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प्रश्नों के उत्तर लिखिए। (प्रत्येक प्रश्न 3 अंक का हे)

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43 questions · self-marked practice — reveal the answer and mark yourself.

Question 13 Marks
योग - व्यवकलन तालिका को पूरा कीजिए :
Answer
We have,
$\frac{2}{3}+\frac{4}{3}=\frac{2+4}{3}=\frac{6}{3}$= 2
$\frac{1}{3}+\frac{2}{3}=\frac{1+2}{3}=\frac{3}{3}$= 1
$\frac{2}{3}-\frac{1}{3}=\frac{2-1}{3}=\frac{1}{3}$
$\frac{4}{3}-\frac{2}{3}=\frac{4-2}{3}=\frac{2}{3}$
and $\frac{1}{3}+\frac{2}{3}=\frac{3}{3}$ = 1
Hence, the above-given number box can be completed as:
$\frac{2}{3}$ $\frac{4}{3}$ 2
$\frac{1}{3}$ $\frac{2}{3}$ 1
$\frac{1}{3}$ $\frac{2}{3}$ 1
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Question 23 Marks
रिक्त स्थान भरिए :$\frac{1}{2}-\square=\frac{1}{6}$
Answer
Let the missing space be x
We have,
$\frac{1}{2}-x=\frac{1}{6}$
x = $\frac{1}{2}-\frac{1}{6}$
= $\frac{1 \times 3-1 \times 1}{6}$
= $\frac{3-1}{6}$
= $\frac{2}{6}$
= $\frac{1}{3}$
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Question 33 Marks
रिक्त स्थान भरिए : ('<', '=', '>')
$\frac{1}{4} \square \frac{2}{8}$
Answer
Let the missing space be x
We have,
x – $\frac{1}{5}=\frac{1}{2}$
x = $\frac{1}{2}+\frac{1}{5}$
= $\frac{1 \times 5+1 \times 2}{10}$
= $\frac{5+2}{10}$
= $\frac{7}{10}$
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Question 43 Marks
रिक्त स्थान भरिए :$\square-\frac{5}{8}=\frac{1}{4}$
Answer
Let the missing space be x
We have,
x – $\frac{5}{8}=\frac{1}{4}$
x = $\frac{1}{4}+\frac{5}{8}$
= $\frac{1 \times 2+5}{8}$
= $\frac{2+5}{8}$
= $\frac{7}{8}$
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Question 53 Marks
नैना को केक का 1,1/2 भाग मिला और नजमा को 1,1/3 भाग । दोनों को केक का कितना भाग मिला ?
Answer
Cake given to Naina $1\frac12=\;\frac{1\times2+1}2=\;\frac{2+1}2=\;\frac32$ piece

