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(2)/(5)times(-(3)/(7))-(1)/(6)times(3)/(2)+(1)/(14)times(2)/(5)

3 min read Jun 16, 2024
(2)/(5)times(-(3)/(7))-(1)/(6)times(3)/(2)+(1)/(14)times(2)/(5)

Simplifying the Expression: (2/5)(-3/7) - (1/6)(3/2) + (1/14)*(2/5)

This article aims to simplify the given expression step by step, explaining the process and principles involved.

Understanding the Expression

The expression we are working with is:

(2/5)(-3/7) - (1/6)(3/2) + (1/14)*(2/5)

This expression involves multiplication and addition of fractions. To simplify it, we will follow the order of operations (PEMDAS/BODMAS) and utilize the rules of fraction arithmetic.

Step-by-Step Simplification

  1. Multiplication of Fractions:

    • (2/5)*(-3/7): When multiplying fractions, we multiply the numerators and the denominators.
      • (2 * -3) / (5 * 7) = -6/35
    • (1/6)*(3/2): Similarly,
      • (1 * 3) / (6 * 2) = 3/12
    • (1/14)*(2/5):
      • (1 * 2) / (14 * 5) = 2/70

  2. Substitution and Addition: Now we have: -6/35 - 3/12 + 2/70 To add fractions, we need a common denominator.

  3. Finding a Common Denominator:

    • The least common denominator for 35, 12, and 70 is 420.
    • We will convert each fraction to an equivalent fraction with a denominator of 420.
    • -6/35 = (-6 * 12) / (35 * 12) = -72/420
    • 3/12 = (3 * 35) / (12 * 35) = 105/420
    • 2/70 = (2 * 6) / (70 * 6) = 12/420

  4. Final Calculation: Now, we have: -72/420 - 105/420 + 12/420 Adding the numerators: (-72 - 105 + 12) / 420 = -165 / 420 Simplifying the fraction by dividing by 15: (-165 / 15) / (420 / 15) = -11/28

Conclusion

The simplified form of the given expression (2/5)(-3/7) - (1/6)(3/2) + (1/14)*(2/5) is -11/28. This simplification involved performing multiplication, finding a common denominator, and then adding the fractions.

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