Question 13 Marks
Ravish takes $2\frac{1}{5}\text{minutes}$ to walk across the school ground. Rahul takes $\frac{7}{4}\text{minutes}$ to do the same. Who takes less time and by what fraction?
AnswerTime taken by Ravish $=2\frac{1}{5}\text{minutes}=\frac{2\times5+1}{5}\text{minutes}=\frac{11}{5}\text{minutes}$Time taken by Rahul $=\frac{7}{4}\text{minutes}$
Comparing $\frac{11}{5}\text{minutes}$ and $\frac{7}{4}\text{minutes},$ we get:
$\frac{11\times4}{5\times4}\text{minutes},\frac{7\times5}{4\times5}\text{minutes}$ (LCM of 4 and 5 is 20, so will we convert each fraction into an equivalent fraction with denominator 20)
$\frac{44}{20}>\frac{35}{20}$
Rahul takes less time, i.e., $\frac{44}{20}-\frac{35}{20}=\frac{44-35}{20}=\frac{9}{20}\text{minutes}$
View full question & answer→Question 23 Marks
Add:
$\frac{3}{4}$ and $\frac{5}{6}$
AnswerGiven: $\frac{3}{4}$ and $\frac{5}{6}$
$\frac{3}{4}+\frac{5}{6}$
LCM of 4 and 6 is 12, so we will convert each fraction into an equivalent fraction with denominator 12.
$=\frac{3\times3}{4\times3}+\frac{5\times2}{6\times2}$
$=\frac{9}{12}+\frac{10}{12}$
$=\frac{9+10}{12}$
$=\frac{19}{12}$
View full question & answer→Question 33 Marks
Simplify:$\frac{3}{10}+\frac{7}{15}+\frac{3}{5}$
AnswerGiven: $\frac{3}{10}+\frac{7}{15}+\frac{3}{5}$$=\frac{3\times3}{10\times3}+\frac{7\times2}{15\times2}+\frac{3\times6}{5\times6}$ (because LCM of 10, 15 and 5 is 30)
$=\frac{9}{30}+\frac{14}{30}+\frac{18}{30}$
$=\frac{9+14+18}{30}$
$=\frac{41}{30}$
View full question & answer→Question 43 Marks
Simplity the following to its lowest term:
$\frac{68}{17}$
Answer$\frac{68}{17}$
Factors of 68 are 1, 2, 4, 17, 34 and 68
Factors of 17 are 1 and 17
Common factor of 68 and 17 is 17
HCF of 68 and 17 is = 17
Dividing both the numerator and denominator by 17, we get:
$\frac{68\div17}{17\div17}=\frac{4}{1}$
Therefore, the simplest form obtained is,
$\frac{68}{17}=\frac{4}{1}$
View full question & answer→Question 53 Marks
Savita bought $\frac{2}{5}\text{m}$ of ribbon and kavita $\frac{3}{4}\text{m}$ of ribbon. What was the total length of the ribbon they bought?
AnswerLength of the ribbon bought by Savita $=\frac{2}{5}\text{m}$
Length of the ribbon bought by Kavita $=\frac{3}{4}\text{m}$
Total length of the ribbon bought by them $=\frac{2}{5}\text{m}+\frac{3}{4}\text{m}$
$=\frac{2\times4}{5\times4}\text{m}+\frac{3\times5}{4\times5}\text{m}$ (because LCM of 5 and 4 is 20)
$=\frac{8}{20}\text{m}+\frac{15}{20}\text{m}$
$=\Big(\frac{8+15}{20}\Big)\text{m}$
$=\frac{23}{20}\text{m}$
View full question & answer→Question 63 Marks
Replace $\Box$ by the correct number:$\Box-\frac{5}{8}=\frac{1}{4}$
Answer$\frac{7}{8}-\frac{5}{8}=\frac{1}{4}$Solution:
Given: $\Box-\frac{5}{8}=\frac{1}{4}$
$\Rightarrow\Box=\frac{5}{8}+\frac{1}{4}$
$\Rightarrow\Box=\frac{5\times1}{8\times1}+\frac{1\times2}{4\times2}$ (because LCM of 8 and 4 is 8)
$\Rightarrow\Box=\frac{5}{8}+\frac{2}{8}$
$\Rightarrow\Box=\frac{5+2}{8}$
$\Box=\frac{7}{8}$
View full question & answer→Question 73 Marks
Simplity the following to its lowest term:
