Question

3/5+-6/13+-8/15+7/26​

Answer 1

$\frac{3}{5 } - \frac{6}{13} - \frac{8}{15} + \frac{7}{26} \\ lcf = 390 \\ \frac{3 \times 78}{5 \times 78} - \frac{6 \times 30}{13 \times 30} - \frac{8 \times 26}{15 \times 26 } \\ \frac{7 \times 15}{26 \times 15} \\ \frac{234 - 180 - 208 + 105}{390}$

$- \frac{49}{390}$

Answer 2

★ How to do :-

Here, we are given with four fractions in which we are asked to find the sum of all those fractions. We cannot find the sum of these fractions as easier that we find the sum of all other numbers. We can observe that all the fractions have a different denominators. So, first we should find the fractions equivalent to each fraction ans make them as a like fractions i.e, all of them should have same denominators. After finding that, we should only add the numerators and keep the denominator as it is. Ao, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{3}{5} + \dfrac{( - 6)}{13} + \dfrac{( - 8)}{15} + \dfrac{7}{26}}$

Convert them into like fractions by taking the LCM of the denominators.

LCM of 5, 13, 15 and 26 is 390.

${\tt \leadsto \dfrac{3 \times 78}{5 \times 78} + \dfrac{( - 6) \times 30}{13 \times 30} + \dfrac{( - 8) \times 26}{15 \times 26} + \dfrac{7 \times 15}{26 \times 15}}$

Multiply the numerators and the denominators of each fractions.

${\tt \leadsto \dfrac{234}{390} + \dfrac{( - 180)}{390} + \dfrac{( - 208)}{390} + \dfrac{105}{390}}$

Now, arrange all the numerators in one fraction as the denominators are common.

${\tt \leadsto \dfrac{234 + ( - 180) + ( - 208) + 105}{390}}$

Now, simplify the signs given in first two integers.

${\tt \leadsto \dfrac{234 - 180 - 208 + 105}{390}}$

Now, simplify two integers together each.

${\tt \leadsto \dfrac{234 - 180 - 103}{390}}$

Now subtract all the numerators to get the actual fraction.

${\tt \leadsto \pink{\underline{\boxed{\tt \dfrac{(-49)}{390}}}}}$

$\Huge\therefore$ The answer of the given problem is ${\tt \dfrac{(-49)}{390}}$