Fractions - Exercise 2(B)

Find the reciprocal of :

$\dfrac{13}{17}$

Answer

We have:

$\dfrac{13}{17}$

To find the reciprocal of a number, we interchange its numerator and denominator.

$\dfrac{13}{17}$ = $\dfrac{17}{13}$

= $1\dfrac{4}{13} \hspace{2cm}\text{[Converting improper to mixed fraction]}$

∴ The reciprocal of $\dfrac{13}{17}$ is $1\dfrac{4}{13}$

Find the reciprocal of :

$\dfrac{3}{313}$

Answer

We have:

$\dfrac{3}{313}$

Interchanging its numerator and denominator we get,

$\dfrac{3}{313}$ = $\dfrac{313}{3}$

= $104\dfrac{1}{3} \hspace{2cm}\text{[Converting improper to mixed fraction]}$

∴ The reciprocal of $\dfrac{3}{313}$ is $104\dfrac{1}{3}$

Find the reciprocal of :

217

Answer

We have:

217

This can be written as $\dfrac{217}{1}$

Interchanging its numerator and denominator we get,

$\dfrac{217}{1}$ = $\dfrac{1}{217}$

∴ The reciprocal of $\dfrac{217}{1}$ is $\dfrac{1}{217}$

Find the reciprocal of :

$\dfrac{1}{1024}$

Answer

We have:

$\dfrac{1}{1024}$

Interchanging its numerator and denominator we get,

$\dfrac{1}{1024}$ = $\dfrac{1024}{1}$ = 1024

∴ The reciprocal of $\dfrac{1}{1024}$ is 1024

Find the reciprocal of :

$3\dfrac{1}{3}$

Answer

We have:

$3\dfrac{1}{3} = \dfrac{10}{3} \hspace{1.5cm}\text{[Converting mixed to improper fraction]}$

Interchanging its numerator and denominator we get,

$\dfrac{10}{3}$ = $\dfrac{3}{10}$

∴ The reciprocal of $\dfrac{10}{3}$ is $\dfrac{3}{10}$

Find the reciprocal of :

$11\dfrac{1}{11}$

Answer

We have:

$11\dfrac{1}{11}$ = $\dfrac{122}{11} \hspace{1.5cm}\text{[Converting mixed to improper fraction]}$

Interchanging its numerator and denominator we get,

$\dfrac{122}{11} = \dfrac{11}{122}$

∴ The reciprocal of $\dfrac{122}{11}$ is $\dfrac{11}{122}$

Find the reciprocal of :

$1\dfrac{1}{2}$

Answer

We have:

$1\dfrac{1}{2} = \dfrac{3}{2} \hspace{1.5cm}\text{[Converting mixed to improper fraction]}$

Interchanging its numerator and denominator we get,

$\dfrac{3}{2}$ = $\dfrac{2}{3}$

∴ The reciprocal of $\dfrac{3}{2}$ is $\dfrac{2}{3}$

Find the reciprocal of :

$125\dfrac{1}{8}$

Answer

We have:

$125\dfrac{1}{8} = \dfrac{1001}{8} \hspace{1.5cm}\text{[Converting mixed to improper fraction]}$

Interchanging its numerator and denominator we get,

$\dfrac{1001}{8}$ = $\dfrac{8}{1001}$

∴ The reciprocal of $\dfrac{1001}{8}$ is $\dfrac{8}{1001}$

Divide :

$\dfrac{1}{2}$ ÷ $\dfrac{1}{3}$

Answer

We have:

$\begin{array}{ll} \phantom{=} \dfrac{1}{2} ÷ \dfrac{1}{3} \\\\ = \dfrac{1}{2} \times \dfrac{3}{1} & [\text{Reciprocal of } \dfrac{1}{3} \text{ is } \dfrac{3}{1}] \\\\ = \dfrac{1 \times 3}{2 \times 1} \\\\ = \dfrac{3}{2} \\\\ = 1\dfrac{1}{2} \end{array}$

∴ The answer is $1\dfrac{1}{2}$

Divide :

$\dfrac{3}{14}$ ÷ $\dfrac{11}{42}$

Answer

We have:

$\begin{array}{ll} \phantom{=} \dfrac{3}{14} ÷ \dfrac{11}{42} \\\\ = \dfrac{3}{14} \times \dfrac{42}{11} & [\text{Reciprocal of } \dfrac{11}{42} \text{ is } \dfrac{42}{11}] \\\\ = \dfrac{3 \times 42}{14 \times 11} \\\\ = \dfrac{3 \times 3}{1 \times 11} & \text{[Simplifying 42 and 14 ⇒ Divide by 14]} \\\\ = \dfrac{9}{11} \\\\ \end{array}$

