-1%2F3%2B5%2F7.jpeg "(x-1/2) 1/3+5/7")
Simplifying Algebraic Expressions: (x-1/2) 1/3 + 5/7
When dealing with algebraic expressions, it's essential to understand how to simplify them to make calculations easier and more manageable. In this article, we'll explore how to simplify the expression (x-1/2) 1/3 + 5/7.
Step 1: Evaluate the Expression Inside the Parentheses
To begin, we need to evaluate the expression inside the parentheses. We have:
x - 1/2
To simplify this expression, we can multiply both the numerator and the denominator of the fraction by 2 to get rid of the fraction:
x - 1/2 = x - 1/2 * (2/2) = x - 1
So, the expression inside the parentheses becomes:
x - 1
Step 2: Multiply by 1/3
Now, we need to multiply the expression x - 1 by 1/3. To do this, we'll multiply each term in the expression by 1/3:
(x - 1) * 1/3 = x/3 - 1/3
Step 3: Add 5/7
Finally, we need to add 5/7 to the expression. To do this, we'll find a common denominator between 1/3 and 5/7, which is 21. We'll convert both fractions to have a denominator of 21:
x/3 = x*7/21
1/3 = 7/21
5/7 = 15/21
Now, we can add the two fractions:
(x/3 - 1/3) + 5/7 = (x*7/21 - 7/21) + 15/21
Simplifying the Expression
To simplify the expression, we can combine like terms:
(x*7/21 - 7/21) + 15/21 = x*7/21 - 7/21 + 15/21
Combine the fractions:
(x*7 - 7 + 15)/21
Simplify the numerator:
(7x + 8)/21
And that's the simplified expression!
