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Simplify. Express your answer as a single fraction in simplest form. \newline7u7u -23\frac{2}{3}

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Q. Simplify. Express your answer as a single fraction in simplest form. \newline7u7u -23\frac{2}{3}
  1. Identify Parts to Combine: Identify the parts of the expression that need to be combined into a single fraction. The expression is 7u237u - \frac{2}{3}. Here, 7u7u is a whole number term and 23-\frac{2}{3} is already a fraction. To combine them into a single fraction, we need to express 7u7u with a common denominator of 33.
  2. Convert Whole Number to Fraction: Convert the whole number term 7u7u into a fraction with the same denominator as 23-\frac{2}{3}. To do this, we multiply 7u7u by 33\frac{3}{3}, which is equivalent to 11, to get the common denominator of 33. 7u×(33)=7u×337u \times \left(\frac{3}{3}\right) = \frac{7u \times 3}{3}
  3. Rewrite with Common Denominator: Rewrite the expression with the common denominator.\newlineNow we have (7u×3)/32/3(7u \times 3)/3 - 2/3. Since both terms have the same denominator, we can combine them.
  4. Combine Numerators: Combine the numerators over the common denominator.\newline(7u×32)/3=(21u2)/3(7u \times 3 - 2)/3 = (21u - 2)/3
  5. Check for Further Simplification: Check if the fraction can be simplified further.\newlineThe fraction (21u2)/3(21u - 2)/3 is already in simplest form because the numerator and the denominator have no common factors other than 11.

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