3 Mark Question

Question 13 Marks

Find the difference of:
$6\text{ and }\frac{23}{3}$

Answer

We have, 6 and $\frac{23}{3}$
The difference between 6 and $\frac{23}{3}$
$=\frac{23}{3}-\frac{18}{3}$
$=\frac{23-18}{3}$
$=\frac{5}{3}$

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Question 23 Marks

Find the difference of:
$\frac{21}{25}\text{ and }\frac{18}{20}$

Answer

We have,
$\frac{21}{25}\text{ and }\frac{18}{20}$
Taking out the LCM of 25 and 20, we get
5 × 5 × 4 = 100
Now, we convert the given fractions tp equivalent fractions by making the denominators 100
$\frac{21\times4}{25\times4}\text{ and }\frac{18\times5}{20\times5}$
The difference between both the fractions are,
$=\frac{90-84}{100}$
$=\frac{6}{100}$
$=\frac{3}{50}$

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Question 33 Marks

Find the product:
$\frac{4}{7}\times\frac{14}{25}$

Answer

We have, $\frac{4}{7}\times\frac{14}{25}$
$=\frac{4\times14}{7\times25}$
$=\frac{56}{175}$
$=\frac{8}{25}$

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Question 43 Marks

lf milk is avaitabte at $₹\ 17\frac{3}{4}$ per litre, find the cost of $7\frac{2}{5}$ litres of milk.

Answer

$₹\ 17\frac{3}{4}=₹\ \frac{71}{4}$
And, $7\frac{2}{5}\text{ litres}=\frac{37}{5}\text{ litres}$
The cost of milk per litre $=₹\ \frac{71}{4}$
The cost of milk per $\frac{37}{5}$ litres
$=₹\ \frac{37}{5}\times\frac{71}{4}$
$=₹\ \frac{2327}{20}$
$=₹\ 131\frac{7}{20}$

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Question 53 Marks

Find the sum:
$2\frac{3}{5}+4\frac{7}{10}+2\frac{4}{15}$

Answer

We have,
$2\frac{3}{5}+4\frac{7}{10}+2\frac{4}{15}$
$=\frac{13}{5}+\frac{47}{10}+\frac{34}{15}$
Taking out the LCM of 5, 10 and 15, we get
5 × 2 × 3 = 30
Now, we convert the given fractions to equivalent fractions by making the denominators 30
$\frac{78}{30}+\frac{141}{30}+\frac{68}{30}$
$=\frac{287}{30}$

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Question 63 Marks

Waht should be added to $5\frac{3}{7}$ to get 12?

Answer

We have,
$5\frac{3}{7}=\frac{38}{7}$
Let x be the number added to $\frac{38}{7}$ to get 12
Therefore,
$\text{x}+387=12$
$\Rightarrow\text{x}=12-\frac{38}{7}$
$\Rightarrow\text{x}=\frac{12\times7-38}{7}$
$\Rightarrow\text{x}=\frac{84-38}{7}$
$\text{x}=\frac{46}{7}$

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Question 73 Marks

Find the sum:
$4\frac{3}{4}+9\frac{2}{5}$

Answer

We have,
$4\frac{3}{4}+9\frac{2}{5}$
$=\frac{19}{4}+\frac{47}{5}$
Taking out the LCM of 4 and 5, we get
4 × 5 = 20
Now, we convert the given fractions to equivalent fractions by making the denominators 20
$=\frac{19\times5}{4\times5}+\frac{47\times4}{5\times4}$
$=\frac{95}{20}+\frac{188}{20}$
$=\frac{95+188}{20}$
$=\frac{283}{20}$

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Question 83 Marks

Find the difference:
$\frac{6}{7}-\frac{9}{11}$

Answer

We have,
$\frac{6}{7}-\frac{9}{11}$
Taking out the LCM of 7 and 11, we get
7 × 11 = 77
Now, we convert the given fractions to equivalent fractions by making the denominators 77
$=\frac{6\times11}{7\times11}\text{ and }\frac{9\times7}{11\times7}$
The difference between both the fractions are,
$=\frac{66-63}{77}$
$=\frac{3}{77}$

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Question 93 Marks

The cost of mathematics book is ₹ $25\frac{3}{4}$ and that of science book is ₹ $20\frac{1}{2}.$ Which costs more and by how much?

