Identify Operations: Identify the two separate multiplication operations within the parentheses and the addition operation that combines them.
Calculate First Multiplication: Calculate the first multiplication (47)×(85). To do this, multiply the numerators together and the denominators together: (7×5)/(4×8).
Perform First Multiplication: Perform the multiplication of the numerators and denominators: 3235.
Calculate Second Multiplication: Calculate the second multiplication (47)×(21). Again, multiply the numerators together and the denominators together: (7×1)/(4×2).
Perform Second Multiplication: Perform the multiplication of the numerators and denominators: 87.
Add Fractions: Add the two results together: 3235+87. To add fractions, they must have a common denominator. The least common denominator for 32 and 8 is 32.
Convert Fraction: Convert 87 to a fraction with a denominator of 32 by multiplying both the numerator and the denominator by 4: (7×4)/(8×4)=3228.
Add Fractions with Common Denominator: Now add 3235 and 3228 together: 3235+3228=32(35+28).
Perform Addition of Numerators: Perform the addition of the numerators: 35+28=63.
Write Final Result: Write the final result as a fraction: 3263.
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