Question

Simplify. $$ \left(\frac{5}{9}+\frac{1}{6}\right) \div\left(\frac{2}{3}-\frac{1}{2}\right) $$

   Simplify.
$$
\left(\frac{5}{9}+\frac{1}{6}\right) \div\left(\frac{2}{3}-\frac{1}{2}\right)
$$

Elementary Algebra

Elementary Algebra

Lynn Marecek 2nd Edition

Chapter 1, Problem 515

Instant Answer

Solved by Expert Luke P

07/15/2021

Step 1

Let's start with the first one: $$ \frac{5}{9}+\frac{1}{6} $$ To add these fractions, we need to find a common denominator. The least common multiple of 9 and 6 is 18. So, we rewrite the fractions with 18 as the Show more…

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Simplify. $$ \left(\frac{5}{9}+\frac{1}{6}\right) \div\left(\frac{2}{3}-\frac{1}{2}\right) $$

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Key Concepts

Simplification of Fractions

Simplification of fractions means reducing the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor. This process results in the simplest form of the fraction, making it easier to interpret or further use in calculations.

Fraction Addition

Fraction addition involves adding two fractions with different denominators by first converting them to equivalent fractions with a common denominator. This allows you to combine the numerators directly while keeping the denominator the same, leading to a simplified result.

Fraction Subtraction

Fraction subtraction is similar to addition but involves subtracting the numerators after ensuring that both fractions share a common denominator. It's essential to find a common baseline to accurately perform the subtraction.

Division of Fractions

Dividing one fraction by another involves multiplying the first fraction by the reciprocal of the second. The reciprocal is obtained by swapping the numerator and denominator of the fraction being divided, transforming the division into a multiplication.

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