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Fractions and Decimals · Rajasthan Board (RBSE) STD 6 (Rajasthan - English Medium). 18 questions.

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Question 11 Mark
The place value of a digit at the tenths place is $10$ times the same digit at the ones place.
Answer
Let $1.1$ be a decimal number having same digits at ones and tenths place.
Now, the place value of $1$ at ones place $= 1 \times 1 = 1$
The place value of $1$ at tenths place $=1\times\frac1{10}=\frac1{10}$
Clearly, the place value of $1$ at tenth place is $\frac1{10}$ times of $1$ at ones place.
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Question 21 Mark
In the questions $66$ to $71$, fill in the blanks using $‘>’, ‘<’ or ‘=’:$
$\frac{12}{75}\ ...\frac{32}{200}$
Answer
In order to compare fractions with different denominators, we will convert them to like fractions.
LCM of 75 and 200.
$\begin{array}{c|c}2&75,200\\\hline2&75,100\\\hline2&75,50\\\hline3&75,25\\\hline5&25,25\\\hline5&5,5,\\\hline&1,1\end{array}$
$\therefore$ $LCM$ of $75$ and $200 = 2 \times 2 \times 2 \times 3 \times 5 \times 5 = 600$
Now, converting each of the given fraction to equivalent fraction with denominator 600.
$\frac{12\times8}{75\times8}=\frac{96}{600}$ and $\frac{32\times3}{200\times3}=\frac{96}{600}$
Clearly, $\frac{96}{600}=\frac{96}{600}$
$\therefore\frac{12}{75}\frac{32}{200}$
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Question 31 Mark
Fractions $\frac{15}{39}$ and $\frac{47wQbNPTDJp9hMYdvogK2hAUiHsGeiybwaWe36bwtRQ3UTpYV7YuZ8FV5j9nauFCWwcjM6dTzpL5s2N79Rp5unwdMvc8ZKUnbsp;are equivalent fractions.
Answer
True.
Solution:
We have,
$\frac{15}{39}$ and $\frac{45}{117}$

$15\times117=39\times45$
$1755=1755$
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Question 41 Mark
In the questions $66$ to $71$, fill in the blanks using $‘>’, ‘<’$ or $‘=’:$
$6.25\ ...\frac{25}{4}$
Answer
For comparing a fraction and a decimal, we will convert both of them to either into like fractions or into like decimals.
Now, $\frac{25}{4}=\frac{25\times25}{4\times25}=\frac{625}{100}=6.25$
Clearly, $6.25=6.25$
$\therefore6.25=\frac{25}{4}$
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Question 51 Mark
What is wrong in the following additions?
$\begin{array}{r}8 \frac{1}{2}=8 \frac{2}{4} \\ +4 \frac{1}{4}=4 \frac{1}{4} \\ \hline=12 \frac{3}{8} \\ \hline\end{array}$
Answer
On observing the sum, we find that the denominators of like fractions are also added which is wrong. So, the correct answer will be $=12\frac34$
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Question 61 Mark
$42.28 - 3.19 = 39.09$
Answer
True. Solution: Given, 47wQbNPTDJp9hMYdvogK2hAUiHsGeiybwaWe36bwtRQ3UTpYV7YuZ8FV5j9nauFCWwcjM6dTzpL5s2N79Rp5unwdMvc8ZKU:verdana">$\begin{bmatrix}\because\ \ \ 42.28\ \ \ \ \ \\\underline{\ -3.19\ }\\\ \ \underline{\ \ \ \ 39.09\ \ \ }\end{bmatrix}$
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Question 71 Mark
In the questions $66$ to $71$, fill in the blanks using $‘>’, ‘<’$ or $‘=’: 3.25 ... 3.4$
Answer
 Here, the whole nember part of both the decimal numbers is same.
Now, tenths part of $3.25=\frac{2}{10}$ and teths part of $3.4=\frac{4}{10}$
Clearly, $\frac{2}{10}<\frac{4}{10}$ $\therefore3.25<3.4$
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Question 81 Mark
In the questions $66$ to $71$, fill in the blanks using $‘>’, ‘<’$ or $‘=’: \frac{9}{15}\ ...\frac{95}{14}$
Answer
 In order to compare fraction with different denominators we will convert them to like fractions.
LCM of 15 and 14 $\begin{array}{c|c}2&15,14\\\hline3&15,7\\\hline5&5,7\\\hline7&1,7\\\hline&1,1\end{array}$
$\therefore LCM$ of $15$ and $14 = 2 \times 3 \times 5 \times 7 = 210$
Now, converting each of the given fraction to an equivalent fraction with denominator $210$.
$\frac{8\times14}{15\times14}=\frac{112}{210}$ and $\frac{95\times15}{14\times15}=\frac{1425}{210}$
Clearly, $\frac{1425}{210}>\frac{112}{210}$
$\therefore\frac{8}{15}<\frac{95}{14}$
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Question 91 Mark
Write the fraction represented by the unshaded portion of the adjoining figure:
Answer
Rectangle is divided into $15$ equal parts and number of unshaded parts are $4$.