∴ The answer is $\dfrac{9}{11}$

Divide :

1 ÷ $6\dfrac{2}{3}$

Answer

We have:

$\begin{array}{ll} \phantom{=} 1 ÷ 6\dfrac{2}{3} \\\\ = 1 ÷ \dfrac{20}{3} & \text{[Converting mixed to improper fraction]} \\\\ = 1 \times \dfrac{3}{20} & [\text{Reciprocal of } \dfrac{20}{3} \text{ is } \dfrac{3}{20}] \\\\ = \dfrac{1}{1} \times \dfrac{3}{20} \\\\ = \dfrac{1 \times 3}{1 \times 20} \\\\ = \dfrac{3}{20} \\\\ \end{array}$

∴ The answer is $\dfrac{3}{20}$

Divide :

$13\dfrac{1}{3}$ ÷ 10

Answer

We have:

$\begin{array}{ll} \phantom{=} 13\dfrac{1}{3} ÷ 10 \\\\ = \dfrac{40}{3} ÷ 10 & \text{[Converting mixed to improper fraction]} \\\\ = \dfrac{40}{3} \times \dfrac{1}{10} & [\text{Reciprocal of } 10 \text{ is } \dfrac{1}{10}] \\\\ = \dfrac{4}{3} \times \dfrac{1}{1} & \text{[Simplifying 40 and 10 ⇒ Divide by 10]} \\\\ = \dfrac{4 \times 1}{3 \times 1} \\\\ = \dfrac{4}{3} \\\\ = 1\dfrac{1}{3} \end{array}$

∴ The answer is $1\dfrac{1}{3}$

Divide :

$12\dfrac{1}{12}$ ÷ $\dfrac{5}{36}$

Answer

We have:

$\begin{array}{ll} \phantom{=} 12\dfrac{1}{12} ÷ \dfrac{5}{36} \\\\ = \dfrac{145}{12} ÷ \dfrac{5}{36} & \text{[Converting mixed to improper fraction]} \\\\ = \dfrac{145}{12} \times \dfrac{36}{5} & [\text{Reciprocal of } \dfrac{5}{36} \text{ is } \dfrac{36}{5}] \\\\ = \dfrac{29}{12} \times \dfrac{36}{1} & \text{[Simplifying 145 and 5 ⇒ Divide by 5]} \\\\ = \dfrac{29}{1} \times \dfrac{3}{1} & \text{[Simplifying 36 and 12 ⇒ Divide by 12]} \\\\ = \dfrac{29 \times 3}{1 \times 1} \\\\ = \dfrac{87}{1} \\\\ = 87 \end{array}$

∴ The answer is 87

Divide :

$\dfrac{13}{46}$ ÷ $2\dfrac{1}{11}$

Answer

We have:

$\begin{array}{ll} \phantom{=} \dfrac{13}{46} ÷ 2\dfrac{1}{11} \\\\ = \dfrac{13}{46} ÷ \dfrac{23}{11} & \text{[Converting mixed to improper fraction]} \\\\ = \dfrac{13}{46} \times \dfrac{11}{23} & [\text{Reciprocal of } \dfrac{23}{11} \text{ is } \dfrac{11}{23}] \\\\ = \dfrac{13 \times 11}{46 \times 23} \\\\ = \dfrac{143}{1058} \end{array}$

∴ The answer is $\dfrac{143}{1058}$

Divide :

$\dfrac{20}{31}$ ÷ 54

Answer

We have:

$\begin{array}{ll} \phantom{=} \dfrac{20}{31} ÷ 54 \\\\ = \dfrac{20}{31} \times \dfrac{1}{54} & [\text{Reciprocal of } 54 \text{ is } \dfrac{1}{54}] \\\\ = \dfrac{10}{31} \times \dfrac{1}{27} & \text{[Simplifying 20 and 54 ⇒ Divide by 2]} \\\\ = \dfrac{10 \times 1}{31 \times 27} \\\\ = \dfrac{10}{837} \end{array}$

∴ The answer is $\dfrac{10}{837}$

Divide :

$9\dfrac{4}{5}$ ÷ $3\dfrac{23}{25}$

Answer

We have:

$\begin{array}{ll} \phantom{=} 9\dfrac{4}{5} ÷ 3\dfrac{23}{25} \\\\ = \dfrac{49}{5} ÷ \dfrac{98}{25} & \text{[Converting mixed to improper fraction]} \\\\ = \dfrac{49}{5} \times \dfrac{25}{98} & [\text{Reciprocal of } \dfrac{98}{25} \text{ is } \dfrac{25}{98}] \\\\ = \dfrac{1}{5} \times \dfrac{25}{2} & \text{[Simplifying 49 and 98 ⇒ Divide by 49]} \\\\ = \dfrac{1}{1} \times \dfrac{5}{2} & \text{[Simplifying 25 and 5 ⇒ Divide by 5]} \\\\ = \dfrac{1 \times 5}{1 \times 2} \\\\ = \dfrac{5}{2} \\\\ = 2\dfrac{1}{2} \end{array}$

∴ The answer is $2\dfrac{1}{2}$

Divide :

$32\dfrac{1}{2}$ ÷ $8\dfrac{3}{4}$

Answer

We have:

$\begin{array}{ll} \phantom{=} 32\dfrac{1}{2} ÷ 8\dfrac{3}{4} \\\\ = \dfrac{65}{2} ÷ \dfrac{35}{4} & \text{[Converting mixed to improper fraction]} \\\\ = \dfrac{65}{2} \times \dfrac{4}{35} & [\text{Reciprocal of } \dfrac{35}{4} \text{ is } \dfrac{4}{35}] \\\\ = \dfrac{13}{2} \times \dfrac{4}{7} & \text{[Simplifying 65 and 35 ⇒ Divide by 5]} \\\\ =\dfrac{13}{1} \times \dfrac{2}{7} & \text{[Simplifying 4 and 2 ⇒ Divide by 2]} \\\\ = \dfrac{13 \times 2}{1 \times 7} \\\\ = \dfrac{26}{7} \\\\ = 3\dfrac{5}{7} \end{array}$

∴ The answer is $3\dfrac{5}{7}$

Divide :

$8\dfrac{1}{21}$ ÷ $1\dfrac{6}{7}$

Answer

We have:

$\begin{array}{ll} \phantom{=} 8\dfrac{1}{21} ÷ 1\dfrac{6}{7} \\\\ = \dfrac{169}{21} ÷ \dfrac{13}{7} & \text{[Converting mixed to improper fraction]} \\\\ = \dfrac{169}{21} \times \dfrac{7}{13} & [\text{Reciprocal of } \dfrac{13}{7} \text{ is} \dfrac{7}{13}] \\\\ = \dfrac{13}{21} \times \dfrac{7}{1} & \text{[Simplifying 169 and 13 ⇒ Divide by 13]} \\\\ = \dfrac{13}{3} \times \dfrac{1}{1} & \text{[Simplifying 7 and 21 ⇒ Divide by 7]} \\\\ = \dfrac{13 \times 1}{3 \times 1} \\\\ = \dfrac{13}{3} \\\\ = 4\dfrac{1}{3} \end{array}$

∴ The answer is $4\dfrac{1}{3}$

Divide :

$6\dfrac{3}{16}$ ÷ $3\dfrac{1}{7}$

Answer

We have:

$\begin{array}{ll} \phantom{=} 6\dfrac{3}{16} ÷ 3\dfrac{1}{7} \\\\ = \dfrac{99}{16} ÷ \dfrac{22}{7} & \text{[Converting mixed to improper fraction]} \\\\ = \dfrac{99}{16} \times \dfrac{7}{22} & [\text{Reciprocal of } \dfrac{22}{7} \text{ is } \dfrac{7}{22}] \\\\ = \dfrac{9}{16} \times \dfrac{7}{2} & \text{[Simplifying 99 and 22 ⇒ Divide by 11]} \\\\ = \dfrac{9 \times 7}{16 \times 2} \\\\ = \dfrac{63}{32} \\\\ = 1\dfrac{31}{32} \end{array}$

∴ The answer is $1\dfrac{31}{32}$

Divide :

$3\dfrac{11}{15}$ ÷ $19\dfrac{3}{5}$

Answer

We have:

$\begin{array}{ll} \phantom{=} 3\dfrac{11}{15} ÷ 19\dfrac{3}{5} \\\\ = \dfrac{56}{15} ÷ \dfrac{98}{5} & \text{[Converting mixed to improper fraction]} \\\\ = \dfrac{56}{15} \times \dfrac{5}{98} & [\text{Reciprocal of } \dfrac{98}{5} \text{ is } \dfrac{5}{98}] \\\\ = \dfrac{56}{3} \times \dfrac{1}{98} & \text{[Simplifying 5 and 15 ⇒ Divide by 5]} \\\\ = \dfrac{4}{3} \times \dfrac{1}{7} & \text{[Simplifying 56 and 98 ⇒ Divide by 14]} \\\\ = \dfrac{4 \times 1}{3 \times 7} \\\\ = \dfrac{4}{21} \end{array}$

∴ The answer is $\dfrac{4}{21}$

By what fraction should $\dfrac{9}{35}$ be multiplied to get $\dfrac{7}{15}$ ?

Answer

Given:

The fraction by which $\dfrac{9}{35}$ must be multiplied to get $\dfrac{7}{15}$ = ?

Let the required fraction be x

Now we have,

$\dfrac{9}{35} \times x = \dfrac{7}{15}$

x = $\dfrac{7}{15} ÷ \dfrac{9}{35}$

$\begin{array}{ll} = \dfrac{7}{15} \times \dfrac{35}{9} & [\text{Reciprocal of } \dfrac{9}{35} \text{ is } \dfrac{35}{9}] \\\\ = \dfrac{7}{3} \times \dfrac{7}{9} & \text{[Simplifying 35 and 15 ⇒ Divide by 5]} \\\\ = \dfrac{7 \times 7}{3 \times 9} \\\\ = \dfrac{49}{27} \\\\ = 1\dfrac{22}{27} \end{array}$

∴ The answer is $1\dfrac{22}{27}$

If the cost of $6\dfrac{1}{4}$ m of cloth is ₹$1421\dfrac{7}{8}$, then find the cost of 1 metre of cloth.

Answer

Given:

Total cost = ₹$1421\dfrac{7}{8} = ₹\dfrac{11375}{8}$

Total length = $6\dfrac{1}{4}\text{ m} = \dfrac{25}{4}\text{ m}$

Cost of 1 metre of cloth = ?

Cost of 1 metre of cloth = (Total cost) ÷ (Total length)

Substituting the values in above, we get:

Cost of 1 metre of cloth = ₹ $\dfrac{11375}{8} ÷ \dfrac{25}{4}$ m

$\begin{array}{ll} = ₹\Big(\dfrac{11375}{8} \times \dfrac{4}{25}\Big) & [\text{Reciprocal of } \dfrac{25}{4} \text{ is } \dfrac{4}{25}] \\\\ = ₹\Big(\dfrac{455}{8} \times \dfrac{4}{1}\Big) & \text{[Simplifying 11375 and 25 ⇒ Divide by 25]} \\\\ = ₹\Big(\dfrac{455}{2} \times \dfrac{1}{1}\Big) & \text{[Simplifying 4 and 8 ⇒ Divide by 4]} \\\\ = ₹\dfrac{455 \times 1}{2 \times 1} \\\\ = ₹\dfrac{455}{2} \\\\ = ₹227\dfrac{1}{2} \end{array}$

∴ The cost of 1 metre of cloth = ₹$227\dfrac{1}{2}$

How many pieces of length $3\dfrac{5}{7}$m each can be cut from a wall paper 52 m long?

Answer

Given:

Piece length = $3\dfrac{5}{7}$ m = $\dfrac{26}{7}$ m $\hspace{1.5cm}\text{[Converting mixed to improper fraction]}$

Total length = 52 m

Number of pieces = ?

Number of pieces = (Total length) ÷ (Piece length)

Substituting the values in above, we get:

Number of pieces = 52 m ÷ $\dfrac{26}{7}$ m

$\begin{array}{ll} = \Big(\dfrac{52}{1} \times \dfrac{7}{26}\Big) & [\text{Reciprocal of } \dfrac{26}{7} \text{ is } \dfrac{7}{26}] \\\\ = \Big(\dfrac{2}{1} \times \dfrac{7}{1}\Big) & \text{[Simplifying 52 and 26 ⇒ Divide by 26]} \\\\ = \Big(\dfrac{2 \times 7}{1 \times 1}\Big) \\\\ = \dfrac{14}{1} \\\\ = 14 \end{array}$

∴ Number of pieces = 14

A log of wood $6\dfrac{2}{7}$m in length, was cut into 11 pieces. What is the length of each piece?

Answer

Given :

Total length of a log of wood = $6\dfrac{2}{7}$ m = $\dfrac{44}{7}$ m

Number of pieces = 11

Length of each piece = ?

