Question

5 5/6 divide by 3 3/4 subtract 2/9

Answer 1

`\( (5 (5)/(6))/(3 (3)/(4)) - (2)/(9)` =
`(19)/(9) \)` or approximately 2.11.

To solve the expression
`\( (5 (5)/(6))/(3 (3)/(4)) - (2)/(9) \),` let's start by converting the mixed numbers to improper fractions.

`\( 5 (5)/(6) \)` can be written as
`\( (35)/(6) \)` because
`\( 5 * 6 + 5 = 35 \).`

Similarly,
`\( 3 (3)/(4) \)` can be expressed as
`\( (15)/(4) \)` because
`\( 3 * 4 + 3 = 15 \).`

Now, the expression becomes
`\( ((35)/(6))/((15)/(4))`
`- (2)/(9) \).`

To divide fractions, multiply by the reciprocal of the divisor, so we get
`\( (35)/(6) * (4)/(15) - (2)/(9) \).`

Simplify the fractions:
`\( (7)/(2) * (2)/(3) - (2)/(9) \).`

Multiply the numerators and denominators separately:
`\( (7 * 2)/(2 * 3) - (2)/(9) \).`

This results in
`\( (14)/(6) - (2)/(9) \).`

Find a common denominator, which is 18:
`\( (14 * 3)/(6 * 3) - (2 * 2)/(9 * 2) \).`

This simplifies to
`\( (42)/(18) - (4)/(18) \).`

Now, subtract the numerators:
`\( (38)/(18) \).`

Finally, simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:
`\( (19)/(9) \).`

So,
`\( (5 (5)/(6))/(3 (3)/(4)) - (2)/(9)`
`= (19)/(9) \) or approximately 2.11.`