$\frac{75}{80}$
Answer$\frac{75}{80}$Factors of 75 are 1, 3, 5, 15, 25 and 75
Factors of 80 are 1, 2, 4, 5, 8, 10, 12, 16, 20, 40 and 80 Common factors of 75 and 80 are 1 and 5 HCF of 75 and 80 is = 5 Dividing both the numerator and denominator by 5, we get: $\frac{75\div5}{80\div5}=\frac{15}{16}$ Therefore, the simplest form obtained is, $\frac{75}{80}=\frac{15}{16}$
View full question & answer→Question 83 Marks
Replace $\Box$ by the correct number:$\frac{1}{2}-\Box=\frac{1}{6}$
Answer$\frac{1}{2}-\frac{1}{3}=\frac{1}{6}$Solution:
Given: $\frac{1}{2}-\Box=\frac{1}{6}$
$\Rightarrow\frac{1}{2}-\frac{1}{6}=\Box$
$\Rightarrow\Box=\frac{1\times3}{2\times3}-\frac{1\times1}{6\times1}$ (because LCM of 2 and 6 is 6)
$\Rightarrow\Box=\frac{3}{6}-\frac{1}{6}$
$\Rightarrow\Box=\frac{2}{6}=\frac{1}{3}$
$\Box=\frac{1}{3}$
View full question & answer→Question 93 Marks
Simplity the following to its lowest term:
$\frac{162}{108}$
Answer$\frac{162}{108}$
Factors of 162 are 1, 2, 3, 6, 9, 18, 27, 54, 81 and 162
Factors of 108 are 108, 1, 2, 3, 4, 6, 9, 12, 18, 27 and 54
Common factor of 162 and 108 are 1, 2, 3, 6, 9, 18, 27, 54
HCF of 162 and 108 is = 54
Dividing both the numerator and denominator by 54, we get:
$\frac{162\div54}{108\div54}=\frac{3}{2}$
Therefore, the simplest form obtained is,
$\frac{162}{108}=\frac{3}{2}$
View full question & answer→Question 103 Marks
Simplify:$7+\frac{7}{4}+5\frac{1}{6}$
AnswerGiven: $7+\frac{7}{4}+5\frac{1}{6}$$=\frac{7}{1}+\frac{7}{4}+\frac{5\times6+1}{6}$
$=\frac{7}{1}+\frac{7}{4}+\frac{31}{6}$
$=\frac{7\times12}{1\times12}+\frac{7\times3}{4\times3}+\frac{31\times2}{6\times2 }$ (because LCM of 1, 4 and 6 is 12)
$=\frac{84}{12}+\frac{21}{12}+\frac{62}{12}$
$=\frac{84+21+62}{12}$
$=\frac{167}{12}$
View full question & answer→Question 113 Marks
Three boxes weight $18\frac{3}{4}\text{kg},7\frac{1}{2}\text{kg}$ and $10\frac{1}{5}\text{kg}$ respectively. A porter carries all the three boxes. What is the total weight carried by the porter?
AnswerSince the porter carries all the three boxes, then total weight.
$=18\frac{3}{4}+7\frac{1}{2}+10\frac{1}{5}$
$=\frac{75}{4}+\frac{15}{2}+\frac{51}{5}$
$=\frac{75\times5}{4\times5}+\frac{15\times10}{2\times10}+\frac{51\times4}{5\times4}$
$=\frac{375}{20}+\frac{150}{20}+\frac{204}{20}$
$=\frac{375+150+204}{20}$
$=\frac{729}{20}$
$=36\frac{9}{20}$
Hence, the total weight carried by the porter is $36\frac{9}{20}\text{kg}.$
View full question & answer→Question 123 Marks
Simplity the following to its lowest term:
$\frac{150}{50}$
Answer$\frac{150}{50}$
Factors of 150 are 1, 2, 3, 5, 6, 10, 15, 25, 50 and 150
Factors of 50 are 1, 2, 5, 10, 25 and 50
Common factor of 150 and 50 is 50
HCF of 150 and 50 is = 50
Dividing both the numerator and denominator by 50, we get:
$\frac{150\div50}{50\div50}=\frac{3}{1}$
Therefore, the simplest form obtained is,
$\frac{150}{50}=\frac{3}{1}$
View full question & answer→Question 133 Marks
Kavita has 44 cassettes. She gives 3434 of them to Sonia. How many does Sonia get? How many does Kavita keep?
