The given problem involves arithmetic operations with fractions. We need to simplify the expression without using a calculator, relying on our knowledge of fractions and order of operations....
Order of Operations (PEMDAS/BODMAS)
To solve the problem correctly, we need to follow the order of operations, which is often remembered by the acronym PEMDAS or BODMAS:
- **P**arentheses (or **B**rackets)
- **E**xponents (or **O**rders)
- **M**ultiplication and **D**ivision (from left to right)
- **A**ddition and **S**ubtraction (from left to right)
Simplifying the Expression
Let's break down the problem step-by-step:
Step 1: Simplify the expression inside the brackets
We have 6/5 + (-1/2). To add fractions, they need to have a common denominator. The least common denominator of 5 and 2 is 10.
So, we can rewrite the expression as:
6/5 + (-1/2) = (6 * 2) / (5 * 2) + (-1 * 5) / (2 * 5) = 12/10 + (-5/10)
Now, we can add the numerators while keeping the denominator the same:
12/10 + (-5/10) = (12 - 5) / 10 = 7/10
Step 2: Convert the mixed number to a fraction
We have 1 3/4, which is a mixed number. To perform multiplication, we need to convert it to an improper fraction.
1 3/4 = (1 * 4 + 3) / 4 = 7/4
Step 3: Multiply the fractions
Now, we need to multiply 7/4 by 7/10. To multiply fractions, we multiply the numerators and the denominators.
7/4 * 7/10 = (7 * 7) / (4 * 10) = 49/40
Final Answer
Therefore, the value of 1 3/4 x [ 6/5 + (-1/2)] is 49/40. This is an improper fraction, which can be converted to a mixed number if desired.
Important Note
It's crucial to remember that order of operations (PEMDAS/BODMAS) is essential for accurately solving mathematical expressions. Carefully following each step ensures that we arrive at the correct solution.