Cake given to Najma $1\frac13=\;\frac{1\times3+1}3=\;\frac{3+1}3=\;\frac43$ piece
∴ Total amount of cake consumed by both of them $\;\frac32$ piece $\;\frac45$ piece $= \frac32+\;\frac43$ piece
$= \frac{3\times3}{2\times3}+\;\frac{4\times2}{3\times2}$ piece . . . . [L.C.M.(2,3) = 6]
$\frac96+\;\frac86=\;\frac{9+8}6=\;\frac{17}6\;=\;2\frac56$ piece
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Question 63 Marks
सरिता ने 2/5 मी. रिबन खरीदा और ललिता ने 3/4 मी. दोनों ने कुल कितना रिबन खरीदा?
Answer
Ribbon bought by Sarita =$\frac25$ m
Ribbon bought by Lalita = $\frac34$ m
∴ Total length of the ribbon they bought = $\frac25$m + $\frac34$ m =$\frac25+\;\frac34$ m
$= \frac{2\times4}{5\times4}+\;\frac{3\times5}{4\times5}$m . . . . L.C.M. (5, 4) = 20
$= \frac8{20}+\;\frac{15}{20}=\;\frac{8+15}{20}=\;\frac{23}{20}\;=\;1\frac3{20}$ m
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Question 73 Marks
हल कीजिए : 2/3 + 3/4 + 1/2
Answer
Here,
LCM of 3, 4, 2 is 12,
Thus,
$\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$
= $\frac{2 \times 4+3 \times 3+1 \times 6}{12}$
= $\frac{8+9+6}{12}$
= $\frac{23}{12}$
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Question 83 Marks
हल कीजिए : 5/6 - 1/3
Answer
Here,
LCM of 6 and 3 is 12,
$\frac{5}{6}-\frac{1}{3}$
= $\frac{5 \times 2-1 \times 4}{12}$
= $\frac{10-4}{12}$
= $\frac{6}{12}$
= $\frac{1}{2}$
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Question 93 Marks
हल कीजिए :3/4 - 1/3
Answer
Here,
LCM of 4 and 3 is 12,
$\frac{3}{4}-\frac{1}{3}$
= $\frac{3 \times 3-1 \times 4}{12}$
= $\frac{9-4}{12}$
= $\frac{5}{12}$
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Question 103 Marks
हल कीजिए : 4/5 + 2/3
Answer
Here,
LCM of 5 and 3 is 15,
$\frac{4}{5}+\frac{2}{3}$
= $\frac{4 \times 3+2 \times 5}{15}$
= $\frac{12+10}{15}$
= $\frac{22}{15}$
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Question 113 Marks
हल कीजिए : 2/5 + 1/6
Answer
Here,
LCM of 5 and 6 is 30,
$\frac{2}{5}+\frac{1}{6}$
= $\frac{2 \times 6+1 \times 5}{30}$
= $\frac{12+5}{30}$
= $\frac{17}{30}$
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Question 123 Marks
हल कीजिए : 5/7 + 1/3
Answer
Here,
LCM of 7 and 3 is 21,
$\frac{5}{7}+\frac{1}{3}$
= $\frac{5 \times 3+1 \times 7}{21}$
= $\frac{15+7}{21}$
= $\frac{22}{21}$
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Question 133 Marks
हल कीजिए : 4/9 + 2/7
Answer
Here,
LCM of 9 and 7 is 63
$\frac{4}{9}+\frac{2}{7}$
= $\frac{4 \times 7+2 \times 9}{63}$
= $\frac{28+18}{63}$
= $\frac{46}{63}$
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Question 143 Marks
हल कीजिए : 3 + 7/15
Answer
$\frac3{10}+\frac7{15}=\frac{3\times3}{10\times3}+\;\frac{7\times2}{15\times2}$ . . . .[L.C.M.(10,15) = 30]
$=\;\frac9{30}+\;\frac{14}{30}=\frac{9+14}{30}=\frac{23}{30}\;$
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Question 153 Marks
हल कीजिए : 4/3 - 1/2
Answer
Here, we have,
$\frac{4}{3}-\frac{1}{2}$
LCM of 3 and 2 is 6,
= $\frac{4 \times 2-1 \times 3}{6}$
= $\frac{8-3}{6}$
= $\frac{5}{6}$
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Question 163 Marks
हल कीजिए : 16 / 5 - 7 /5
Answer
$\frac{16}5-\;\frac75=\;\frac{16-7}5=\;\frac95=\;1\frac45\;$
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Question 173 Marks
हल कीजिए : 4,2/3 + 3,1/2
Answer
Here, we have,
$​​$$4 \frac{2}{3}+3 \frac{1}{4}$
= $\frac{14}{3}+\frac{13}{4}$
= $\frac{14 \times 4+13 \times 3}{12}$
= $\frac{56+39}{12}$
= $\frac{95}{12}$
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Question 183 Marks
हल कीजिए : 1,1/3 + 3,2/3
Answer
Here, we have,
$1 \frac{1}{3}+3 \frac{2}{3}$
= $\frac{4}{3}+\frac{11}{3}$
= $\frac{4+11}{3}$
= $\frac{15}{3}$
= 5
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Question 193 Marks
हल कीजिए : 1/2 + 1/3 + 1/6
Answer
Here,
$\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$
= $\frac{1 \times 3+1 \times 2+1 }{6}$ [LCM of 2, 3, 6 is 6]
= $\frac{3+2+1}{6}$
= $\frac{6}{6}$
= 1
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Question 203 Marks
हल कीजिए : 2/3 + 1/7
Answer
Given that,
$\frac{2}{3}+\frac{1}{7}$
Cross multiplying, we get,
= $\frac{2 \times 7+1 \times 3}{21}$
= $\frac{14+3}{21}$
= $\frac{17}{21}$
