Express the following as improper fractions:
(a) $ 7 \frac{3}{4} $
(b) $ 5 \frac{6}{7} $
(c) $ 2 \frac{5}{6} $
(d) $ 10 \frac{3}{5} $
(e) $ 9 \frac{3}{7} $
(f) $ 8 \frac{4}{9} $

To do :

We have to convert the given fractions to improper fractions.

Solution :

To convert a mixed fraction to an improper fraction, follow these steps:

1. Multiply the whole number part by the fraction's denominator.

2. Add the result to the numerator.

3. Then write the result on top of the denominator keeping denominator unchanged.

(a) $7\frac{3}{4}$.

1. $7\times 4 + 3 = 28 + 3 = 31$ is the numerator.

2. Denominator remains unchanged.

3. So, $7 \frac{3}{4} =\frac{31}{4}$.

Therefore, improper fraction of $7 \frac{3}{4}$ is $\frac{31}{4}$.

(b) $5\frac{6}{7}$.

1. $5\times 7 + 6= 35 + 6 = 41$ is the numerator.

2. Denominator remains unchanged.

3. So, $5 \frac{6}{7} =\frac{41}{7}$.

Therefore, improper fraction of $5 \frac{6}{7}$ is $\frac{41}{7}$.

(c) $2\frac{5}{6}$.

1. $2\times 6+ 5= 12 + 5 = 17$ is the numerator.

2. Denominator remains unchanged.

3. So, $2 \frac{5}{6} =\frac{17}{6}$.

Therefore, improper fraction of $2 \frac{5}{6}$ is $\frac{17}{6}$.

(d) $10\frac{3}{5}$.

1. $10\times 5+ 3= 50 + 3 = 53$ is the numerator.

2. Denominator remains unchanged.

3. So, $10 \frac{3}{5} =\frac{53}{5}$.

Therefore, improper fraction of $10 \frac{3}{5}$ is $\frac{53}{5}$.

(e) $9\frac{3}{7}$.

1. $9\times 7+ 3= 63 + 3 = 66$ is the numerator.

2. Denominator remains unchanged.

3. So, $9 \frac{3}{7} =\frac{66}{7}$.

Therefore, improper fraction of $9 \frac{3}{7}$ is $\frac{66}{7}$.

(f) $8\frac{4}{9}$.

1. $8\times 9+ 4= 72 + 4 = 76$ is the numerator.

2. Denominator remains unchanged.

3. So, $8 \frac{4}{9} =\frac{76}{9}$.

Therefore, improper fraction of $8 \frac{4}{9}$ is $\frac{76}{9}$.

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Updated on: 10-Oct-2022

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