$If the improper fraction 86211 can be written as the mixed fraction 78pq, find p + q.$

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Solution

11 ) 862 ( 78
-858
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4
$Therefore, \frac{862}{11} = \frac{11 \times 78 + 4}{11} = 78 \frac{4}{11} Comparing with 78 \frac{p}{q}, p = 4 and q = 11 . Therefore, p + q = 4 + 11 = 15$

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All improper fractions can be represented as mixed fractions.

The mixed fraction $3 \frac{p}{q}$ can be written as the product of $3$ and $\frac{p}{q}, i . e . 3 \frac{p}{q} = 3 \times \frac{p}{q}$ .

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