Есептеңіз: 4 2/7 : 1 5/21 + (4 3/13 · 14/15 - 3 1/3).

Steps to Solve

1. Convert mixed numbers to improper fractions Convert (4 \frac{2}{7}), (3 \frac{1}{3}), and (4 \frac{3}{13}) to improper fractions:

   • (4 \frac{2}{7} = \frac{4 \times 7 + 2}{7} = \frac{30}{7})
   • (3 \frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{10}{3})
   • (4 \frac{3}{13} = \frac{4 \times 13 + 3}{13} = \frac{55}{13})

2. Perform division with fractions Use the formula (a : b = a \times \frac{1}{b}):

   • Calculate (\frac{30}{7} : \frac{10}{3} = \frac{30}{7} \times \frac{3}{10} = \frac{90}{70} = \frac{9}{7})

3. Perform multiplication with fractions

   • Calculate (\frac{55}{13} \times \frac{14}{15}): [ \frac{55 \times 14}{13 \times 15} = \frac{770}{195} ] Simplifying this fraction, we divide the numerator and denominator by 5: [ = \frac{154}{39} ]

4. Perform subtraction

   • Next, calculate (\frac{154}{39} - \frac{10}{3}): Convert (\frac{10}{3}) to have a common denominator of 39: [ \frac{10}{3} = \frac{130}{39} ] Now perform the subtraction: [ \frac{154}{39} - \frac{130}{39} = \frac{24}{39} ]

5. Add the results Now combine the two computed values: [ \frac{9}{7} + \frac{24}{39} ] Get a common denominator, which is 91: [ \frac{9 \times 13}{7 \times 13} + \frac{24 \times 7}{39 \times 7} = \frac{117}{91} + \frac{168}{91} = \frac{285}{91} ]

6. Convert back to a mixed number Finally, convert (\frac{285}{91}) back to a mixed number: [ 285 \div 91 = 3 \quad \text{(remainder: 12)} ] Thus, [ 3 \frac{12}{91} ]