Question 13 Marks
Add the fractions $\frac{3}{8}$ and $6\frac34$
AnswerWe have, $\frac38+6\frac34$
$\because$ Mised fraction = Improper fraction $=\frac{\text{Whole number}\times\text{Denominator}+\text{Numerator}}{\text{Denominator}}$
$=\frac38+\frac{6\times4+3}{4}=\frac38+\frac{27}{4}$
$=\frac{3\times1}{8\times1}+\frac{27\times2}{4\times2}$ [$\because$ $LCM$ of $8$ and $4$ is $8,$ So convert each fraction to an equivalent fraction with denominator $8]$
$\frac{3}{8}+\frac{54}8=\frac{3+54}{8}=\frac{57}8=7\frac{1}8$
View full question & answer→Question 23 Marks
Write the fraction representing the total number of natural numbers in the collection of numbers $-3, -2, -1, 0, 1, 2, 3$. What fraction will it be for whole numbers? What fraction will it be for integers?
AnswerGiven collection is $-3 -2, -1, 0, 1, 2, 3$.Natural numbers $= 1, 2, 3$.
The fraction of natural numbers to the collection $= \frac37$
Now, whole numbers $= 0, 1, 2, 3.$
The fraction of whole numbers to the collection $= \frac47$
And integers $= -3, -2, -1, 0, 1, 2, 3.$
The fraction of integers to the collection $=\frac77 = \frac11$
View full question & answer→Question 33 Marks
Which one is greater? $1$ metre $40$ centimetres + $60$ centimetres or $2.6$ metres.
AnswerIn order to find which of the following is greater, we will first convert them into same unit and them compare.
So, $1m + 40\ cm + 60\ cm$
$=1\text{m}\frac{40}{100}\text{m}+\frac{60}{100}\text{m}[\because1\text{m}=100\text{cm}]$
$=1\text{m}+0.40\text{m}+0.60\text{m}$
$=2.00\text{m}$
Clearly, $2m < 2.6m$
Hence, $2.6m$ is greater than $1m$
$40\ cm + 60\ cm.$
View full question & answer→Question 43 Marks
Convert $2009$ paise to rupees and express the result as a mixed fraction.
AnswerWe know that, $Rs. 1 = 100$ paise
Now, for converting paise into rupees, we have to divide the given value by $100$.
$\therefore2009\text{paise}=₹20.09$
View full question & answer→Question 53 Marks
Mary bought $3\frac12$ $m$ of lace. She used $1\frac34$ m of lace for her new dress. How much lace is left with her?
AnswerGiven, many bought lace $=3\frac12\text{m}$
And lace used for new dress $=1\frac34\text{m}$
In order to find the lace left with her, we will subtract $1\frac34\text{m}$ from $3\frac12\text{m}$
$\therefore$ Lace left with her $=3\frac{1}2-1\frac34{}$
$=\frac{3\times2+1}{2}-\frac{4\times1+3}{4}$
$\because$ Mixed fraction = improper fraction $=\frac{\text{Whole number×Denominator+Numerator}}{\text{Denominator}}$
$=\frac{7}{2}-\frac74=\frac{7\times2}{2\times2}-\frac{7\times1}{4\times1}$ $LCM$ of $2$ and $4$ is $4$ so convert each fraction to an equivalent fraction with denominator $4]$
$=\frac{14}{2}-\frac{7}{4}=\frac{7}{4}=1\frac34\text{m}$
So, $1\frac34$ m lace is left with her. View full question & answer→Question 63 Marks
Arrange the fractions $\frac23,\frac34,\frac12$ and $\frac56$ in ascending order.
AnswerIn order to arrange the given fractions in ascending order, we have to convert them into like fractions.
So, $LCM$ of the denominators, i.e. $3, 4, 2$ and $6 = 2 \times 2 \times 3 = 12.$
$\begin{array}{c|c}2&3,4,2,6\\\hline2&3,2,1,3\\\hline3&3,1,1,3\\\hline&1,1,1,1\end{array}$
$\frac{2\times4}{3\times4}=\frac{8}{12},\frac{3\times3}{4\times3}=\frac{9}{12}$
$\frac{1\times6}{2\times6}=\frac{6}{12},\frac{5\times2}{6\times2}=\frac{10}{12}$
Clearly, $\frac{6}{12}<\frac{8}{12}<\frac{9}{102}<\frac{10}{12}$ [In the fractions, the fraction whose numerator is smaller will be smaller]
$\therefore\frac{1}{2}<\frac{2}{3}<\frac{3}{4}<\frac{5}{6}$
View full question & answer→Question 73 Marks
Find the fraction that represents the number of natural numbers to total numbers in the collection $0, 1, 2, 3, 4, 5$. What fraction will it be for whole numbers?
