Evaluating the Expression: 3/4(1/3+2/7)
When evaluating expressions involving fractions, it's essential to follow the order of operations (PEMDAS) and to have a solid understanding of fraction operations. In this article, we'll break down the step-by-step process to evaluate the expression 3/4(1/3+2/7) as a fraction.
Step 1: Evaluate the Expression Inside the Parentheses
To start, let's evaluate the expression inside the parentheses:
1/3 + 2/7
To add these fractions, we need to find a common denominator, which is 21. So, we'll convert both fractions to have a denominator of 21:
7/21 + 6/21
Now, we can add the numerators (7 + 6 = 13) and keep the denominator the same:
13/21
So, the expression inside the parentheses is equal to 13/21.
Step 2: Multiply by 3/4
Now, we'll multiply the result by 3/4:
(3/4) × (13/21)
To multiply fractions, we multiply the numerators (3 × 13 = 39) and multiply the denominators (4 × 21 = 84):
39/84
Result as a Simplified Fraction
The final result is:
39/84
We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3:
13/28
So, the final result is:
13/28
In conclusion, the expression 3/4(1/3+2/7) evaluates to 13/28 as a simplified fraction.