AnswerKavita has 44 cassettes.
She gives 34 of the cassettes to Sonia.
For this, Kavita divides 44 cassettes in 4 equal parts and takes 3 parts.
Therefore, $=\frac{44}{4}=11$
It means that Kavita gives 33 cassettes to Sonia.
Number of cassettes Kavita has = 44 - 33 = 11
View full question & answer→Question 143 Marks
Reduce each of the following fractions to its lowest term (simplest form):
$\frac{80}{24}$
Answer$\frac{80}{24}$Factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40 and 80
Factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24
Common factors of 80 and 24 are 1, 2 , 4 , 8
HCF = 8
Divide both the numerator & denominator by 8
$\frac{80\div8}{24\div8}=\frac{10}{3}$Therefore, the simplest form obtained is $=\frac{10}{3}$
View full question & answer→Question 153 Marks
Aarushi was given $\frac{5}{7}$ of a basket of oranges. What fraction of oranges was left in the basket.
AnswerLet the total number of oranges in the basket $= 1$
Fraction of oranges given to Aarushi $=\frac{5}{7}$
Fraction of oranges left $=1-\frac{5}{7}$
$=\frac{1\times7}{1\times7}-\frac{5}{7}$
$=\frac{7}{7}-\frac{5}{7}$
$=\frac{7-5}{7}$
$=\frac{2}{7}$
Thus, $\frac{2}{7}$ fraction of oranges was left in the basket.
View full question & answer→Question 163 Marks
Find the difference of:$\frac{13}{24}$ and $\frac{7}{16}$
Answer$\frac{13}{24}-\frac{7}{16}$
$=\frac{13\times2}{24\times2}-\frac{7\times3}{16\times3}$
$=\frac{26}{48}-\frac{21}{48}$ (because LCM of 24 and 16 is 48)
$=\frac{26-21}{48}$
$=\frac{5}{48}$
View full question & answer→Question 173 Marks
Reduce each of the following fractions to its lowest term (simplest form):
$\frac{40}{72}$
Answer$\frac{40}{72}$
Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
Common factors of 40 and 72 are 1, 2, 4 and 8
HCF = 8
Divide both the numerator & denominator by 8
$\frac{40\div8}{72\div8}=\frac{5}{9}$
Therefore, the simplest form obtained is $=\frac{5}{9}$
View full question & answer→Question 183 Marks
Find the difference of:$\frac{5}{18}$ and $\frac{4}{15}$
Answer$\frac{5}{18}-\frac{4}{15}$
$=\frac{5\times5}{18\times5}-\frac{4\times6}{15\times6}$
$=\frac{25}{90}-\frac{24}{90}$ (because LCM of 18 and 15 is 90)
$=\frac{25-24}{90}$
$=\frac{1}{90}$
View full question & answer→Question 193 Marks
Subtract as indicated:$4\frac{2}{5}-2\frac{1}{5}$
Answer$4\frac{2}{5}-2\frac{1}{5}$$=\frac{4\times5+2}{5}-\frac{2\times5+1}{5}$
$=\frac{22}{5}-\frac{11}{5}$
$=\frac{22-11}{5}$
$=\frac{11}{5}$
View full question & answer→Question 203 Marks
Add:
$\frac{4}{5}$ and $\frac{7}{15}$
AnswerGiven: $\frac{4}{5}$ and $\frac{7}{15}$
$\frac{4}{5}+\frac{7}{15}$
LCM of 5 and 15 is 15, so we will convert each fraction into an equivalent fraction with denominator 15.
$=\frac{4\times3}{5\times3}+\frac{7\times1}{15\times1}$
$=\frac{12}{15}+\frac{7}{15}$
$=\frac{12+7}{15}$
$=\frac{19}{15}$
View full question & answer→Question 213 Marks
Subtract:$\frac{4}{15}$ from $2\frac{1}{5}$
Answer$\because2\frac{1}{5}=\frac{2\times5+1}{5}=\frac{11}{5}$
$\frac{11}{5}-\frac{4}{15}$
LCM of 5 and 15 is 15, so we will convert each fraction into an equivalent fraction with denominator 15.
