Question

Simplify (1/2-3/4) ÷ (-3/10x5/8)​

Answer 1

Hello!

Answer:

`\Large \boxed{\sf (4)/(3)}`

Explanation:

→ We want to simplify this expression:

`\sf ((1)/(2) - (3)/(4)) / (-(3)/(10) * (5)/(8) )`

◼ Put the fractions to the same denominator:

`\sf ((1 * 2)/(2 * 2) - (3)/(4)) / (-(3 )/(10 ) * (5 )/(8 ) )`

`\sf ((2)/(4) - (3)/(4)) / (-(3)/(10) * (5)/(8) )`

◼ Simplify the fractions:

`\sf ((2-3)/(4) ) / (-(3 * 5)/(10 * 8) )`

`\sf (-(1)/(4) ) / (-(15)/(80) )`

`\sf (-(1)/(4) ) / (-( 3 * 5 )/(16 * 5) )`

`\sf (-(1)/(4) ) / (-(3)/(16) )`

◼ We know that a/b ÷ c/d is equal to a/b × d/c:

`\sf (-(1)/(4) ) * (-(16)/(3) )`

◼ Simplify the multiplication:

`\sf ((-1) *(-16))/(4 *3)`

◼ Simplify the fraction:

`\sf (16)/(12)`

`\sf (4* 4)/(3* 4)`

`\boxed{\sf (4)/(3)}`

Conclusion:

The expression (1/2 - 3/4) ÷ (-3/10 × 5/8)​ is equal to 4/3.