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Question 213 Marks
निम्नलिखित भिन्नों को उनके सरलतम रूप में बदलिए : 84/98
Answer
Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84
Factors of 98 are 1, 2, 7, 14, 49 and 98.
$\therefore$ Common factors of 84 and 98 are 1, 7 and 14.
Highest of these common factors is 14.
$\therefore$ H.C.F. of 84 and 98 is 14.
Now,$\frac{84}{98}=\frac{84\div14}{98\div\;14}=\frac67$
Hence, the simplest form of $\frac{84}{98}$ is$\frac67$
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Question 223 Marks
निम्नलिखित भिन्नों को उनके सरलतम रूप में बदलिए : 150/60
Answer
Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75 and 150
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60
$\therefore$ Common factors of 150 and 60 are 1, 2, 3, 5, 6, 10, 15 and 30.
Highest of these common factors is 30.
$\therefore$ H.C.F. of 150 and 60 is 30.
Now,$\frac{150}{60}=\frac{150\div30}{60\div\;30}=\frac52$
Hence, the simplest form of $\frac{150}{60}$ is$\frac52$
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Question 233 Marks
निम्नलिखित भिन्नों को उनके सरलतम रूप में बदलिए : 48/60
Answer
Factors of 48 are 1, 2, 3, 4, ,6, 8, 12, 16, 24 and 48.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60.
$\therefore$ Common factors of 48 and 60 are 1, 2, 3, 4, 6 and 12.
Highest of these common factors is 12.
$\therefore$ H.C.F. of 48 and 60 is 12
Now,$\frac{48}{60}=\frac{48\div12}{60\div\;12}=\frac45$
Hence, the simplest form of$\frac{48}{60}$ is$\frac45$
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Question 243 Marks
जाँच कीजिए कि निम्न भिन्न तुल्य है या नहीं : 7/13, 5/11
Answer
$\frac73,\frac5{11}$
7 × 11 = 77
3 × 5 = 15
So, 77 $\neq$ 15
$\therefore$ The given fractions$\frac73$ and$\frac5{11}$ are not equivalent.
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Question 253 Marks
जाँच कीजिए कि निम्न भिन्न तुल्य है या नहीं : 3/10, 12/50
Answer
$\frac3{10},\frac{12}{50}$
3 × 50 = 150
10 × 12 = 120
So, 150 $\neq$ 120
$\therefore$ The given fractions$\frac3{10}$ and $\frac{12}{50}$ are not equivalent.
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Question 263 Marks
जाँच कीजिए कि निम्न भिन्न तुल्य है या नहीं : 5/9, 30/54
Answer
$\frac59 = \frac{30}{54}$
5 × 54 = 270
9 × 30 = 270
$\therefore$ 5 × 54 = 9 × 30
$\therefore$ The given fractions $\frac59$ and$\frac{30}{54}$ are equivalent.
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Question 273 Marks
36/48 के तुल्य वह भिन्न ज्ञात कीजिए जिसका अंश 27 है
Answer
$\frac{36}{48}=\frac{36\div12}{48\div\;12}=\frac34$
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Question 283 Marks
36/48 के तुल्य वह भिन्न ज्ञात कीजिए जिसका अंश 9 है
Answer
$\frac{36}{48}=\frac{36\div4}{48\div\;4}=\frac9{12}$
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Question 293 Marks
3/5 के तुल्य वह भिन्न ज्ञात कीजिए जिसका अंश 27 है
Answer
$\frac35=\frac{3\times9}{5\;\times\;9}=\frac{27}{45}$
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Question 303 Marks
3/5 के तुल्य वह भिन्न ज्ञात कीजिए जिसका हर 30 है
Answer
$\frac35=\frac{3\times6}{5\;\times\;6}=\frac{18}{30}$
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Question 313 Marks
3/5 के तुल्य वह भिन्न ज्ञात कीजिए जिसका अंश 9 है 
Answer
$\frac35=\frac{3\times3}{5\;\times\;3}=\frac9{15}$
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Question 323 Marks
3/5 के तुल्य वह भिन्न ज्ञात कीजिए जिसका हर 20 है 
Answer
$\frac35=\frac{3\times4}{5\;\times\;4}=\frac{12}{20}$
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Question 333 Marks
Replace $\square$ by the correct number: $\frac{18}{24}=\frac{\square}4$
Answer
$\frac{18}{24}=\frac{a}4$
$\therefore$ 18 × 4 = 24 × a
$\therefore$ a =$\frac{18 ×4}{24}=\frac{72}{24}$
$\therefore$ a = 3
$\therefore$$\frac{18}{24}=\frac{3}4$
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Question 343 Marks
Replace $\square$ by the correct number: $\frac{45}{60}=\frac{15}{\square}$
Answer
$\frac{45}{60}=\frac{15}{a}$
∴ 45 × a = 60 × 15
∴ $a = \frac{60 ×15}{45}=\frac{900}{45}$
a = 20
∴$\frac{45}{60}=\frac{15}{20}$
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Question 353 Marks
Replace $\square$ by the correct number: $\frac35=\frac{\square}{20}$
Answer
$\frac35=\frac{a}{20}$

