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MATHS 5 Marks Questions

Fractions · Rajasthan Board (RBSE) STD 6 (Rajasthan - English Medium). 3 questions.

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Question 15 Marks
Match the equivalent fractions and write another $2$ for each:
$(i)$ $\frac{250}{400}$ $(a)$ $\frac{2}{3}$
$(ii)$ $\frac{180}{200}$ $(b)$ $\frac{2}{5}$
$(iii)$ $\frac{660}{990}$ $(c)$ $\frac{1}{2}$
$(iv)$ $\frac{180}{360}$ $(d)$ $\frac{5}{8}$
$(v)$ $\frac{220}{550}$ $(e)$ $\frac{9}{10}$
Answer
$(i)$ $\frac{250}{400}$ $(d)$ $\frac{5}{8}$
$(ii)$ $\frac{180}{200}$ $(e)$ $\frac{9}{10}$
$(iii)$ $\frac{660}{990}$ $(a)$ $\frac{2}{3}$
$(iv)$ $\frac{180}{360}$ $(c)$ $\frac{1}{2}$
$(v)$ $\frac{220}{550}$ $(b)$ $\frac{2}{5}$
 
Solution:
$i.\ \frac{250}{400}$
Dividing both the numerator & denominator by the $HCFs$ of $250\ \&\ 400,$ we get:
$=\frac{\frac{250}{50}}{\frac{400}{50}}$
$=\frac{5}{8}$
$ii.\ \frac{180}{200}$
Dividing both the numerator & denominator by the $HCFs$ of $180\ \&\ 200,$ we get:
$=\frac{\frac{180}{20}}{\frac{200}{20}}$
$=\frac{9}{10}$
$iii.\ \frac{660}{990}$
Dividing both the numerator & denominator by the $HCFs$ of $660\ \&\ 990,$ we get:
$=\frac{\frac{660}{30}}{\frac{990}{30}}$
$=\frac{\frac{22}{11}}{\frac{33}{11}}$
$=\frac{2}{3}$
$iv.\ \frac{180}{360}$
​​​​​​​Dividing both the numerator & denominator by the $HCFs$ of $180\ \&\ 360,$ we get:
$=\frac{\frac{180}{180}}{\frac{360}{180}}$
$=\frac{1}{2}$
$v.\ \frac{220}{550}$​​​​​​​
​​​​​​​​​​​​​​​​​​​​​Dividing both the numerator & denominator by the $HCFs$ of $220\ \&\ 550,$ we get:
$=\frac{\frac{220}{11}}{\frac{550}{11}}$
​​​​​​​$=\frac{20}{50}$
$=\frac{\frac{20}{10}}{\frac{50}{10}}$
$=\frac{2}{5}$
 
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Question 35 Marks
Ravish's house is $\frac{9}{10}\text{km}$ from his school. He walked some distance and then took a bus for $\frac{1}{2}\text{km}$ up to the school. How far did he walk$?$
Answer
Total distance between the house and the school $=\frac{9}{10}\text{km}$Distance covered in the bus $=\frac{1}{2}\text{km}$
Total distance between the house and the school $=$ Distance covered by walking $+$ distance covered in the bus
Distance covered by walking $=$ Total distance between the house and the school $–$ Distance covered in the bus
Distance covered by walking $=\frac{9}{10}\text{km}-\frac{1}{2}\text{km}$
$LCM$ of $10$ and $2$ is $10,$ so we convert each fraction into an equivalent fraction with denominator $10$
$=\frac{9\times1}{10\times1}-\frac{1\times5}{2\times5}$
$=\frac{9}{10}-\frac{5}{10}$
$=\frac{9-5}{10}$
$=\frac{4}{10}$
$=\frac{2}{5}\text{km}$
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