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Evaluate the expression: 74 ÷ 85 ÷ 49 - (41 - 35 ÷ 9 × 2)

Mathematics

ScanSolve AI Answer

Answer

−124466937485\frac{-1244669}{37485}

Step-by-step solution

3 steps

Here's how to solve the expression step-by-step using the order of operations (BODMAS/PEMDAS):

The expression is interpreted as:

74÷85÷49−(41−35÷9×2)74 \div 85 \div 49 - (41 - 35 \div 9 \times 2)
  1. Evaluate the expression inside the parentheses (41−35÷9×2)(41 - 35 \div 9 \times 2).

    Within the parentheses, perform division and multiplication from left to right.
    First, perform the division:

    35÷9=35935 \div 9 = \frac{35}{9}

    Substitute this back:

    (41−359×2)(41 - \frac{35}{9} \times 2)

    Next, perform the multiplication:

    359×2=709\frac{35}{9} \times 2 = \frac{70}{9}

    Substitute this back:

    (41−709)(41 - \frac{70}{9})

    Now, perform the subtraction. To do this, find a common denominator:

    41=41×99=369941 = \frac{41 \times 9}{9} = \frac{369}{9}

    So, the expression inside the parentheses becomes:

    3699−709=369−709=2999\frac{369}{9} - \frac{70}{9} = \frac{369 - 70}{9} = \frac{299}{9}
  2. Evaluate the first part of the main expression

    74÷85÷4974 \div 85 \div 49.
    Perform division from left to right.
    First, 74÷8574 \div 85:

    74÷85=748574 \div 85 = \frac{74}{85}

    Next, divide this result by 49:

    7485÷49=7485×149=7485×49\frac{74}{85} \div 49 = \frac{74}{85} \times \frac{1}{49} = \frac{74}{85 \times 49}

    Calculate the product in the denominator:

    85×49=416585 \times 49 = 4165

    So, the first part of the expression is 744165\frac{74}{4165}.

  3. Substitute the results from Step 1 and Step 2 back into the main expression and perform the final subtraction.

    The expression is now:

    744165−2999\frac{74}{4165} - \frac{299}{9}

    To subtract these fractions, find a common denominator, which is the product of the denominators: 4165×9=374854165 \times 9 = 37485.
    Convert the first fraction:

    744165=74×94165×9=66637485\frac{74}{4165} = \frac{74 \times 9}{4165 \times 9} = \frac{666}{37485}

    Convert the second fraction:

    2999=299×41659×4165=124533537485\frac{299}{9} = \frac{299 \times 4165}{9 \times 4165} = \frac{1245335}{37485}

    Now, perform the subtraction:

    66637485−124533537485=666−124533537485\frac{666}{37485} - \frac{1245335}{37485} = \frac{666 - 1245335}{37485} 666−1245335=−1244669666 - 1245335 = -1244669

    So, the final result is:

    −124466937485\frac{-1244669}{37485}
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