fraction by a factor that turns the original denominator into the LCD.
For 2/3: (2/3) * (5/5) = 10/15
For 1/5: (1/5) * (3/3) = 3/15
So, 2/3 is equivalent to 10/15, and 1/5 is equivalent to 3/15.
Step 3: Subtract the numerators
Now that the fractions have the same denominator, we can subtract the numerators. Subtracting 10/15 - 3/15 gives us:
(10/15) - (3/15) = (10 - 3) / 15 = 7/15
Therefore, 2/3 - 1/5 simplifies to 7/15.