$=\frac{11\times3}{5\times3}-\frac{4\times1}{15\times1}$
$=\frac{33}{15}-\frac{4}{15}$
$=\frac{33-4}{15}$
$=\frac{29}{15}$
View full question & answer→Question 223 Marks
The cost of a pen is $\text{Rs. }6\frac{2}{3}$ and that of a pencil is $\text{Rs. }4\frac{1}{6}.$ Which costs more and by how much?
AnswerCost of a pen $=\text{Rs. }6\frac{2}{3}=\text{Rs. }\frac{20}{3}=\text{Rs. }\frac{40}{6}$ Cost of pencil $=\text{Rs. }4\frac{1}{6}=\text{Rs. }\frac{25}{6}$ We know, $25 < 40$ $\Rightarrow\text{Rs. }\frac{25}{6}<\text{Rs. }\frac{40}{6}$$\Rightarrow\text{Rs. }4\frac{1}{6}<\text{Rs. }6\frac{2}{3}$
Thus, cost of a pen is more. Now, $\frac{40}{6}-\frac{25}{6}=\frac{40-25}{6}=\frac{15}{6}=\frac{5}{2}=2\frac{1}{2}$ Hence, a pen costs more than a pencil by $\text{Rs. }2\frac{1}{2}.$
View full question & answer→Question 233 Marks
Reduce each of the following fractions to its lowest term (simplest form):
$\frac{84}{56}$
Answer$\frac{84}{56}$ Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84 Factors of 56 are 1, 2, 4, 7, 8, 14, 28 and 56 Common factors of 84 & 56 are 1, 2, 4, 7, 14 and 28 HCF = 28 Divide both the numerator & denominator by 28 $\frac{84\div28}{56\div28}=\frac{3}{2}$Therefore, the simplest form obtained is $=\frac{3}{2}$
View full question & answer→Question 243 Marks
Subtract as indicated:$\frac{8}{3}-\frac{5}{9}$
Answer$\frac{8}{3}-\frac{5}{9}$
$=\frac{8\times3}{3\times3}-\frac{5\times1}{9\times1}$
$=\frac{24}{9}-\frac{5}{9}$ (because LCM of 3 and 9 is 9)
$=\frac{24-5}{9}$
$=\frac{19}{9}$
View full question & answer→Question 253 Marks
Reduce the following fractions to its lowest term (simplest form):
$\frac{40}{75}$
Answer$\frac{40}{75}$Factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40
Factors of 75 are 1, 3, 5, 15 and 75
Common factors of 40 and 75 are 1 and 5
So, HCF = 5
Divide both the numerator & denominator by 5
$\frac{40\div5}{75\div5}=\frac{8}{15}$
Therefore, the simplest form obtained is $=\frac{8}{15}$
View full question & answer→Question 263 Marks
Simplity the following to its lowest term:
$\frac{52}{76}$
Answer$\frac{52}{76}$
Factors of 52 are 1, 2, 4, 13, 26 and 52
Factors of 76 are 1, 2, 4, 19, 38 and 76
Common factors of 52 and 76 are 1, 2 and 4
HCF of 52 and 76 is = 4
Dividing both the numerator and denominator by 4, we get:
$\frac{52\div4}{76\div4}=\frac{13}{19}$
Therefore, the simplest form obtained is,
$\frac{52}{76}=\frac{13}{19}$
View full question & answer→Question 273 Marks
Simplify:
$5\frac{1}{6}-3\frac{1}{4}+3\frac{1}{3}+4$
Answer$5\frac{1}{6}-3\frac{1}{4}+3\frac{1}{3}+4=\frac{31}{6}-\frac{13}{4}+\frac{10}{3}+\frac{4}{1}$
$=\frac{31\times2}{6\times2}-\frac{13\times3}{4\times3}+\frac{10\times4}{3\times4}+\frac{4\times12}{1\times12}$
$=\frac{62}{12}-\frac{39}{12}+\frac{40}{12}+\frac{48}{12}$
$=\frac{62-39+40+48}{12}$
$=\frac{111}{12}$
$=\frac{37}{4}$
$=9\frac{1}{4}$
View full question & answer→Question 283 Marks
Simplify:$\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$
