Division of Fractions

Reciprocal:
The reciprocal of \frac { a }{ b } (b\neq 0), is \frac { b }{ a }, i.e. the numerator goes down and the denominator comes up.

The reciprocal of \frac { 3 }{ 2 } is \frac { 2 }{ 3 }

The reciprocal of \frac { 5 }{ 4 } is \frac { 4 }{ 5 }

The reciprocal of 1\frac { 2 }{ 7 } is? Here 1\frac { 2 }{ 7 } =\frac { 9 }{ 7 } (improper)

Therefore, the reciprocal of 1\frac { 2 }{ 7 } =\frac { 7 }{ 9 }

The reciprocal of 3=\frac { 1 }{ 3 } because 3=\frac { 3 }{ 1 }

The reciprocal of 2\frac { 1 }{ 5 } =\frac { 5 }{ 11 }

The reciprocal of -2=-\frac { 1 }{ 2 }

When dividing a fraction by another fraction, we should first convert the second fraction in its reciprocal form, then the division becomes multiplication.

So, if we have
\frac { a }{ b } \div \frac { c }{ d }
This becomes \frac { a }{ b } \times \frac { d }{ c }; we take the reciprocal of c/d which is d/c and the division becomes multiplication.


Examples


Find \frac { 2 }{ 3 } \div \frac { 1 }{ 4 }

\frac { 2 }{ 3 } \div \frac { 1 }{ 4 } =\frac { 2 }{ 3 } \times \frac { 4 }{ 1 }

=\frac { 8 }{ 3 }

=2\frac { 2 }{ 3 }

The reciprocal of \frac { 1 }{ 4 } is \frac { 4 }{ 1 } and division becomes multiplication.


Find 2\frac { 1 }{ 3 } \div \frac { 13 }{ 5 }


Here 2\frac { 1 }{ 3 } \div \frac { 7 }{ 3 } and =1\frac { 3 }{ 5 } =\frac { 8 }{ 5 }

Therefore 2\frac { 1 }{ 3 } \div \frac { 13 }{ 5 } =\frac { 7 }{ 3 } \div \frac { 8 }{ 5 }

=\frac { 35 }{ 24 }

=1\frac { 11 }{ 24 }


Evaluate =3\frac { 1 }{ 4 } \div 1\frac { 2 }{ 3 }

=3\frac { 1 }{ 4 } \div \frac { 13 }{ 4 } and =1\frac { 2 }{ 3 } =\frac { 5 }{ 3 }

Therefore =3\frac { 1 }{ 4 } =\frac { 12 }{ 3 } =\frac { 13 }{ 4 } \div \frac { 5 }{ 3 }

=\frac { 13 }{ 4 } \times \frac { 5 }{ 3 }

=\frac { 39 }{ 20 }

=1\frac { 19 }{ 20 }