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}$
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}$
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}$
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 $30$.
$=\frac{7\times3}{10\times3}+\frac{5\times2}{15\times2}$
$=\frac{21}{30}+\frac{4}{30}$
$=\frac{21+4}{30}$
$=\frac{25}{30}$
View full question & answer→