To solve the equation \( K + 2 \frac{1}{4} = 4 \frac{1}{3} \), we first convert the mixed numbers to improper fractions.
-
Convert \( 2 \frac{1}{4} \): \[ 2 \frac{1}{4} = 2 \times 4 + 1 = 8 + 1 = \frac{9}{4} \]
-
Convert \( 4 \frac{1}{3} \): \[ 4 \frac{1}{3} = 4 \times 3 + 1 = 12 + 1 = \frac{13}{3} \]
Now, we rewrite the equation using these improper fractions: \[ K + \frac{9}{4} = \frac{13}{3} \]
Next, we will isolate \( K \) by subtracting \( \frac{9}{4} \) from both sides: \[ K = \frac{13}{3} - \frac{9}{4} \]
To subtract these fractions, we need a common denominator. The least common multiple of 3 and 4 is 12. We convert both fractions:
-
Convert \( \frac{13}{3} \): \[ \frac{13}{3} = \frac{13 \times 4}{3 \times 4} = \frac{52}{12} \]
-
Convert \( \frac{9}{4} \): \[ \frac{9}{4} = \frac{9 \times 3}{4 \times 3} = \frac{27}{12} \]
Now we can subtract: \[ K = \frac{52}{12} - \frac{27}{12} = \frac{52 - 27}{12} = \frac{25}{12} \]
Thus, the solution is: \[ K = \frac{25}{12} \]
If you prefer it in a mixed number format, it can be expressed as: \[ K = 2 \frac{1}{12} \]