5 marks

Question 15 Marks

The sum of two fractions is $5 \frac{3}{9}$. If one of the fractions is $2 \frac{3}{4}$, find the other fraction

Answer

$\text { Sum of two fractions }=5 \frac{3}{9} $
$ \text { One of them }=2 \frac{3}{4} $
$ \therefore \text { The other fraction }=5 \frac{3}{9}-2 \frac{3}{4}$
$=\frac{48}{9}-\frac{11}{4}$
$ =\frac{16}{3}-\frac{11}{4} $
$=\frac{(16 \times 4)-(11 \times 3)}{3 \times 4}$
$ =\frac{64-33}{12} $
$\frac{\frac{2}{31}}{\frac{24}{7}}$
$ =\frac{31}{12}$
$=2 \frac{7}{12}$

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Question 25 Marks

What fraction is to be subtracted from $9 \frac{3}{7}$ to get $3 \frac{1}{5} ?$

Answer

$9 \frac{3}{7}-(\text { The number to be subtracted })=3 \frac{1}{5}$
$\therefore 9 \frac{3}{7}-3 \frac{1}{5}=$ The number to be subtracted
$\therefore$ The number to be subtracted $=\left(9+\frac{3}{7}\right)-\left(3+\frac{1}{5}\right)$
$=(9-3)+\left(\frac{3}{7}-\frac{1}{5}\right) $
$=6+\left(\frac{(3 \times 5)-(1 \times 7)}{7 \times 5}\right) $
$=6+\left(\frac{15-7}{35}\right) $
$=6+\frac{8}{35}$
$\therefore$ The fraction to be subtracted $=6 \frac{8}{35}$

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Question 35 Marks

Add the difference between $1 \frac{1}{3}$ and $3 \frac{1}{6}$ and the difference between $4 \frac{1}{6}$ and $2 \frac{1}{3}$

Answer

We have to find $\left(3 \frac{1}{6}-1 \frac{1}{3}\right)+\left(4 \frac{1}{6}-2 \frac{1}{3}\right)$
$=\left(\frac{19}{6}-\frac{4}{3}\right)+\left(\frac{25}{6}-\frac{7}{3}\right) \ldots\left[\because 3 \frac{1}{6}>1 \frac{1}{3} \text { and } 4 \frac{1}{6}>2 \frac{1}{3}\right]$
$=\left(\frac{19}{6}-\frac{8}{6}\right)+\left(\frac{25}{6}-\frac{14}{6}\right)$
$=\frac{11}{6}+\frac{11}{6}$
6) $\frac{3}{22}$
$=\frac{18}{4} $
$=3 \frac{4}{6} $
$=3 \frac{2}{3}$

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Question 45 Marks

The length of the staircase is $5 \frac{1}{2} m$. If one step is set at $\frac{1}{4} m$, then how many steps will be there in the staircase?

Answer

Length of the staircase $=5 \frac{1}{2} m$
Distance between each step $=\frac{1}{4} m$
$\therefore$ Number of steps in the staircase $=5 \frac{1}{2} \div \frac{1}{4}$
$
=\frac{11}{2} \div \frac{1}{4}
$
$=\frac{11}{2} \times \frac{4}{1}$ There will be 22 steps in the staircase
$
=22
$

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Question 55 Marks

Mangai bought $6 \frac{3}{4} kg$ of apples. If Kalai bought $1 \frac{1}{2}$ times as Mangai bought, then how many kilograms of apples did Kalai buy?

Answer

Weight of apples Mangai bought $=6 \frac{3}{4} kg$
Weight of apples Kalai bought $=1 \frac{1}{2}$ times of Mangai bought
$ =1 \frac{1}{2} \times 6 \frac{3}{4}$
$=\frac{3}{2} \times \frac{27}{4}$
$=\frac{3 \times 27}{2 \times 4}$
$=\frac{81}{8}$
$=10 \frac{1}{8} kg $
$10$
$8$) $\overline{81}$
$80$
$01$ Weight of apples Kalai bought $=10 \frac{1}{8} kg$

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Question 65 Marks

Which is smaller? The difference between $2 \frac{1}{2}$ and $3 \frac{2}{3}$ or the sum of $1 \frac{1}{2}$ and $2 \frac{1}{4}$

Answer

Difference between $2 \frac{1}{2}$ a
$=\frac{11}{3}-\frac{5}{2} $
$=\frac{(11 \times 2)-(5 \times 3)}{6} $
$=\frac{22-15}{6} \quad \text { Sum of } 1 \frac{1}{2} \text { and } 2 \frac{1}{4}=1 \frac{1}{2}+2 \frac{1}{4} $
$=\frac{7}{6} $
$=1 \frac{1}{6} $
$=\frac{3}{2}+\frac{9}{4} $
$=\frac{6}{4}+\frac{9}{4} $
$=\frac{6+9}{4} $
$=\frac{15}{4} $
$3 $
$4) $
$\frac{12}{3} $
$=3 \frac{3}{4} \text { Here } 1 \frac{1}{6}<3 \frac{3}{4} $
$\therefore \text { Diferem }$
$\therefore$ Difference between $2 \frac{2}{1}$ and $3 \frac{2}{3}$ is smaller.

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Question 75 Marks

From his office, a person wants to reach his house on foot which is at a distance of $5 \frac{3}{4} km$. If he had walked $2 \frac{1}{2} km$, how much distance still he has to walk to reach his house?

