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{:((7)/(4)×(5)/(8))+(7)/(4)×(1)/(2))=

(74×58)+(74×12)= \left.\left(\frac{7}{4} \times \frac{5}{8}\right)+(\frac{7}{4} \times \frac{1}{2}\right)=

Full solution

Q. (74×58)+(74×12)= \left.\left(\frac{7}{4} \times \frac{5}{8}\right)+(\frac{7}{4} \times \frac{1}{2}\right)=
  1. Identify Operations: Identify the two separate multiplication operations within the parentheses and the addition operation that combines them.
  2. Calculate First Multiplication: Calculate the first multiplication (74)×(58)(\frac{7}{4}) \times (\frac{5}{8}). To do this, multiply the numerators together and the denominators together: (7×5)/(4×8)(7 \times 5) / (4 \times 8).
  3. Perform First Multiplication: Perform the multiplication of the numerators and denominators: 3532\frac{35}{32}.
  4. Calculate Second Multiplication: Calculate the second multiplication (74)×(12)(\frac{7}{4}) \times (\frac{1}{2}). Again, multiply the numerators together and the denominators together: (7×1)/(4×2)(7 \times 1) / (4 \times 2).
  5. Perform Second Multiplication: Perform the multiplication of the numerators and denominators: 78\frac{7}{8}.
  6. Add Fractions: Add the two results together: 3532+78\frac{35}{32} + \frac{7}{8}. To add fractions, they must have a common denominator. The least common denominator for 3232 and 88 is 3232.
  7. Convert Fraction: Convert 78\frac{7}{8} to a fraction with a denominator of 3232 by multiplying both the numerator and the denominator by 44: (7×4)/(8×4)=2832(7 \times 4) / (8 \times 4) = \frac{28}{32}.
  8. Add Fractions with Common Denominator: Now add 3532\frac{35}{32} and 2832\frac{28}{32} together: 3532+2832=(35+28)32\frac{35}{32} + \frac{28}{32} = \frac{(35 + 28)}{32}.
  9. Perform Addition of Numerators: Perform the addition of the numerators: 35+28=6335 + 28 = 63.
  10. Write Final Result: Write the final result as a fraction: 6332.\frac{63}{32}.

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