(5/2) - (4/15) × (8/7) - (4/11) ÷ (6/22)
Answer (1)
To solve the expression 2 5 − 15 4 × 7 8 − 11 4 ÷ 22 6 , we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Identify and Solve Multiplication and Division First:
Multiply 15 4 by 7 8 : 15 4 × 7 8 = 15 × 7 4 × 8 = 105 32 .
Divide 11 4 by 22 6 : 11 4 ÷ 22 6 = 11 4 × 6 22 = 11 × 6 4 × 22 = 66 88 = 3 4 . (Here, we simplified 66 88 to 3 4 by dividing both the numerator and the denominator by 22.)
Perform Subtraction:
Now substitute back into the expression: 2 5 − 105 32 − 3 4 .
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 2, 105, and 3 is 630.
Convert each fraction to have this common denominator:
2 5 = 2 × 315 5 × 315 = 630 1575 .
105 32 = 105 × 6 32 × 6 = 630 192 .
3 4 = 3 × 210 4 × 210 = 630 840 .
Now subtract the fractions: 630 1575 − 630 192 − 630 840 = 630 543 ≈ 0.862.
Therefore, the result of the expression is approximately 0.862 .
