Simplify: $30\left(\frac{5}{6}+\frac{4}{5}\right)=$
Answer (1)
Find a common denominator for the fractions: 6 5 + 5 4 = 30 25 + 30 24 .
Add the fractions: 30 25 + 30 24 = 30 49 .
Multiply by 30: 30 × 30 49 = 49 .
The simplified expression is 49 .
Explanation
Initial Analysis We are asked to simplify the expression 30\[\left(\frac{5}{6}+\frac{4}{5}\right)\] . To do this, we first need to find a common denominator for the two fractions inside the parentheses.
Finding Common Denominator The least common multiple of 6 and 5 is 30. So, we rewrite the fractions with the common denominator of 30: 6 5 = 6 × 5 5 × 5 = 30 25 5 4 = 5 × 6 4 × 6 = 30 24
Adding Fractions Now we can add the two fractions: 30 25 + 30 24 = 30 25 + 24 = 30 49
Multiplying by 30 Next, we multiply the result by 30: 30 × 30 49 = 30 30 × 49 Since 30 appears in both the numerator and the denominator, we can cancel them out: 30 30 × 49 = 49
Final Answer Therefore, the simplified expression is 49.
Examples
Understanding how to simplify expressions with fractions is useful in many real-life situations. For example, if you are baking a cake and need to adjust the recipe to make a larger or smaller cake, you will need to work with fractions. Suppose a recipe calls for 6 5 cup of flour and 5 4 cup of sugar. If you want to triple the recipe, you would need to calculate 3 × ( 6 5 + 5 4 ) . Simplifying this expression helps you determine the total amount of flour and sugar needed for the tripled recipe. This skill is also useful when calculating discounts or sales tax, where you might need to find a fraction of a price.