Answer

$\text { Distance of the house from office }=5 \frac{3}{4} km$
$ \text { Distance he walked }=2 \frac{1}{2} km $
$ \therefore \text { Remaining distance }=5 \frac{3}{4}-2 \frac{1}{2} km$
$=5+\frac{3}{4}-\left(2+\frac{1}{2}\right) $
$ =(5-2)+\left(\frac{3}{4}-\frac{1}{2}\right) km $
$ =3+\left(\frac{3}{4}-\frac{2}{4}\right) km$
$=3+\left(\frac{3-2}{4}\right) km $
$ =3 \frac{1}{4} km$

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Question 85 Marks

Sankari purchased $2 \frac{1}{2} m$ cloth to stich a long skirt and $1 \frac{3}{4} m$ cloth to stitch blouse. If the cost is $Rs. 120$ per metre then find the cost of cloth purchased by her.

Answer

Total cloth purchased
$=\left(2 \frac{1}{2}+1 \frac{3}{4}\right) m $
$=\left(\frac{5}{2}+\frac{7}{4}\right) m $
$=\left(\frac{10}{4}+\frac{7}{4}\right) m $
$=\left(\frac{10+7}{4}\right) m $
$=\frac{17}{4} m$
cost of 1 metre $= Rs. 120$
Total cost of cloth purchased
$=\text { Rs. } 120 \times \frac{17}{4} $
$=\text { Rs. } 510$

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Question 95 Marks

Look at the picture and answer the following questions:

i) What is the distance from School to Library via Bus stop?
ii) What is the distance between School and Library via Hospital?
iii) Which is the shortest distance between (i) and (ii)?
iv) The distance between School and Hospital is ____________ times the distance between School and Bus stop.

Answer

i) Distance between school and bus stop $=\frac{3}{4} km$
Distance between bus stop and library $=3 \frac{1}{2} km$
$\therefore$ Distance between school and library $=\frac{3}{4}+3 \frac{1}{2} km$
$=\frac{3}{4}+\frac{7}{2} km$
$=\frac{3}{4}+\frac{14}{4} km$
$=\frac{3+14}{4} km$
$\text { 4) } \frac{4}{17}$
$\frac{16}{1}$
$=\frac{17}{4} km$
$=4 \frac{1}{4} km$
Distance from school to library via bus stop $=4 \frac{1}{4} km$
ii) Distance between school and Hosptial $=4 \frac{1}{2} km$
Distance between Hospital and library $=1 \frac{1}{4} km$
$\therefore$ Distance between school and library $=4 \frac{1}{2}+1 \frac{1}{4} km$
$=\left(4+\frac{1}{2}\right)+\left(1+\frac{1}{4}\right) km$
$=(4+1)+\left(\frac{1}{2}+\frac{1}{4}\right) km$
$=5+\left(\frac{2}{4}+\frac{1}{4}\right) km$
$=5+\frac{3}{4} km$
$=5 \frac{3}{4} km$
$\therefore$ Distance between school and library via Hospital $=5 \frac{3}{4} km$
iii) Distance of (i) [via bus stop] $=4 \frac{1}{4} km$
Distance of (ii) [via Hospital] $=5 \frac{3}{4} km$
$4 \frac{1}{4}<5 \frac{3}{4}$
$\therefore$ (i) is the shortest distance via bus stop
iv) Distance between school and Hospital $=4 \frac{1}{2} km$
Distance between school and bus stop $=\frac{3}{4} km$
$\text { Ratio }=4 \frac{1}{2}: \frac{3}{4}$
$=\frac{9}{2}: \frac{3}{4}$
$=\frac{18}{4}: \frac{3}{4}$
$=6: 1$
The distance between school and Hospital is $6$ times the distance between school and bus stop.

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Question 105 Marks

A rabbit has to cover $26 \frac{1}{4} m$ to fetch its food. If it covers $1 \frac{3}{4} m$ in one jump, then how many jumps will it take to fetch its food?

Answer

Total distance to be covered by the rabbit $=26 \frac{1}{4} m$
Distance covered in one jump $=1 \frac{3}{4} m$
$\therefore$ Number of jumps $=26 \frac{1}{4} \div 1 \frac{3}{4}$
$=\frac{105}{4} \div \frac{7}{4}$
$=\frac{105}{4} \times \frac{4}{7}$
$=15$
$\therefore$ The rabbit jumps 15 times to fetch its food.

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Question 115 Marks

Complete the fifth row in the Leibnitz triangle which is based on subtraction.

Answer

$
\frac{1}{4} \times \frac{1}{5}=\frac{1}{20} \text { Also } \frac{1}{5} \times \frac{1}{6}=\frac{1}{30}
$
$\therefore$ Leibnitz triangle becomes

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Question 125 Marks

An oil tin contains $3 \frac{3}{4}$ litres of oil of which $2 \frac{1}{2}$ litres of oil is used. How much oil is leftover?

Answer

Total available oil in the tin $=3 \frac{3}{4}$ litres
Quantity of oil used $=2 \frac{1}{2}$ litres
Quantity of oil leftover $=3 \frac{3}{4}-2 \frac{1}{2}$
$=3+\frac{3}{4}-\left(2+\frac{1}{2}\right) $
$=(3-2)+\left(\frac{3}{4}-\frac{1}{2}\right) $
$=1+\left(\frac{3}{4}-\frac{2}{4}\right) $
$=1+\left(\frac{3-2}{4}\right) $
$=1+\frac{1}{4} $
$=1 \frac{1}{4}$
Quantity of oil leftover $=1 \frac{1}{4}$ litres.

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