AnswerGiven: $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$$=\frac{2\times4}{3\times4}+\frac{3\times3}{4\times3}+\frac{1\times6}{2\times6}$ (because LCM of 3, 4 and 2 is 12)
$=\frac{8}{12}+\frac{9}{12}+\frac{6}{12}$
$=\frac{8+9+6}{12}$
$=\frac{23}{12}$
View full question & answer→Question 293 Marks
Reduce the following fractions to its lowest term (simplest form):
$\frac{42}{28}$
Answer$\frac{42}{28}$Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
Factors of 28 are 1, 2, 4, 7, 14, 28
Common factors of 42 & 28 are 1, 2, 7 and 14
So, HCF = 14
Divide both the numerator & denominator by 14
$\frac{42\div14}{28\div14}=\frac{3}{2}$
Therefore, the simplest form obtained is $=\frac{3}{2}$
View full question & answer→Question 303 Marks
Simplify:$7\frac{1}{3}+3\frac{2}{3}+5\frac{1}{6}$
AnswerGiven: $7\frac{1}{3}+3\frac{2}{3}+5\frac{1}{6}$$=\frac{7\times3+1}{3}+\frac{3\times3+2}{3}+\frac{5\times6+1}{6}$
$=\frac{22}{3}+\frac{11}{3}+\frac{31}{6}$
$=\frac{22\times2}{3\times2}+\frac{11\times2}{3\times2}+\frac{31\times1}{6\times1}$ (because LCM of 3, 3 and 6 is 6)
$=\frac{44}{6}+\frac{22}{6}+\frac{31}{6}$
$=\frac{44+22+31}{6}$
$=\frac{97}{6}$
View full question & answer→Question 313 Marks
Reduce each of the following fractions to its lowest term (simplest form):
$\frac{12}{52}$
Answer$\frac{12}{52}$
Factors of 12 are 1, 2, 3, 4, 6 and 12
Factors of 52 are 1, 2, 4, 13, 26 and 52
Common factors of 12 and 52 are 1, 2 and 4
HCF = 4
Divide both the numerator & denominator by 4
$\frac{12\div4}{52\div4}=\frac{3}{13}$
Therefore, the simplest form obtained is $=\frac{3}{13}$
View full question & answer→Question 323 Marks
Simplify:$\frac{7}{18}+\frac{5}{6}+1\frac{1}{12}$
AnswerGiven: $\frac{7}{18}+\frac{5}{6}+1\frac{1}{12}$$=\frac{7}{18}+\frac{5}{6}+\frac{1\times12+1}{12}$
$=\frac{7}{18}+\frac{5}{6}+\frac{13}{12}$
$=\frac{7\times2}{18\times2}+\frac{5\times6}{6\times6}+\frac{13\times3}{12\times3 }$ (because LCM of 18, 6 and 12 is 36)
$=\frac{14}{36}+\frac{30}{36}+\frac{39}{36}$
$=\frac{14+30+39}{36}$
$=\frac{83}{36}$
View full question & answer→Question 333 Marks
Subtract as indicated:$4\frac{3}{4}-2\frac{1}{6}$
Answer$4\frac{3}{4}-2\frac{1}{6}$$=\frac{4\times4+3}{4}-\frac{2\times6+1}{6}$
$=\frac{19}{4}-\frac{13}{6}$
$=\frac{19\times3}{4\times3}-\frac{13\times2}{6\times2}$ (because LCM of 4 and 6 is 12)
$=\frac{57}{12}-\frac{26}{12}$
$=\frac{57-26}{12}$
$=\frac{31}{12}$
View full question & answer→Question 343 Marks
Simplify:$\frac{5}{8}+\frac{2}{5}+\frac{3}{4}$
AnswerGiven: $\frac{5}{8}+\frac{2}{5}+\frac{3}{4}$$=\frac{5\times5}{8\times5}+\frac{2\times8}{5\times8}+\frac{3\times10}{4\times10}$ (because LCM of 8, 5 and 4 is 40)
$=\frac{25}{40}+\frac{16}{40}+\frac{30}{40}$
$=\frac{25+16+30}{40}$
$=\frac{71}{40}$
View full question & answer→Question 353 Marks
Subtract:$\frac{21}{25}$ from $\frac{18}{20}$
Answer$\frac{18}{20}-\frac{21}{25}$
LCM of 20 and 25 is 100, so we will convert each fraction into an equivalent fraction with denominator 100.
