(-(3)/(2)times(4)/(5))+((9)/(5)times(-10)/(3))-((1)/(2)times(3)/(4))

3 min read Jun 16, 2024

Solving the Expression: (-(3)/(2)times(4)/(5))+((9)/(5)times(-10)/(3))-((1)/(2)times(3)/(4))

This article will guide you through the steps involved in solving the given mathematical expression:

(-(3)/(2)times(4)/(5))+((9)/(5)times(-10)/(3))-((1)/(2)times(3)/(4))

Step 1: Simplifying Multiplication

We start by performing the multiplications within each set of parentheses. Remember, when multiplying fractions, we multiply the numerators and the denominators:

(-(3)/(2)times(4)/(5)) = - (3 * 4) / (2 * 5) = -12/10
((9)/(5)times(-10)/(3)) = (9 * -10) / (5 * 3) = -90/15
((1)/(2)times(3)/(4)) = (1 * 3) / (2 * 4) = 3/8

Step 2: Substituting Simplified Terms

Now we substitute the simplified terms back into the original expression:

-12/10 + (-90/15) - 3/8

Step 3: Finding a Common Denominator

To add or subtract fractions, they must have the same denominator. The least common denominator for 10, 15, and 8 is 120. We need to convert each fraction to an equivalent fraction with a denominator of 120:

-12/10 = (-12 * 12) / (10 * 12) = -144/120
-90/15 = (-90 * 8) / (15 * 8) = -720/120
3/8 = (3 * 15) / (8 * 15) = 45/120

Step 4: Adding and Subtracting Fractions

With the same denominator, we can now add and subtract the fractions:

-144/120 + (-720/120) - 45/120 = (-144 - 720 - 45) / 120

Step 5: Simplifying the Result

Finally, we simplify the result:

-899 / 120

Therefore, the solution to the expression (-(3)/(2)times(4)/(5))+((9)/(5)times(-10)/(3))-((1)/(2)times(3)/(4)) is -899/120.