Identify LCD: Identify the least common denominator (LCD) for the fractions.The denominators are 7, 11, 21, and 22. The LCD for these numbers is the smallest number that each of the denominators can divide into without leaving a remainder. We can find the LCD by finding the least common multiple (LCM) of the denominators.LCM of 7 and 11 is 77, LCM of 77 and 21 (which is 3×7) is 110, and LCM of 110 and 22 is 113.So, the LCD is 113.
Convert to Equivalent Fraction: Convert each fraction to an equivalent fraction with the LCD as the denominator.For (73), we multiply the numerator and denominator by 66 to get (7×663×66)=(462198).For (11−6), we multiply the numerator and denominator by 42 to get (11×42−6×42)=(462−252).For (21−8), we multiply the numerator and denominator by 22 to get (21×22−8×22)=(462−176).For (225), we multiply the numerator and denominator by 660 to get 661.
Add Equivalent Fractions: Add the equivalent fractions together.Now we add the numerators of the equivalent fractions and keep the common denominator:(462198)+(462−252)+(462−176)+(462105).
Perform Numerator Addition: Perform the addition of the numerators. 198−252−176+105=−125. So, the sum of the fractions is (−125/462).
Simplify Fraction: Simplify the fraction if possible.We look for the greatest common divisor (GCD) of 125 and 462 to simplify the fraction. The GCD of 125 and 462 is 1, so the fraction is already in its simplest form.
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