Question

7\frac{5}{12} - 2\frac{3}{5}

Explanation:

Step1: Convert mixed numbers to improper fractions

To convert a mixed number \( a\frac{b}{c} \) to an improper fraction, we use the formula \( \frac{a\times c + b}{c} \).

For \( 7\frac{5}{12} \):
\( a = 7 \), \( b = 5 \), \( c = 12 \)
\( 7\frac{5}{12}=\frac{7\times12 + 5}{12}=\frac{84 + 5}{12}=\frac{89}{12} \)

For \( 2\frac{3}{5} \):
\( a = 2 \), \( b = 3 \), \( c = 5 \)
\( 2\frac{3}{5}=\frac{2\times5+3}{5}=\frac{10 + 3}{5}=\frac{13}{5} \)

Step2: Find a common denominator

The denominators are 12 and 5. The least common multiple of 12 and 5 is \( 12\times5 = 60 \).

Step3: Rewrite the fractions with the common denominator

For \( \frac{89}{12} \):
\( \frac{89}{12}=\frac{89\times5}{12\times5}=\frac{445}{60} \)

For \( \frac{13}{5} \):
\( \frac{13}{5}=\frac{13\times12}{5\times12}=\frac{156}{60} \)

Step4: Subtract the fractions

\( \frac{445}{60}-\frac{156}{60}=\frac{445 - 156}{60}=\frac{289}{60} \)

Step5: Convert the improper fraction back to a mixed number (optional)

To convert \( \frac{289}{60} \) to a mixed number, divide 289 by 60:
\( 289\div60 = 4 \) with a remainder of \( 289-60\times4 = 289 - 240 = 49 \)
So, \( \frac{289}{60}=4\frac{49}{60} \)

Answer:

\( 4\frac{49}{60} \) (or \( \frac{289}{60} \))