Answer

Given,
The cost of Mathematics book is ₹ $25\frac{3}{4}$ and that of science book is $20\frac{1}{2}$
We need the compare the cost of mathematics and science book,
$25\frac{3}{4}=\frac{103}{4}\text{ and }20\frac{1}{2}=\frac{41}{2}$
Taking out the LCM of 4 and 2, we get
2 × 2 = 4
Now, we convert the given fractions to equivalent fractions by making the denominators 4, we get,
$=\frac{103}{4}$
And $\frac{41\times2}{2\times2}=\frac{82}{4}$
As we know, 103 > 82
Therefore, $\frac{103}{4}>\frac{82}{4}$
Hence, the cost of mathematics book is more than of the cost of the science book.

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Question 103 Marks

Find the sum:
$\frac{5}{8}+\frac{3}{10}$

Answer

We have,
$\frac{5}{8}+\frac{3}{10}$
Taking the LCM of 8 and 10, we get
2 × 4 × 5 = 40
Now, we convert the given fractions to equivalent fractions by making the denominators 40,
$=\frac{5\times5}{8\times5}+\frac{3\times4}{10\times4}$
$=\frac{25}{40}+\frac{12}{40}$
$=\frac{25+12}{40}$
$=\frac{37}{40}$

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Question 113 Marks

Find the sum:
$\frac{5}{6}+3+\frac{3}{4}$

Answer

We have,
$\frac{5}{6}+3+\frac{3}{4}$
Taking out the LCM of 6 and 4, we get
2 × 2 × 3 = 12
Now, we convert the given fractions to equivalent fractions by making the denominators 12
$=\frac{5\times2}{6\times2}+\frac{3\times12}{12}+\frac{3\times3}{4\times3}$
$=\frac{10}{12}+\frac{36}{12}+\frac{9}{12}$
$=\frac{10+36+9}{12}$
$=\frac{55}{12}$

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Question 123 Marks

Find the difference of:
$3\frac{3}{10}\text{ and }2\frac{7}{15}$

Answer

We have,
$3\frac{3}{10}\text{ and }2\frac{7}{15}$
$=\frac{33}{10}\text{ and }\frac{37}{15}$
taking out the LCM of 10 and 15, we get
2 × 3 × 5 = 30
Now, we convert the given fractions tp equivalent fractions by making the denominators 30
$=\frac{33\times3}{10\times3}\text{ and }\frac{37\times2}{15\times2}$
$=\frac{99}{30}\text{ and }\frac{74}{30}$
The difference between both the fractions are
$=\frac{99-74}{30}$
$=\frac{25}{30}$
$=\frac{5}{6}$

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Question 133 Marks

Compare the following fractions by using the symbo > or < or =
$\frac{7}{9}\text{ and }\frac{8}{13}$

Answer

We have,
$\frac{7}{9}\text{ and }\frac{8}{13}$
Taking the LCM of 9 and 13 we get,
9 × 3 = 117
Now, we convert the given fractions to equivalent fractions by making the denominator 117.
$\frac{7\times13}{9\times13}\text{ and }\frac{8\times9}{13\times9}$
$\frac{91}{117}\text{ and }\frac{72}{117}$
As we know, 91 > 72
Therefore, $\frac{91}{117}>\frac{72}{117}$

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Question 143 Marks

Find the area of a rectangular park which is $41\frac{2}{3}\text{m}$ long and $18\frac{3}{5}\text{m}$ broad.

Answer

Given, $41\frac{2}{3}\text{m}=\frac{145}{3}\text{m}$
And, $18\frac{3}{5}\text{m}=\frac{93}{5}\text{m}$
Area of a rectangular park = (length × breadth)
$=\Big(\frac{125}{3}\text{m}\times\frac{93}{5}\text{m}\Big)$
$=\Big(\frac{125\times93}{15}\Big)\text{m}^2$
$=\Big(\frac{11625}{15}\Big)\text{m}^2$
$=775\text{m}^2$

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Maths 3 Mark Question

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