Length of each piece = (Total length of a log of wood) ÷ (Number of pieces)

Substituting the values in above, we get:

Length of each piece = $\dfrac{44}{7}$ m ÷ 11

$\begin{array}{ll} = \Big(\dfrac{44}{7} \times \dfrac{1}{11}\Big)\text{ m} & [\text{Reciprocal of } 11 \text{ is } \dfrac{1}{11}] \\\\ = \Big(\dfrac{4}{7} \times \dfrac{1}{1}\Big)\text{ m} & \text{[Simplifying 44 and 11 ⇒ Divide by 11]} \\\\ = \dfrac{4}{7}\text{ m} \\\\ \end{array}$

∴ The length of each piece = $\dfrac{4}{7}$ m

A car covers $641\dfrac{1}{4}$km in $43\dfrac{1}{8}$ litres of fuel. How much distance can this car cover in 1 litre of fuel ?

Answer

Given:

Total distance = $641\dfrac{1}{4}\text{ km} = \dfrac{2565}{4}$ km

Total fuel = $43\dfrac{1}{8}\text{ litres} = \dfrac{345}{8}\text{ litres}$

Distance per litre = ?

Distance per litre = (Total distance) ÷ (Total fuel)

Substituting the values in above, we get:

Distance per litre = $\dfrac{2565}{4}\text{ km} ÷ \dfrac{345}{8}\text{ litres}$

$\begin{array}{ll} = \Big(\dfrac{2565}{4} \times \dfrac{8}{345}\Big)\text{ km} & [\text{Reciprocal of } \dfrac{345}{8} \text{ is } \dfrac{8}{345}] \\\\ = \Big(\dfrac{2565}{1} \times \dfrac{2}{345}\Big)\text{ km} & \text{[Simplifying 8 and 4 ⇒ Divide by 4]} \\\\ = \Big(\dfrac{171}{1} \times \dfrac{2}{23}\Big)\text{ km} & \text{[Simplifying 2565 and 345 ⇒ Divide by 15]} \\\\ = \dfrac{171 \times 2}{1 \times 23} \text{ km} \\\\ = \dfrac{342}{23} \text{ km} \\\\ = 14\dfrac{20}{23} \text{ km} \end{array}$

∴ The distance per litre of petrol = $14\dfrac{20}{23}$ km

The area of a rectangular plot of land is $817\dfrac{4}{5}$sq. m. If its breadth is $21\dfrac{3}{4}$m, find its length.

Answer

Given:

Area of rectangular plot of land = $817\dfrac{4}{5}\text{ m}^2 = \dfrac{4089}{5}\text{ m}^2$

Breadth = $21\dfrac{3}{4}\text{ m} = \dfrac{87}{4} \text{ m}$

Length of rectangular plot of land = ?

Length of rectangular plot of land = (Area of rectangular plot of land) ÷ (Breadth)

Substituting the values in above, we get:

Length of rectangular plot of land = $\dfrac{4089}{5}\text{ m}^2 ÷ \dfrac{87}{4} \text{ m}$

$\begin{array}{ll} = \Big(\dfrac{4089}{5} \times \dfrac{4}{87}\Big)\text{ m} & [\text{Reciprocal of } \dfrac{87}{4} \text{ is } \dfrac{4}{87}] \\\\ = \Big(\dfrac{47}{5} \times \dfrac{4}{1}\Big)\text{ m} & \text{[Simplifying 2565 and 345 ⇒ Divide by 15]} \\\\ = \dfrac{47 \times 4}{5 \times 1} \text{ m} \\\\ = \dfrac{188}{5} \text{ m} \\\\ = 37\dfrac{3}{5}\text{ m} \end{array}$

∴ The breadth of rectangular plot of land = $37\dfrac{3}{5}$ m

The area of a sheet of paper is $623\dfrac{7}{10}$ sq. cm. If its length is $29\dfrac{7}{10}$cm, find its width.

Answer

Given:

Area of a sheet of paper = $623\dfrac{7}{10}\text{ cm}^2 = \dfrac{6237}{10}\text{ cm}^2$

Length = $29\dfrac{7}{10}\text{ cm} = \dfrac{297}{10}\text{ cm}$

Width = ?