$=\frac{18\times5}{20\times5}-\frac{21\times4}{25\times4}$
$=\frac{90}{100}-\frac{84}{100}$
$=\frac{90-84}{100}$
$=\frac{6}{100}$
$=\frac{3}{50}$
View full question & answer→Question 363 Marks
Simplify:$\frac{3}{4}+\frac{7}{16}+\frac{5}{8}$
AnswerGiven: $\frac{3}{4}+\frac{7}{16}+\frac{5}{8}$$=\frac{3\times4}{4\times4}+\frac{7\times1}{16\times1}+\frac{5\times2}{8\times2}$ (because LCM of 4, 16 and 8 is 16)
$=\frac{12}{16}+\frac{7}{16}+\frac{10}{16}$
$=\frac{12+7+10}{16}$
$=\frac{29}{16}$
View full question & answer→Question 373 Marks
Shikha and priya have bookshelves of the same size Shikha's shelf is $\frac{5}{6}$ full of book and Priya's shelf is $\frac{2}{5}$ full. Whose bookshelf is more full? By what fraction?
AnswerFraction of Shikha's filled bookshelf $=\frac{5}{6}$ Fraction of Priya's filled bookshelf $=\frac{2}{5}$ Comparing $\frac{5}{6}$ and $\frac{2}{5},$ we get: LCM of 5 & 6 is 30, so we will convert each fraction into an equivalent fraction with denominator 30. $=\frac{5\times5}{6\times5},\frac{2\times6}{5\times6}$ $\frac{25}{30}>\frac{12}{30}$Shikha's shelf is more full.
Therefore,
$\frac{25}{30}-\frac{12}{30}=\frac{25-12}{30}=\frac{13}{30}$
View full question & answer→Question 383 Marks
Simplity the following to its lowest term:
$\frac{84}{98}$
Answer$\frac{84}{98}$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
Common factors of 84 and 98 are 1, 2, 7 and 14
HCF of 84 and 98 is = 14
Dividing both the numerator and denominator by 14, we get:
$\frac{84\div14}{98\div14}=\frac{6}{7}$ Therefore, the simplest form obtained is, $\frac{84}{98}=\frac{6}{7}$
View full question & answer→Question 393 Marks
The teacher taught $\frac{3}{5}$ of the book, Vivek revised $\frac{1}{5}$ more on his own. How much does he still have to revise?
AnswerFraction of the book taught by the teacher $=\frac{3}{5}$
Fraction of the book revised by Vivek $=\frac{1}{5}$
Fraction of the book still left for revision by Vivek $=\frac{3}{5}-\frac{1}{5}$
$=\frac{3-1}{5}$
$=\frac{2}{5}$
Therefore, fraction of the book still left for revision by Vivek is $\frac{2}{5}$
View full question & answer→Question 403 Marks
Subtract:$\frac{2}{7}$ from $\frac{19}{21}$
Answer$\frac{19}{21}-\frac{2}{7}$
LCM of 21 and 7 is 21, so we will convert each fraction into an equivalent fraction with denominator 21.
$=\frac{19\times1}{21\times1}-\frac{2\times3}{7\times3}$
$=\frac{19}{21}-\frac{6}{21}$
$=\frac{19-6}{21}$
$=\frac{13}{21}$
View full question & answer→Question 413 Marks
Replace $\Box$ by the correct number:$\Box-\frac{1}{5}=\frac{1}{2}$
Answer$\frac{7}{10}-\frac{1}{5}=\frac{1}{2}$Solution:
Given: $\Box-\frac{1}{5}=\frac{1}{2}$
$\Rightarrow\Box=\frac{1}{5}+\frac{1}{2}$
$\Rightarrow\Box=\frac{1\times2}{5\times2}+\frac{1\times5}{2\times5}$ (because LCM of 5 and 2 is 10)
$\Rightarrow\Box=\frac{2}{10}+\frac{5}{10}$
$\Rightarrow\Box=\frac{2+5}{10}$
$\Box=\frac{7}{10}$
View full question & answer→Question 423 Marks
Shikha painted $\frac{1}{5}$ of the wall space in her room. Her brother ravish helped and painted $\frac{3}{5}$ of the wall space. How much did they paint together? How much the room is left unpainted?
AnswerShikha painted $\frac{1}{5}$ of the wall space in her room.
Ravish painted $\frac{3}{5}$ of the wall space.
Wall space painted by both of them together $=\frac{1}{5}+\frac{3}{5}$
$=\frac{1+3}{5}$
$=\frac{4}{5}$
Unpainted part of the room $=1-\frac{4}{5}$
$=\frac{5-4}{5}$
$=\frac{1}{5}$
View full question & answer→Question 433 Marks
Ravish had 20 pencils, Sikha had 50 pencils and Priya had 80 pencils. After 4 months, Ravish used up 10 pencils. Shikha used up 25 pencils and Priya used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of their pencils?
