Question

Find m if 13/11×22/39×m=1/9​

Answer 1

Answer:

1/6

Step-by-step explanation:

- 13/11 × 22/39 × x = 1/9

- 1 × 2/3x x = 1/9

-2/3x x=1/9

- x= 1/9 ×3/2

-x= 1/3 × 3/2

Finally x = 1/6

Answer 2

★ How to do :-

Here, we are given with two rational numbers that should be multiplied by an other number. We are also given with the answer obtained while multiplying those three fractions. But, we aren't given with the third number that the first two numbers should be multiplied with. We are asked to find the same. To find the answer, we make use of some other concepts such as variables and the transaction of numbers from one hand side to the other. While we are using this method, the sign of the appropriate number changes. We can also check out our answer by verification method. So, let's solve!!

$\:$

➤ Solution :-

${\sf \leadsto \dfrac{13}{11} \times \dfrac{22}{39} \times m = \dfrac{1}{9}}$

Write the fractions on LHS of the statement in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{13}{11} \times \cancel \dfrac{22}{39} \times m = \dfrac{1}{9}}$

Write the obtaining fraction.

${\sf \leadsto \dfrac{1}{1} \times \dfrac{2}{3} \times m = \dfrac{1}{9}}$

Multiply the fractions on LHS.

${\sf \leadsto \dfrac{2}{3} \times m = \dfrac{1}{9}}$

Shift the fraction on LHS to RHS.

${\sf \leadsto m = \dfrac{1}{9} \div \dfrac{2}{3}}$

Take the reciprocal of second fraction and multiply both fractions.

${\sf \leadsto m = \dfrac{1}{9} \times \dfrac{3}{2}}$

Write both numerators and denominators with a common fraction.

${\sf \leadsto m = \dfrac{1 \times 3}{9 \times 2}}$

Multiply the numbers and write the fraction in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{3}{18} = \dfrac{1}{6}}$

$\:$

${\red{\underline{\boxed{\bf So, \: the \: value \: of \: m \: is \: \dfrac{1}{6}.}}}}$

━━━━━━━━━━━━━━━━━━━━━━━

Verification :-

${\sf \leadsto \dfrac{13}{11} \times \dfrac{22}{39} \times m = \dfrac{1}{9}}$

Substitute the value of m.

${\sf \leadsto \dfrac{13}{11} \times \dfrac{22}{39} \times \dfrac{1}{6} = \dfrac{1}{9}}$

Write all numerators and denominators with a common fraction.

${\sf \leadsto \dfrac{13 \times 22 \times 1}{11 \times 39 \times 6} = \dfrac{1}{9}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \dfrac{\cancel{13} \times \cancel{22} \times 1}{\cancel{11} \times \cancel{39} \times 6} = \dfrac{1}{9}}$

Write the obtaining fraction.

${\sf \leadsto \dfrac{1 \times 2 \times 1}{1 \times 3 \times 6} = \dfrac{1}{9}}$

Multiply the remaining numbers.

${\sf \leadsto \dfrac{2}{18} = \dfrac{1}{9}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \dfrac{1}{9} = \dfrac{1}{9}}$

So,

${\sf \leadsto LHS = RHS}$

$\:$

Hence verified !!