Question

What number should be subtracted from (3/4) - (2/3) to get -1 / 6​

Answer 1

Hello!

Answer:

`\large \boxed{\sf x= (1)/(4)}`

Explanation:

→ We want what number should be subtracted from (3/4) - (2/3) to get -1/6​.

→ Let x be this number.

→ So we have this equation:

`\sf ((3)/(4) - (2)/(3) ) - x = (-1)/(6)`

→ Let's solve this equation to find the number:

◼ Simplify the left side:

`\sf ((3* 3)/(4* 3) - (2* 4)/(3* 4) ) - x = (-1)/(6)`

`\sf ((9)/(12) - (8)/(12) ) - x = (-1)/(6)`

`\sf (1)/(12) - x = (-1)/(6)`

◼ Subtract 1/12 to both sides:

`\sf (1)/(12) - x -(1)/(12)= (-1)/(6) -(1)/(12)`

◼ Simplify both sides:

`\sf - x = (-1)/(6) -(1)/(12)`

`\sf - x = (-1* 2)/(6* 2 ) -(1)/(12)`

`\sf - x = (-2)/(12 ) -(1)/(12)`

`\sf - x = (-3)/(12 )`

◼ Divide both sides by -1:

`\sf - x / -1= (-3)/(12 ) / -1`

◼ Simplify both sides:

`\sf x= (-3)/(12 ) * (1)/(-1)`

`\sf x= (-3*1)/(12*(-1) )`

`\sf x= (-3)/(-12)`

`\sf x= (3)/(12)`

`\boxed{\sf x= (1)/(4)}`

Conclusion:

The number is 1/4.