AnswerTotal pencils Ravish had = 20
Pencils used by Ravish = 10
Fraction of pencils used by ravish $=\frac{10\div10}{20\div10}=\frac{1}{2}$ (Dividing both the numerator & denominator by the HCFs of 10 & 20 )
Total pencils Shikha had = 50
Pencils used by Shikha = 25
Fraction of pencils used by Shikha $=\frac{25\div25}{50\div25}=\frac{1}{2}$ (Dividing both the numerator & denominator by the HCFs of 25 & 50)
Total pencils Priya had = 80
Pencils used by Priya = 40
Fraction of pencils used by Priya $=\frac{40\div40}{80\div40}=\frac{1}{2}$ (Dividing both the numerator & denominator by the HCFs of 40 & 80)
Yes, each of them has utilized an equal fraction of pencils.
View full question & answer→Question 443 Marks
Subtract:$\frac{7}{16}$ from $2$
Answer$\frac{2}{1}-\frac{7}{16}$
LCM of 1 and 16 is 16, so we will convert each fraction into an equivalent fraction with denominator 16.
$=\frac{2\times16}{1\times16}-\frac{7\times1}{16\times1}$
$=\frac{32}{16}-\frac{7}{16}$
$=\frac{32-7}{16}$
$=\frac{25}{16}$
View full question & answer→Question 453 Marks
Simplify:$\frac{5}{6}+3+\frac{3}{4}$
AnswerGiven: $\frac{5}{6}+3+\frac{3}{4}$$=\frac{5}{6}+\frac{3}{1}+\frac{3}{4}$
$=\frac{5\times2}{6\times2}+\frac{3\times12}{1\times12}+\frac{3\times3}{4\times3 }$ (because LCM of 6, 1 and 4 is 12)
$=\frac{10}{12}+\frac{36}{12}+\frac{9}{12}$
$=\frac{10+36+9}{12}$
$=\frac{55}{12}$
View full question & answer→Question 463 Marks
Ramesh bought $2\frac{1}{2}\text{kg}$ sugar whereas Rohit bought $3\frac{1}{2}\text{kg}$ or sugar. Find the total amount of sugar bought by both of them.
AnswerQuantity of sugar bought by Ramesh $=2\frac{1}{2}\text{kg}$
$=\frac{(2\times2)+1}{2}$
$=\frac{5}{2}\text{kg}$
Quantity of sugar bought by Rohit $=3\frac{1}{2}\text{kg}$
$=\frac{(2\times3)+1}{2}$
$=\frac{7}{2}\text{kg}$
Total amount of sugar bought by them = Quantity of sugar bought by Rohit + Quantity of sugar bought by Ramesh
$=\frac{5}{2}\text{kg}+\frac{7}{2}\text{kg}$
$=\Big(\frac{5+7}{2}\Big)\text{kg}$
$=\Big(\frac{12}{2}\Big)\text{kg}$
$=6\text{kg}$
View full question & answer→Question 473 Marks
$\frac{2}{3}$ and $\frac{6}{7}$
Answer$\frac{2}{3}-\frac{6}{7}$$=\frac{2\times7}{3\times7}-\frac{6\times3}{7\times3}$ (because LCM of 3 and 7 is 21)
$=\frac{14}{21}-\frac{18}{21}$
$=\frac{14-18}{21}$
$=\frac{-4}{21}$
View full question & answer→Question 483 Marks
Simplify:$4\frac{2}{3}+3\frac{1}{4}+7\frac{1}{2}$
AnswerGiven: $4\frac{2}{3}+3\frac{1}{4}+7\frac{1}{2}$$=\frac{4\times3+2}{3}+\frac{3\times4+1}{4}+\frac{7\times2+1}{2}$
$=\frac{14}{3}+\frac{13}{4}+\frac{15}{2}$
$=\frac{14\times4}{3\times4}+\frac{13\times3}{4\times3}+\frac{15\times6}{2\times6}$ (because LCM of 3, 4 and 2 is 12)
$=\frac{56}{12}+\frac{39}{12}+\frac{90}{12}$
$=\frac{56+39+90}{12}$
$=\frac{185}{12}$
View full question & answer→Question 493 Marks
Find the difference of:$\frac{1}{12}$ and $\frac{3}{4}$
Answer$\frac{1}{12}-\frac{3}{4}$
$=\frac{1\times1}{12\times1}-\frac{3\times3}{4\times3}$
$=\frac{1}{12}-\frac{9}{12}$ (because LCM of 4 and 12 is 12)
$=\frac{1-9}{12}$
$=\frac{-8}{12}$
$=\frac{-2}{3}$
View full question & answer→Question 503 Marks
Subtract as indicated:$5\frac{6}{7}-2\frac{2}{3}$
Answer$5\frac{6}{7}-2\frac{2}{3}$$=\frac{5\times7+6}{7}-\frac{2\times3+2}{3}$
$=\frac{41}{7}-\frac{8}{3}$
$=\frac{41\times3}{7\times3}-\frac{8\times7}{3\times7}$ (because LCM of 7 and 3 is 21)
$=\frac{123}{21}-\frac{56}{21}$
$=\frac{123-56}{21}$
$=\frac{67}{21}$
View full question & answer→Question 513 Marks
A piece of a wire $\frac{7}{8}\text{metres}$ long broke into two pieces. One piece was $\frac{1}{4}\text{metres}$ long. How long is the other piece?
