Simplifying Algebraic Expressions
In this article, we will explore the simplification of algebraic expressions involving fractions. Specifically, we will examine the expression:
1 in 2 + 3 4 in 2 + 3 4 in 2 + 9 16 in2
To simplify this expression, we need to follow the order of operations (PEMDAS) and combine like terms.
Step 1: Simplify the Fractions
First, let's simplify the fractions:
1 in 2 = 1/2 3 4 in 2 = 3/4 in 2 = 3/8 4 in 2 = 1/2 9 16 in2 = 9/16 in2 = 9/32
Step 2: Combine Like Terms
Now, let's combine like terms:
(1/2) + (3/8) + (1/2) + (9/32)
Step 3: Add Fractions
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 2, 8, 2, and 32 is 32. So, we can rewrite the fractions with a denominator of 32:
(16/32) + (12/32) + (16/32) + (9/32)
Step 4: Add and Simplify
Now, let's add the fractions:
(16 + 12 + 16 + 9)/32 = 53/32
Final Answer
The simplified expression is:
53/32
