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

User Sharcoux
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1 Answer

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\( (5 (5)/(6))/(3 (3)/(4)) - (2)/(9) =
(19)/(9) \) 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.

User David Schoonover
by
8.2k points

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