Question 25 of 58beginner🔧 ApplyNumerical1 mark

Simplify the expression: (−14)+(512)\left(-\frac{1}{4}\right) + \left(\frac{5}{12}\right).

Correct Answer

16\frac{1}{6}

Exercise: Exercise Set 3.4 | Q: 3 | (Page 12)
For More Understanding

Explanation

To add rational numbers with different denominators, we first make the denominators equal by finding their LCM. Once the denominators are the same, we add the numerators. Finally, we simplify the resulting fraction to its lowest terms.

Solution Steps

  1. Step 1: Find the LCM of the denominators 4 and 12, which is 12.

  2. Step 2: Convert the fractions to have a common denominator of 12: −14=−1×34×3=−312-\frac{1}{4} = -\frac{1 \times 3}{4 \times 3} = -\frac{3}{12}.

  3. Step 3: Add the fractions: −312+512=−3+512=212-\frac{3}{12} + \frac{5}{12} = \frac{-3 + 5}{12} = \frac{2}{12}.

  4. Step 4: Simplify the resulting fraction by dividing the numerator and denominator by their HCF (2): 212=16\frac{2}{12} = \frac{1}{6}.

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