How do you simplify $∣ ∣ ∣ \frac{1}{5} - \frac{1}{3} ∣ ∣ ∣$ $abs(1/5-1/3)$ ?

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How do you simplify $∣ ∣ ∣ \frac{1}{5} - \frac{1}{3} ∣ ∣ ∣$ $abs(1/5-1/3)$ ?

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Answer 1 · 2018-03-24T11:09:13

$\frac{2}{15}$ $2/15$

Explanation:

$evaluating the fractions as a first step$ $"evaluating the fractions as a first step"$

$Before subtracting we require a common denominator$ $"Before subtracting we require a "color(blue)"common denominator"$

$the lowest common multiple of 5 and 3 is 15$ $"the lowest common multiple of 5 and 3 is 15"$

$\Rightarrow \frac{1}{5} - \frac{1}{3} = \frac{1 \times 3}{5 \times 3} - \frac{1 \times 5}{3 \times 5} = \frac{3}{15} - \frac{5}{15}$ $rArr1/5-1/3=(1xx3)/(5xx3)-(1xx5)/(3xx5)=3/15-5/15$

$subtract the numerators leaving the denominator$ $"subtract the numerators leaving the denominator"$

$\Rightarrow \frac{3}{15} - \frac{5}{15} = \frac{3 - 5}{15} = - \frac{2}{15}$ $rArr3/15-5/15=(3-5)/15=-2/15$

$the absolute value is always positive$ $"the "color(blue)"absolute value is always positive"$

$\Rightarrow ∣ ∣ ∣ - \frac{2}{15} ∣ ∣ ∣ = \frac{2}{15}$ $rArr|-2/15|=2/15$

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