To simplify this expression, we need to follow the order of operations - PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
Step 1: Perform division first 3/14 ÷ (-4.1/2) To divide by a fraction, we multiply by the reciprocal: 3/14 * (-2/4.1) = -6/57.4 = -3/28.7
Now the expression becomes: 2/3 * 5/7 - 3/28.7 - 2.2/3
Step 2: Multiply fractions 2/3 * 5/7 = 10/21
Now the expression becomes: 10/21 - 3/28.7 - 2.2/3
Step 3: Find a common denominator Since 21, 28.7, and 3 have different denominators, we need to find a common denominator. The least common multiple of these numbers is 60.
To simplify this expression, we need to follow the order of operations - PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
Given expression: 2/3 * 5/7 - 3/14 / (-4.1/2) - 2.2/3
Step 1: Perform division first
3/14 ÷ (-4.1/2)
To divide by a fraction, we multiply by the reciprocal:
3/14 * (-2/4.1) = -6/57.4 = -3/28.7
Now the expression becomes: 2/3 * 5/7 - 3/28.7 - 2.2/3
Step 2: Multiply fractions
2/3 * 5/7 = 10/21
Now the expression becomes: 10/21 - 3/28.7 - 2.2/3
Step 3: Find a common denominator
Since 21, 28.7, and 3 have different denominators, we need to find a common denominator. The least common multiple of these numbers is 60.
10/21 = (10 60)/(2160) = 600/126
3/28.7 = (3 60)/(28.7 60) = 180/1722
2.2/3 = 44/60
Now the expression becomes: 600/126 - 180/1722 - 44/60
Step 4: Subtract the fractions
600/126 - 180/1722 - 44/60
= 600/126 - 180/1722 - 44/60
Step 5: Perform the subtraction
600/126 = 50/10 = 5
180/1722 = 10/95
44/60 = 22/30 = 11/15
Now the expression becomes: 5 - 10/95 - 11/15
Step 6: Subtract the fractions
5 - 10/95 - 11/15
= 5 - (1015)/(9515) - (1195)/(1595)
= 5 - 150/1425 - 1045/1425
= 5 - 1195/1425
= 3025/1425 - 1195/1425
= 1830/1425
= 122/95
Therefore, 2/3 * 5/7 - 3/14 / (-4.1/2) - 2.2/3 simplifies to 122/95.