Division of fraction involves multiplication of the dividend with the reciprocal of the divisor. The numerator of the dividend is multiplied by the denominator of the divisor and this constitutes the numerator of the quotient. The denominator of the dividend is multiplied by the numerator of the divisor and this constitutes the denominator of the quotient. Similar to multiplication of fractions, mixed numbers should be converted into improper fractions first and also reduced the quotient to lowest terms as possible.

The dividend is 2/5 and the divisor is `4/15`.

Multiply the dividend by the reciprocal of the divisor.

`2/5 × 15/4 = 30/20`

Reduce the quotient to lowest terms;

`30/20 = (2 × 3 × 5)/(2 × 2 × 5) = 3/2`

Therefore, 2/5 ÷ 4/15 = 3/2

The dividend is `7 1/2` and the divisor is `3 3/4`.

Convert the mixed numbers into improper fractions.

`7 1/2 = ((7 × 2)+ 1)/2 = (14 + 1)/2 = 15/2`

`3 3/4 = ((3 × 4)+ 3)/4 = (12 + 3)/4 = 15/4`

The dividend is `15/2` and the divisor is `15/4`.

Multiply the dividend by the reciprocal of the divisor.

`15/2 × 4/15 = 60/30`

Reduce the quotient to lowest terms.

`60/30 = (2 × 2 × 3 × 5)/(2 × 3 × 5) = 2`

Therefore, `7 1/2 ÷ 3 3/4 = 2`

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