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Maths 5 Mark Question

Fractions · Maharashtra Board STD 6 (MSBSHSE - Semi English Medium). 3 questions.

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5 Mark Question

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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:
  1. $\frac{250}{400}$
Dividing both the numerator & denominator by the HCFs of 250 & 400, we get:
$=\frac{\frac{250}{50}}{\frac{400}{50}}$
$=\frac{5}{8}$
  1. $\frac{180}{200}$
Dividing both the numerator & denominator by the HCFs of 180 & 200, we get:
$=\frac{\frac{180}{20}}{\frac{200}{20}}$
$=\frac{9}{10}$
  1. $\frac{660}{990}$
Dividing both the numerator & denominator by the HCFs of 660 & 990, we get:
$=\frac{\frac{660}{30}}{\frac{990}{30}}$
$=\frac{\frac{22}{11}}{\frac{33}{11}}$
$=\frac{2}{3}$
  1. $\frac{180}{360}$​​​​​​​
​​​​​​​​​​​​​​Dividing both the numerator & denominator by the HCFs of 180 & 360, we get:
$=\frac{\frac{180}{180}}{\frac{360}{180}}$
$=\frac{1}{2}$
  1. $\frac{220}{550}$​​​​​​​
​​​​​​​​​​​​​​​​​​​​​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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