Question

(3_4/11×11/5)÷(3/7×x)=4/3​

Answer 1

Given:

$\sf{ \bigg( 3\dfrac{4}{11} \times \dfrac{11}{5} \bigg) \div \bigg( \dfrac{3}{7} \times x\bigg) = \dfrac{4}{3}}$

What To Find:

We have to find the value of x.

Solution:

$\sf{ \bigg( 3\dfrac{4}{11} \times \dfrac{11}{5} \bigg) \div \bigg( \dfrac{3}{7} \times x\bigg) = \dfrac{4}{3}}$

Convert the mixed fraction into an improper fraction,

⇒ $\sf{ \bigg( \dfrac{37}{11} \times \dfrac{11}{5} \bigg) \div \bigg( \dfrac{3}{7} \times x\bigg) = \dfrac{4}{3}}$

Solve the 1st bracket by canceling 11,

⇒ $\sf{ \bigg( \dfrac{37}{5} \bigg) \div \bigg( \dfrac{3}{7} \times x\bigg) = \dfrac{4}{3}}$

Solve the 2nd bracket,

⇒ $\sf{ \bigg( \dfrac{37}{5} \bigg) \div \bigg( \dfrac{3x}{7} \bigg) = \dfrac{4}{3}}$

Remove the brackets,

⇒ $\sf{ \dfrac{37}{5} \times \dfrac{7}{3x} = \dfrac{4}{3}}$

Multiply the fractions,

⇒ $\sf{ \dfrac{259}{15x} = \dfrac{4}{3}}$

Now use cross multiplication,

⇒ 259 × 3 = 15x × 4

Multiply 259 by 3,

⇒ 777 = 15x × 4

Multiply 15x by 4,

⇒ 777 = 60x

Take 60 to LHS,

⇒ $\sf{\dfrac{777}{60} = x}$

Divide 777 by 60,

⇒ $\sf{\dfrac{259}{20} = x}$

Convert it into decimal (if needed)

⇒ 12.95 = x

∴ Hence the value of x of the given equation is 12.95.