∴ 3 × 20 = 5 × a
∴$a= \frac{3 ×20}5=\frac{60}{5}$
a = 12.
∴$\frac35=\frac{12}{20}$

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Question 363 Marks
Replace $\square$ by the correct number: $\frac58=\frac{10}{\square}$
Answer
$\frac58=\frac{10}{m}$
∴ 5 × m = 8 × 10
∴ $m = \frac{8 ×10}5$
∴ $m = \frac{80}5$
∴ m = 16
∴$\frac58=\frac{10}{16}$
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Question 373 Marks
Replace $\square$ by the correct number: $\frac27=\;\frac8{\square}$
Answer
If value taken as m
$\frac27=\;\frac8{m}$

∴ 2 × m = 7 × 8
∴ $m=\;\frac{7\times8}2=\;\frac{56}2=28$
m = 28
∴$\frac27=\;\frac8{28}$

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Question 383 Marks

छायांकित भागों के लिए भिन्नों के लिए लिखिए और प्रत्येक पंक्ति में से तुल्य भिन्नों को चुनिए |

Answer
  1. Here,
    The figure is divided into two equal parts
    And,
    One part is shaded out of these two parts
    Hence,
    The figure represents a fraction of $\frac{1}{2}$.
  2. Here,
    The figure is divided into six equal parts
    And,
    Four parts are shaded out of these six parts
    Hence,
    The figure represents a fraction of $\frac{4}{6}$ or $\frac{2}{3}$
  3. Here,
    The figure is divided into nine equal parts
    And,
    Three parts are shaded out of these nine parts
    Hence,
    The figure represents a fraction of $\frac{3}{9} \text { or } \frac{1}{3}$

  4. Here,
    The figure is divided into nine equal parts
    And,
    Three parts are shaded out of these nine parts
    Hence,
    The figure represents a fraction of $\frac{2}{8} \text { or } \frac{1}{4}$

  5. Here,
    The figure is divided into four equal parts
    And,
    Three parts are shaded out of these four parts
    Hence,
    The figure represents a fraction of $\frac{3}{4}$