AnswerGiven collection is $0, 1, 2, 3, 4, 5$.Natural numbers $= 1, 2, 3, 4, 5.$
The fraction of natural numbers to the collection $=\frac56$
Now, whole numbers $= 0, 1, 2, 3, 4, 5, 6.$
The fraction of whole numbers to the collection $=\frac66 = \frac11$
View full question & answer→Question 83 Marks
Express $6.03$ as a mixed fraction.
AnswerWe know that, a decimal can be converted into a fraction by taking the numerator as the number obtained by removing the decimal point from the given decimal and taking the denominator as the number obtained by inserting as many zeroes with $1$ as there are number of places in the decimal part. Finally, converting the obtained fraction in its lowest form by dividing numerator and denominator by their $HCF$. $6.03=\frac{603}{100}=6\frac3{100}$
View full question & answer→Question 93 Marks
Convert $1537\ cm$ to m and express the result as an improper fraction.
AnswerWe know that, $1 m = 100 \ cm$ Now, for converting $cm$ into $m$, we have to divide the given value by $100.$ $\therefore1537\text{cm}=\frac{1537}{100}\text{m}=15\frac{37}{100}\text{m}=15.37\text{m}$
View full question & answer→Question 103 Marks
Express $0.041$ as a fraction.
AnswerWe know that, a decimal can be converted into a fraction by taking the numerator as the number obtained by removing the decimal point from the given decimal and taking the denominator as the number obtained by inserting as many zeroes with $1$ as there are numbers of place in the decimal part. Finally, converting the obtained fraction in its lowest form by dividing numerator and denominator by this $HCF$.
$\therefore0.041=\frac{041}{1000}=\frac{41}{1000}$
View full question & answer→Question 113 Marks
Subtract $\frac{1}{6}$ from $\frac12.$
AnswerConverting the given fractions into lke fractions.$LCM$ of the denominators of $\frac16$ and $\frac12$
$\begin{array}{c|c}2&6,2\\\hline3&3,1\\\hline&1,1\end{array}$
$\therefore$ $LCM$ of $6$ and $2 = 2 \times 3 = 6$
Now, we convert the given fractions into equivalent fractions with denominator $6$.
So, $\frac{1\times1}{6\times1}=\frac16$ and $\frac{1}{2}=\frac{1\times3}{2\times3}=\frac{3}{6}$
$\therefore\frac12-\frac16=\frac{3}{6}-\frac{1}{6}=\frac{3-1}{6}=\frac{3\div2}{6\div2}=\frac13$
[$\because$ for reducing a fraction to its lowest term, we divide its numerator and denominator by their $HCF$]
View full question & answer→Question 123 Marks
Grip size of a tennis racquet is $11\frac9{80}\text{cm}.$ Express the size as an improper fraction.
AnswerGiven, grip size of a tennis $=11\frac{9}{80}\text{cm}.$In order to convert a mixed fraction into an improper fraction, we use following formula Improper fraction.
Improper fraction $=\frac{\text{Whole number×Denominator+Numerator}}{\text{Denominator}}$
$\therefore11\frac{9}{80}=\frac{11\times80+9}{80}=\frac{880+9}{80}=\frac{889}{80}\text{cm}.$
View full question & answer→Question 133 Marks
Add the fractions $\frac38$ and $\frac23$
AnswerConverting the given fration into like factions, we have
$LCM$ of the denominators of $\frac38$ and $\frac23$
$\begin{array}{c|c}2&8,3\\\hline2&4,3\\\hline2&2,3\\\hline3&1,3\\\hline&1,1\end{array}$
$\therefore$ $LCM$ of $8$ and $3 = 2 \times 2 \times 2 \times 3 = 24$
Now, we convert the given fractions into an equivalent fraction with denominator 24.
So, $\frac38=\frac{3\times3}{8\times9}=\frac{9}{24}$ and $\frac{2}{3}=\frac{2\times8}{3\times8}=\frac{16}{24}$
$\therefore\frac38+\frac23=\frac{9}{24}+\frac{16}{24}=\frac{25}{24}$
View full question & answer→Question 143 Marks
Subtract $1\frac14$ from $6\frac12$
AnswerWe have, $6\frac12-1\frac14$$\frac{6\times2+1}{2}-\frac{1\times4+1}{4}$
$\because$ Mixed fraction = Improper fraction $=\frac{\text{Whole number×Denominator+Numerator}}{\text{Denominator}}$
$=\frac{13}{2}-\frac54=\frac{13\times2}{2\times2}-\frac{5\times1}{4\times1}$ [$\because$ $LCM$ of $2$ and $4$ is $4$ so convert each fraction to an equivalent fraction with denominator $4$]
$=\frac{26}{4}-\frac{5}4{}$
$=\frac{26-5}{4}=\frac{21}{4}=5\frac{1}4{}$
View full question & answer→Question 153 Marks
Mr. Rajan got a job at the age of $24$ years and he got retired from the job at the age of $60$ years. What fraction of his age till retirement was he in the job?
