Q. Simplify. Express your answer as a single fraction in simplest form. 27u+4u
Identify LCD: Identify the least common denominator (LCD) for the fractions.The denominators are 2 and 4. The LCD for these denominators is 4 because 4 is the smallest number that both denominators can divide into without a remainder.
Rewrite fractions: Rewrite each fraction with the LCD as the new denominator.For the first fraction, 27u, we need to multiply both the numerator and the denominator by 2 to get the LCD of 4 in the denominator. This gives us (2×27u×2)=414u.For the second fraction, 4u, the denominator is already the LCD, so we do not need to change it.
Add fractions: Add the fractions with the common denominator.Now that both fractions have the same denominator, we can add them together.(414u)+(4u)=414u+u
Combine like terms: Combine like terms in the numerator.In the numerator, we have 14u and u, which are like terms and can be combined.414u+u=415u
Check for simplification: Check if the fraction can be simplified further.The fraction (15u)/4 is already in simplest form because 15 and 4 have no common factors other than 1.
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