The sheet of paper will be in rectangular shape,

∴ Area = Length x Width

Width = Area ÷ Length

Substituting the values in above, we get:

Width = $\dfrac{6237}{10}\text{ cm}^2$ ÷ $\dfrac{297}{10}\text{ cm}$

$\begin{array}{ll} = \Big(\dfrac{6237}{10} \times \dfrac{10}{297}\Big)\text{ cm} & [\text{Reciprocal of } \dfrac{297}{10} \text{ is } \dfrac{10}{297}] \\\\ = \Big(\dfrac{6237}{1} \times \dfrac{1}{297}\Big)\text{ cm} & \text{[Simplifying 10 and 10 ⇒ Divide by 1]} \\\\ = \dfrac{6237 \times 1}{1 \times 297} \text{ cm} \\\\ = \dfrac{6237}{297}\text{ cm} \\\\ = 21 \text{ cm} \end{array}$

∴ The width of a sheet of paper = 21 cm

A bundle of 500 sheets of paper has a net weight of $2\dfrac{3}{10}$kg. Find the weight of 1 sheet of paper.

Answer

Given:

Total weigth = $2\dfrac{3}{10} \text{ kg} = \dfrac{23}{10} \text{ kg}$

Number of sheets = 500

Weigth of 1 sheet of paper = (Total weigth) ÷ (Number of sheets)

Substituting the values in above, we get:

Weigth of 1 sheet of paper = $\dfrac{23}{10}$ kg ÷ 500

$\begin{array}{ll} = \Big(\dfrac{23}{10} \times \dfrac{1}{500}\Big)\text{ kg} & [\text{Reciprocal of } 500 \text{ is } \dfrac{1}{500}] \\\\ = \dfrac{23 \times 1}{10 \times 500} \text{ kg} \\\\ = \dfrac{23}{5000} \text{ kg} \end{array}$

∴ The weigth of 1 sheet of paper = $\dfrac{23}{5000}$ kg

A car travels $283\dfrac{1}{2}$ km in $4\dfrac{2}{3}$ hours. How far does this car go in 1 hour, travelling at the same speed?

Answer

Given:

Total distance = $283\dfrac{1}{2}\text{ km} = \dfrac{567}{2}\text{ km}$

Total time = $4\dfrac{2}{3}\text{ hours} = \dfrac{14}{3}\text{ hours}$

Distance covered in 1 hour = ?

Distance covered in 1 hour = (Total distance) ÷ (Total time)

Substituting the values in above, we get:

Distance covered in 1 hour = $\dfrac{567}{2}\text{ km} ÷ \dfrac{14}{3}\text{ hours}$

$\begin{array}{ll} = \Big(\dfrac{567}{2} \times \dfrac{3}{14}\Big) \text{ km} & [\text{Reciprocal of } \dfrac{14}{3} \text{ is } \dfrac{3}{14}] \\\\ = \Big(\dfrac{81}{2} \times \dfrac{3}{2}\Big) \text{ km} & \text{[Simplifying 567 and 14 ⇒ Divide by 7]} \\\\ = \dfrac{81 \times 3}{2 \times 2}\text{ km} \\\\ = \dfrac{243}{4}\text{ km} \\\\ = 60\dfrac{3}{4}\text{ km} \end{array}$

∴ The distance covered in 1 hour = $60\dfrac{3}{4}$ km

The product of two fractions is $8\dfrac{7}{25}$. If one of them is $3\dfrac{1}{15}$ find the other.

Answer

Given:

Let the two fractions be p and q.

p = $3\dfrac{1}{15} = \dfrac{46}{15}$

Let the other fraction be q.

p x q = $8\dfrac{7}{25} = \dfrac{207}{25}$

q = $\dfrac{207}{25}$ ÷ p $\hspace{2cm}\text{[Solving for q]}$

Substituting the value of p, we get:

q = $\dfrac{207}{25} ÷ \dfrac{46}{15}$

$\begin{array}{ll} = \dfrac{207}{25} \times \dfrac{15}{46} & [\text{Reciprocal of } \dfrac{46}{15} \text{ is } \dfrac{15}{46}] \\\\ = \dfrac{207}{5} \times \dfrac{3}{46} & \text{[Simplifying 15 and 25 ⇒ Divide by 5]} \\\\ = \dfrac{9}{5} \times \dfrac{3}{2} & \text{[Simplifying 207 and 46 ⇒ Divide by 23]} \\\\ = \dfrac{9 \times 3}{5 \times 2} \\\\ = \dfrac{27}{10} \\\\ = 2\dfrac{7}{10} \end{array}$

∴ The other fraction = $2\dfrac{7}{10}$