Fraction of unshaded portion to the total portion $=\frac{4}{15}$
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Question 101 Mark
In the questions $66$ to $71$, fill in the blanks using $‘>’, ‘<’$ or$ ‘=’: \frac{11}{16}\ ...\frac{14}{15}$
Answer
In order to compare fractions with different denominators, we will convert them to like fractions.
$LCM$ of $16$ and $15$
$\begin{array}{c|c}2&16,15\\\hline2&8,15\\\hline2&4,15\\\hline2&2,15\\\hline3&1,15\\\hline5&1,5\\\hline&1,1\end{array}$
$\therefore$ LCM of 16 and 15 = 2 \times 2 \times 2 \times 2 \times 3 \times 5 = 240
Now, converting each of the given fraction to an equivalent fraction wit denominator $240.$
$\frac{11\times15}{16\times15}=\frac{165}{240}$ and $\frac{14\times16}{15\times16}=\frac{240}{240}$
Clearly, $\frac{224}{240}>\frac{165}{240}$
$\therefore\frac{11}{16}<\frac{14}{15}$
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Question 111 Mark
$4.55 + 9.73 =$ ______.
Answer
We have,
$\ \ \ \ 4.55\\\underline{-\ 9.73\ \ \ }\\ \underline{\ \ 14.28\ \ \ }$
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Question 121 Mark
The decimal $23.2=23\frac{2}{5}$
Answer
False. Solution: We 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 place in the decimal part. Finally, converting the obtained fraction in its lowest form by dividing numerator and denominator by their $HCF$ and converting it to mixed fraction if required. $23.2=\frac{232}{10}=\frac{232 \div 2}{10 \div 2}=23 \frac{1}{5}$
$\begin{gathered}\because 5) 116(23 \\ \frac{10}{16} \\ \frac{15}{1}\end{gathered}$
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Question 131 Mark
$9\frac14-\frac54=$ ______________.
Answer
We have, $9\frac{1}{4}-\frac{5}{4}=\frac{9\times4+1}{4}-\frac{5}{4}$
$\Big[\because$ Mixed fraction = Improper fraction $=\frac{\text{(Whole number} \times\text{Denominator)}+\text{Numerator}}{\text{Denominator}}\Big]$
$=\frac{37}{4}-\frac54$
$=\frac{37-5}{4}=\frac{32}{4}$
$=\frac{32\div4}{4\div4}[\because$ $HCF$ of $32$ and denominator $4$ is 4$]$
$=8$
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Question 141 Mark
Add the following: $20.02$ and $2.002.$
Answer
Converting the given decimals to like decimals, we have $20.020$ and $2.002.$
Now, $\ \ 20.020\\ \underline{+\ 2.002\ \ }\\ \underline{\ \ \ 22.022\ \ }$
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Question 151 Mark
$\frac{25}{19}+\frac{6}{19}=\frac{31}{38}$
Answer
False. Solution: Since, fractions with same denominators can be added by simply adding the numerators and writing the common denominator as it is. $\frac{25}{19}+\frac{6}{19}=\frac{25+6}{19}=\frac{31}{19}$
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Question 161 Mark
In the questions $66$ to $71$, fill in the blanks using $‘>’, ‘<’$ or $‘=’: \frac{18}{15}\ ...\ 1.3$
Answer
 For comparing a fraction and a decimal, we will convert both of them to either into like fractions or into like decimals.
Now, $1.3=\frac{13}{10} LCM$ of $10$ and $15$
$\begin{array}{c|c}2&10,15\\\hline3&5,15\\\hline5&5,5\\\hline&1,1\end{array}$
$\therefore LCM$ of $10$ and $15 = 2 \times 3 \times 5 = 30$
Now, converting each of the given factions to equivalent fractions with denominator $30.$
$\frac{18\times2}{15\times2}=\frac{36}{30}$ and $\frac{13\times3}{10\times3}=\frac{39}{30}$
Clearly, $\frac{36}{30}<\frac{39}{30}$
$\therefore\frac{18}{15}<1.3$
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Question 171 Mark
$9+\frac{2}{10}+\frac{6}{100}$ is equal to the decimal number _______________ .
Answer
$9+\frac{2}{10}+\frac{6}{100}$ is equal to the decimal number 9.26.Solution:
Here,
$9+\frac{2}{10}+\frac{6}{100}$ $=9+0.2+0.06=9.26$
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Question 181 Mark
$\frac{18}{135}$ and $\frac{90}{675}$ are proper, unlike and ______ fractions.
Answer
$\frac{18}{135}$ and $\frac{90}{675}$ are proper, unlike and
equivalent fractions.
Solution: We know that, two fraction $\frac{\text{a}}{\text{b}}$ and $\frac{\text{c}}{\text{d}}$ are equivalent, if $\text{a}\times\text{d}=\text{c}\times\text{b}$
$\Rightarrow18\times675=90\times135$
$\Rightarrow12150=12150$
Hence, $\frac{18}{135}$ and $\frac{90}{675}$ are equivalent fraction.
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