*a%5E2%2F6.jpeg "(1/5a+1/2a)*a^2/6")
Simplifying the Expression: (1/5a + 1/2a) * a^2/6
This article will guide you through the steps involved in simplifying the algebraic expression: (1/5a + 1/2a) * a^2/6.
Step 1: Finding a Common Denominator for the Fractions
To add the fractions inside the parentheses, we need a common denominator. The least common multiple of 5 and 2 is 10. We can rewrite the fractions as:
- 1/5a = 2/10a
- 1/2a = 5/10a
Now our expression becomes: (2/10a + 5/10a) * a^2/6
Step 2: Adding the Fractions
Since the denominators are now the same, we can add the numerators:
(2/10a + 5/10a) = 7/10a
Our expression now looks like: (7/10a) * a^2/6
Step 3: Multiplying the Fractions
To multiply fractions, we multiply the numerators and the denominators:
(7/10a) * (a^2/6) = (7 * a^2) / (10a * 6)
Step 4: Simplifying the Expression
We can simplify the expression by cancelling out common factors:
(7 * a^2) / (10a * 6) = (7 * a * a) / (2 * 5 * a * 2 * 3)
Canceling out 'a' in the numerator and denominator, we get:
(7 * a) / (2 * 5 * 2 * 3) = 7a/60
Conclusion
Therefore, the simplified form of the expression (1/5a + 1/2a) * a^2/6 is 7a/60.