AnswerLength of the wire $=\frac{7}{8}\text{metres}$
Length of one piece of wire $=\frac{1}{4}\text{metres}$
Let the length of the second piece of wire be x m.
Therefore, Length of the wire = Length of one piece + Length of the second piece
$\frac{7}{8}\text{metres}=\frac{1}{4}\text{metres}+\text{x}$
$\Rightarrow\text{x}=\frac{7}{8}\text{metres}-\frac{1}{4}\text{metres}$
$\Rightarrow\text{x}=\frac{7\times1}{8\times1}\text{metres}-\frac{1\times2}{4\times2}\text{metres}$ (because LCM of 8 and 4 is 8)
$\Rightarrow\text{x}=\frac{7}{8}\text{metres}-\frac{2}{8}\text{metres}$
$\Rightarrow\text{x}=\Big(\frac{7-2}{8}\Big)\text{metres}$
$\Rightarrow\text{x}=\frac{5}{8}\text{metres}$
Therefore, the length of the second piece is $\frac{5}{8}\text{m}.$
View full question & answer→Question 523 Marks
Isha read 25 pages of a book containing 100 pages. Nagma read $\frac{1}{2}$ of the same book. Who read less?
AnswerTotal pages in the book $= 100$
Fraction of the book read by Isha $=\frac{25\div25}{100\div25}=\frac{1}{4}$ (Dividing numerator & denominator by the HCF of 25 & 100)
Fraction of the book read by Nagma $=\frac{1}{2}$
Now, compare $\frac{1}{4}\ \&\ \frac{1}{2}$
L.C.M of 4 & 2 is 4
Convert each fraction into equivalent fraction with 4 as its denominator.
$\frac{1\times1}{4\times1}\ \&\ \frac{1\times2}{2\times2}$
$\frac{1}{4}\ \&\ \frac{2}{4}$
$\frac{1}{4}<\frac{2}{4}$
Therefore, Isha read less.
View full question & answer→Question 533 Marks
Add:
$\frac{8}{13}$ and $\frac{2}{3}$
AnswerGiven: $\frac{8}{13}$ and $\frac{2}{3}$
$\frac{8}{13}+\frac{2}{3}$
LCM of 13 and 3 is 39, so we will convert each fraction into an equivalent fraction with denominator 39.
$=\frac{8\times3}{13\times3}+\frac{2\times13}{3\times13}$
$=\frac{24}{39}+\frac{26}{39}$
$=\frac{24+26}{39}$
$=\frac{50}{39}$
View full question & answer→Question 543 Marks
Add:
$\frac{7}{10}$ and $\frac{2}{15}$
AnswerGiven: $\frac{7}{10}$ and $\frac{2}{15}$
$\frac{7}{10}+\frac{2}{15}$
LCM of 10 and 15 is 30, so we will convert each fraction into an equivalent fraction with denominator 30.
$=\frac{7\times3}{10\times3}+\frac{5\times2}{15\times2}$
$=\frac{21}{30}+\frac{4}{30}$
$=\frac{21+4}{30}$
$=\frac{25}{30}$
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