AnswerGiven, Rajan’s age on the joining $= 24$ year and retirement age $= 60$ year.
$\therefore$ The fraction of his age till retirement, when he was in the job.
$=\frac{\text{Total years he did the job}}{\text{Retirement age}}=\frac{36}{60}$ [$\because$ $HCF$ of $36$ and $60 = 12$]
Hence, the required fraction is $\frac35.$
View full question & answer→Question 163 Marks
Convert $2435m$ to $km$ and express the result as mixed fraction.
AnswerWe know that, $1 \ km = 1000 m$ Now, for converting m into $km$, we have divide the given value by $1000.$ $\therefore2435\text{m}=\frac{2435}{1000}\text{km}$ $=2\frac{435}{1000}\text{km}$ $=2.435\text{km}$
View full question & answer→Question 173 Marks
On an average $\frac{1}{10}$ of the food eaten is turned into organism’s own body and is available for the next level of consumer in a food chain. What fraction of the food eaten is not available for the next level?
AnswerQuantity of food eaten which turned into organism's own body $=\frac{1}{10}$ of the total food Now, the Quantity of food eaten which is not available for the next level$=1-\frac{1}{10}=\frac{1\times10}{1\times10}=\frac{10}{10}-\frac{1}{10}=\frac{10-1}{10}=\frac{9}{10}$
Hence, the required fraction $=\frac{9}{10}.$
View full question & answer→Question 183 Marks
Express $3\frac25$ as a decimal.
AnswerIn order to convert fraction into decimal, we first convert it into an equivalent fraction with denominator $10$ or $100$ or $1000$ and then write its numerator and mark decimal point after one place on two place or three places from right towards left, if the denominator is $10$ or $100$ or $1000$ respectively.
If the numerator is short of digits, insert zeroes at the left of the numerator.
$\therefore3\frac25=\frac{5\times3+2}{5}$ $=\frac{17}{5}$
$\because$ Mixed fraction = Improper fraction $=\frac{\text{Whole number}\times\text{Denominator}+\text{Numerator}}{\text{Denominator}}$
Now, $\frac{17\times2}{5\times2}=\frac{34}{10}=3.4$
$\therefore3\frac25=3.4$
View full question & answer→Question 193 Marks
A rectangle is divided into certain number of equal parts. If $16$ of the parts so formed represent the fraction $\frac14,$ find the number of parts in which the rectangle has been divided.
AnswerLet a rectangle be devided into $x$ equal parts.Now, $16$ of the parts represent $=\frac14$
Also, $16$ parts of $\text{x}=\frac{16}{\text{x}}$
$\therefore\frac{16}{\text{x}}=\frac14$
$\Rightarrow\text{x}=16\times4=64$ parts.
Hence, the rectangle is divide into $64$ equal parts.
View full question & answer→Question 203 Marks
Add $1\frac14$ and $6\frac12.$
AnswerWe have, $1\frac{1}4{}+6\frac12$$=\frac{1\times4+1}{4}+\frac{6\times2+1}{2}$
$\because$ Mixed fraction = Improper fraction $=\frac{\text{Whole number×Denominator+Numerator}}{\text{Denominator}}$
$=\frac{5}{4}+\frac{13}{2}=\frac{5\times1}{4\times1}+\frac{13\times2}{2\times2}$[$\because$ $LCM$ of $4$ and $2$ is $4$, so convet each fraction to an equivalent fraction with denominator $12$]
$=\frac{5}{4}+\frac{26}{4}$
$=\frac{5+26}{4}=\frac{31}{4}=7\frac34$
View full question & answer→Question 213 Marks
Subtract $8\frac13$ from $\frac{100}{9}$
AnswerWe have, $\frac{100}{9}-8\frac{1}{3}$$=\frac{100}{9}-\frac{8\times3+1}{3}$
$\because$ Mixed fraction = Improper fraction $=\frac{\text{Whole number}\times\text{denominator}+\text{Numerator}}{\text{Denominator}}$
$=\frac{100}{9}-\frac{25}{3}=\frac{100\times1}{9\times1}-\frac{25\times3}{3\times3}$[$\because$ $LCM$ of $9$ and is $9$, so convert each fraction to an equivalent fraction with denominator $9$]
$=\frac{100}{9}-\frac{75}{9}=\frac{25}{9}=2\frac79$
View full question & answer→