Evaluating the Expression: 1 3/5 - (5/8 x 0.8 + 1 3/5) ²
The Expression
Let's break down the given expression: 1 3/5 - (5/8 x 0.8 + 1 3/5) ²
. This expression involves mixed numbers, fractions, and decimals. To evaluate it, we need to follow the order of operations (PEMDAS).
Converting Mixed Numbers to Improper Fractions
First, let's convert the mixed numbers to improper fractions:
1 3/5 = 8/5
1 3/5 = 8/5
Evaluating the Expression Inside the Parentheses
Now, let's evaluate the expression inside the parentheses:
(5/8 x 0.8) = (5/8 x 4/5) = 2/8 = 1/4
Add 1 3/5
(which is 8/5
) to the result:
1/4 + 8/5 = 1/4 + 32/20 = 33/20
Evaluating the Exponent
Next, we need to evaluate the exponent (33/20) ²
:
(33/20) ² = 1089/400
Subtracting the Two Expressions
Now, let's subtract the two expressions:
8/5 - 1089/400
To subtract these fractions, we need to find the least common multiple (LCM) of 5 and 400, which is 2000.
8/5 = 3200/2000
1089/400 = 1089/400
Subtracting the two fractions:
3200/2000 - 1089/400 = 2111/2000
The Final Result
Thus, the final result of the expression 1 3/5 - (5/8 x 0.8 + 1 3/5) ²
is:
2111/2000
Or, in decimal form:
1.0555