Question

Solve the puzzle. Fill in the grey box. Don't spam.​

Answer 1

Answer:

Crossword Puzzle on Rational Numbers

Step-by-step-explanation:

NOTE: Refer to the attachment first.

Let the gray coloured boxes be x.

In the first column ( vertical line ),

$\displaystyle\sf\:5\:\dfrac{1}{3}\:\times\:x\:=\:6\\\\\\\implies\sf\:\dfrac{5\:\times\:3\:+\:1}{3}\:\times\:x\:=\:6\\\\\\\implies\sf\:\dfrac{16}{3}\:\times\:x\:=\:6\\\\\\\implies\sf\:x\:=\:\dfrac{6\:\times\:3}{16}\\\\\\\implies\sf\:x\:=\:\cancel{\dfrac{18}{16}}\\\\\\\implies\boxed{\red{\sf\:x\:=\:\dfrac{9}{8}}}$

In the second column,

$\displaystyle\sf\:\dfrac{6}{7}\:-\:x\:=\:1\:\dfrac{1}{14}\\\\\\\implies\sf\:\dfrac{6}{7}\:-\:x\:=\:\dfrac{14\:\times\:1\:+\:1}{14}\\\\\\\implies\sf\:\dfrac{6}{7}\:-\:x\:=\:\dfrac{14\:+\:1}{14}\\\\\\\implies\sf\:\dfrac{6}{7}\:-\:x\:=\:\dfrac{15}{14}\\\\\\\implies\sf\:x\:=\:\dfrac{6}{7}\:-\:\dfrac{15}{14}\\\\\\\implies\sf\:x\:=\:\dfrac{6\:\times\:2}{7\:\times\:2}\:-\:\dfrac{15}{14}\\\\\\\implies\sf\:x\:=\:\dfrac{12}{14}\:-\:\dfrac{15}{14}\\\\\\\implies\sf\:x\:=\:\dfrac{12\:-\:15}{14}\\\\\\\implies\boxed{\red{\sf\:x\:=\:-\:\dfrac{3}{14}}}$

In the first row ( horizontal line ),

$\displaystyle\sf\:\dfrac{6}{7}\:+\:x\:=\:\dfrac{9}{14}\\\\\\\implies\sf\:x\:=\:\dfrac{9}{14}\:-\:\dfrac{6}{7}\\\\\\\implies\sf\:x\:=\:\dfrac{9}{14}\:-\:\dfrac{6\:\times\:2}{7\:\times\:2}\\\\\\\implies\sf\:x\:=\:\dfrac{9}{14}\:-\:\dfrac{12}{14}\\\\\\\implies\sf\:x\:=\:\dfrac{9\:-\:12}{14}\\\\\\\implies\boxed{\red{\sf\:x\:=\:-\:\dfrac{3}{14}}}$

In the third column,

$\displaystyle\sf\:-\:\dfrac{3}{14}\:\times\:-\:\dfrac{5}{6}\:=\:x\\\\\\\implies\sf\:x\:=\:\dfrac{-\:3\:\times\:-\:5}{14}{6}\\\\\\\implies\sf\:x\:=\:\dfrac{-\:1\:\times\:-\:5}{14\:\times\:2}\\\\\\\implies\boxed{\red{\sf\:x\:=\:\dfrac{5}{28}}}$

In the second row,

$\displaystyle\sf\:-\:\dfrac{5}{6}\:-\:x\:=\:-\:\dfrac{1}{4}\\\\\\\implies\sf\:x\:=\:-\:\dfrac{5}{6}\:+\:\dfrac{1}{4}\\\\\\\implies\sf\:x\:=\:\dfrac{-\:5\:\times\:4\:+\:1\:\times\:6}{6\:\times\:4}\\\\\\\implies\sf\:x\:=\:\dfrac{-\:20\:+\:6}{24}\\\\\\\implies\sf\:x\:=\:-\:\dfrac{14}{24}\\\\\\\implies\boxed{\red{\sf\:x\:=\:-\:\dfrac{7}{12}}}$

In the fourth column,

$\displaystyle\sf\:\dfrac{9}{14}\:=\:-\:\dfrac{7}{12}\:\times\:x\\\\\\\implies\sf\:x\:=\:\dfrac{9\:\times\:12}{14\:\times\:-\:7}\\\\\\\implies\sf\:x\:=\:-\:\dfrac{108}{98}\\\\\\\implies\boxed{\red{\sf\:x\:=\:-\:\dfrac{54}{49}}}$

In the last column,

$\displaystyle\sf\:-\:\dfrac{1}{4}\:-\:x\:=\:-\:1\\\\\\\implies\sf\:x\:=\:-\:\dfrac{1}{4}\:+\:1\\\\\\\implies\sf\:x\:=\:\dfrac{-\:1\:+\:4\:\times\:1}{4}\\\\\\\implies\sf\:x\:=\:\dfrac{-\:1\:+\:4}{4}\\\\\\\implies\boxed{\red{\sf\:x\:=\:\dfrac{3}{4}}}$

In the last row,

$\displaystyle\sf\:x\:=\:\dfrac{7}{9}\:+\:\left(\:-\:1\:\right)\\\\\\\implies\sf\:x\:=\:\dfrac{7}{9}\:-\:1\\\\\\\implies\sf\:x\:=\:\dfrac{7\:-\:9\:\times\:1}{9}\\\\\\\implies\sf\:x\:=\:\dfrac{7\:-\:9}{9}\\\\\\\implies\boxed{\red{\sf\:x\:=\:-\:\dfrac{2}{9}}}$