Question

(3 1/4+2 1/6):2 3/5-2/3*2 1/4

Answer 1

(3 1/4 + 2 1/6) : 2 3/5 - 2/3 * 2 1/4 = 7/12,

1) 3 1/4 + 2 1/6 = (3 + 2) + (1/4 + 1/6) = 5 + (3/12 + 2/12) = 5 + 5/12 = 5 5/12,

2) 5 5/12 : 2 3/5 = 65/12 : 13/5 = 65/12 * 5/13 = 25/12 = 2 1/12,

3) 2/3 * 2 1/4 = 2/3 * 9/4 = 3/2 = 1 1/2,

4) 2 1/12 - 1 1/2 = 25/12 - 3/2 = 25/12 - 18/12 = 7/12

Answer 2

Let's break down the given expression step by step:

1. Adding Fractions:
   $3 \frac{1}{4} + 2 \frac{1}{6}$
   To add these fractions, we need to have a common denominator, which is 12 in this case.

   $3 \frac{1}{4} = \frac{13}{4}$
   $2 \frac{1}{6} = \frac{13}{6}$

   Now add them: $\frac{13}{4} + \frac{13}{6} = \frac{39}{12} + \frac{26}{12} = \frac{65}{12}$

2. Dividing by a Mixed Number:
   $\frac{65}{12} \div 2 \frac{3}{5}$
   First, convert the mixed number to an improper fraction:

   $2 \frac{3}{5} = \frac{13}{5}$

   Now divide: $\frac{65}{12} \div \frac{13}{5} = \frac{65}{12} \times \frac{5}{13} = \frac{325}{156}$

3. Multiplying Fractions:
   $\frac{325}{156} - \frac{2}{3} \times 2 \frac{1}{4}$
   Convert the mixed number to an improper fraction:

   $2 \frac{1}{4} = \frac{9}{4}$

   Now multiply: $\frac{2}{3} \times \frac{9}{4} = \frac{18}{12}$

   Subtract the result from the previous step: $\frac{325}{156} - \frac{18}{12}$

   To subtract these fractions, we need to have a common denominator, which is 156 in this case.

   $\frac{325}{156} = \frac{325}{156}$
   $\frac{18}{12} = \frac{39}{26}$

   Now subtract them: $\frac{325}{156} - \frac{39}{26} = \frac{325}{156} - \frac{234}{156} = \frac{91}{156}$

So, the final result of the expression is $\frac{91}{156}$, which can be simplified to $\frac{7}{12}$ in lowest terms.