  1. Here,
    The figure is divided into eighteen equal parts
    And,
    Six parts are shaded out of these eighteen parts
    Hence,
    The figure represents a fraction of $\frac{6}{18} \text { or } \frac{1}{3}$

  2. Here,
    The figure is divided into eight equal parts
    And,
    Four parts are shaded out of these eight parts
    Hence,
    The figure represents a fraction of $\frac{4}{8} \text { or } \frac{1}{2}$

  3. Here,
    The figure is divided into sixteen equal parts
    And,
    Twelve parts are shaded out of these sixteen parts
    Hence,
    The figure represents a fraction of $\frac{12}{16} \text { or } \frac{3}{4}$

  4. Here,
    The figure is divided into twelve equal parts
    And,
    Eight parts are shaded out of these twelve parts
    Hence,
    The figure represents a fraction of $\frac{8}{12} \text { or } \frac{2}{3}$

  5. Here,
    The figure is divided into sixteen equal parts
    And,
    Four parts are shaded out of these sixteen parts
    Hence,
    The figure represents a fraction of $\frac{4}{16} \text { or } \frac{1}{4}$

Pair up with the equivalent fractions: (a) - (ii), (b) - (iv), (c) - (i), (d) - (v), (e) - (iii)

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Question 393 Marks
Write the fractions. Are all these fraction equivalent ?

Answer


The figure (i) represents 4 shaded circles out of 12 circles. So $\frac4{12}=\;\frac{4\div4}{12\div4}=\;\frac13$ [$\therefore$HCF (4, 12) = 4]
The figure (ii) represents 3 shaded circles out of 9 circles. So $\frac3{9}=\;\frac{3\div3}{9\div3}=\;\frac13$ [$\therefore$HCF (3, 9) = 3]
The figure (iii) represents 2 shaded circles out of 6 circles. So $\frac2{6}=\;\frac{2\div2}{6\div2}=\;\frac13$ [$\therefore$HCF (2, 6) = 2]
The figure (iv) represents 1 shaded circle out of 3 circles. So $\;\frac13$
The figure (v) represents 6 shaded circles out of 15 circles. So $\frac6{15}=\;\frac{6\div3}{15\div3}=\;\frac25$ [$\therefore$HCF (6, 15) = 3]
So, all these fractions are not equivalent.
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Question 403 Marks
प्रत्येक चित्र में छायांकित भागों के लिए भिन्न लिखिए | क्या सभी भिन्न तुल्य हैं ?
Answer


The first figure represents 1 shaded parts out of 2 equal parts= $\frac12$
The second figure represents 2 shaded parts out of 4 equal parts= $\frac24=\;\frac{2\div2}{4\div2}=\;\frac12$
The third figure represents 3 shaded parts out of 6 equal parts. $\frac36=\;\frac{3\div3}{6\div6}=\;\frac12$
The fourth figure represents 4 shaded parts out of 8 equal parts. $\frac48=\;\frac{4\div4}{8\div4}=\;\frac12$
So, all these fractions are equivalent.
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Question 413 Marks

निम्न में, यदि कोई गलती है, तो पहचानिए : यह 3/4 है

Answer

We know that,
A fraction is a number that represents part of a whole and the parts needs to be equally divided.

Here,
we can see that,
The shape is not divided into equal parts.
Hence,
The given figure does not represent the fraction.

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Question 423 Marks

निम्न में, यदि कोई गलती है, तो पहचानिए : यह 1/4 है

Answer

We know that,
A fraction is a number that represents part of a whole and the parts needs to be equally divided.

Here,
we can see that,
The given figure is not divided into equal parts.
Hence,
The given figure does not represent the given fraction.

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Question 433 Marks

निम्न में, यदि कोई गलती है, तो पहचानिए :यह 1/2 है



Answer

We know that,
A fraction is a number that represents part of a whole and the parts need to be equally divided.

Here,
The whole may be a single object or a group of objects.
But from the above, figure, we can see that,
It is not divided into equal parts.
Hence,
The given figures do not represent the given fraction.

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