Simplifying Fractions with Negative Numbers

To simplify the expression (6/55*-22/9)-(26/125*-10/39), we need to follow the order of operations, which is PEMDAS: Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction. Let's start by simplifying the fractions with negative numbers.

Multiplying Fractions

To multiply fractions, we multiply the numerators together and the denominators together. For example:

2/3 * 4/5 = (2 * 4) / (3 * 5) = 8/15

Using this method, we can simplify the fractions in the expression as follows:

(6/55 * -22/9) - (26/125 * -10/39)
= (-132/495) - (-260/4875)

Adding and Subtracting Fractions

To add or subtract fractions, we need to find a common denominator. To do this, we find the least common multiple (LCM) of the denominators. For example:

1/4 + 2/5 = (5/20) + (8/20) = 13/20

Using this method, we can add and subtract the fractions in the expression as follows:

(-132/495) - (-260/4875)
= (-260/4875) + (132/495)
= (-260 * 99) / (4875 * 99) + (132 * 98) / (495 * 98)
= (-25740 + 12936) / 487650
= -0.028

Final Answer

Therefore, the simplified expression is -0.028.

-16/75