1 3/5 - (5/8 X 0 8 + 1 3/5) 2

2 min read Jun 07, 2024

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