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Maths 4 Mark Question

Decimal Fractions · Maharashtra Board STD 6 (MSBSHSE - Semi English Medium). 9 questions.

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4 Mark Question

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Question 14 Marks
A road is 4 km 800 m long. If trees are planted on both its sides at intervals of 9.6 m, how many trees were planted?
Answer
Length of road = 4 km 800 m
= 4 × 1000 m + 800 m
= 4000 m + 800 m
= 4800 m
Number of trees on one side = 4800 ÷ 9.6
$=\frac{4800}{1} \div \frac{96}{10}=\frac{4800}{1} \times \frac{10}{96}=\frac{48000}{96}$
= 500
∴ Number of trees on both sides = 2 x number of trees on one side
= 2 x 500 = 1000
If the trees are planted at the beginning of the road, then
Total number of trees = 1000 + 2 = 1002
∴ Total number of trees planted is 1000 or 1002.
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Question 24 Marks
Carry out the following divisions.
i. 4.8÷2
ii. 17.5÷5
iii. 20.6÷2
iv. 32.5÷25
Answer
$\begin{aligned} & \text { i. } 4.8 \div 2 \\ & =\frac{48}{10} \div \frac{2}{1}=\frac{48}{10} \times \frac{1}{2}=\frac{48}{20} \\ & =\frac{48 \times 5}{20 \times 5}=\frac{240}{100}=2.4\end{aligned}$

$\begin{aligned} & \text { ii. } 17.5 \div 5 \\ & =\frac{175}{10} \div \frac{5}{1}=\frac{175}{10} \times \frac{1}{5}=\frac{175}{50} \\ & =\frac{175 \times 2}{50 \times 2}=\frac{350}{100}= 3 . 5 \end{aligned}$

$\begin{aligned} & \text { iii. } 20.6 \div 2 \\ & =\frac{206}{10} \div \frac{2}{1}=\frac{206}{10} \times \frac{1}{2}=\frac{206}{20} \\ & =\frac{206 \times 5}{20 \times 5}=\frac{1030}{100}=10.3\end{aligned}$

$\begin{aligned} & \text { iv. } 32.5 \div 25 \\ & =\frac{325}{10} \div \frac{25}{1}=\frac{325}{10} \times \frac{1}{25}=\frac{325}{250} \\ & =\frac{325 \times 4}{250 \times 4}=\frac{1300}{1000}=1.3\end{aligned}$

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Question 34 Marks
Vedika has 23.5 metres of cloth. She used it to make 5 curtains of equal size. If each curtain required 4 metres 25 cm to make, how much cloth is left over?
Answer
We know, that 1 m = 100 cm
Cloth required to make 1 curtain = 4 m 25 cm
$\begin{aligned}= & 4 m +\frac{25}{100} m \\ = & 4 m +0.25 m \\ & 4.00 \\ + & \frac{0.25}{4.25} \\ = & 4.25 m \end{aligned}$

∴ Cloth required to make 5 curtains = 5 × 4.25

$\begin{aligned} & =\frac{5}{1} \times \frac{425}{100}=\frac{5 \times 425}{1 \times 100}=\frac{2125}{100} \\ & =21.25 m \end{aligned}$
Cloth remaining with Vedika = Total cloth with Vedika – Cloth used
= 23.5 m – 21.25 m
$\begin{array}{r}23.50 \\ -21.25 \\ \hline 2.25\end{array}$
= 2.25 m
∴ The length of cloth remaining with Vedika is 2.25 m.

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Question 44 Marks
Virendra bought 18 bags of rice, each bag weighing 5.250 kg. How much rice did he buy altogether? If the rice costs Rs 42 per kg, how much did he pay for it?
Answer
Weight of one bag of rice = 5.250 kg
Number of bags of rice = 18
∴ Total Weight = 18 × 5.250
$=\frac{18}{1} \times \frac{525}{100}=\frac{18 \times 525}{1 \times 100}=\frac{9450}{100}=94.5 kg$
Cost of 1 kg of rice = Rs 42
∴ Cost of 94.5 kg of rice = 42 × 94.5
$=\frac{42}{1} \times \frac{945}{10}=\frac{42 \times 945}{1 \times 10}=\frac{39690}{10}=₹ 3969$
∴ Total rice bought by Virendra is 94.5 kg, and the amount paid for it is Rs 3969.
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Question 54 Marks
i. 2.7 × 1.4
ii. 6.17 × 3.9
iii. 0.57 × 2
iv. 5.04 × 0.7
Answer
$\begin{aligned}& \text { i. } 2.7 \times 1.4 \\& =\frac{27}{10} \times \frac{14}{10} \\

& =\frac{27 \times 14}{10 \times 10}=\frac{378}{100} \\& =3.75\end{aligned}$

$\text { ii. } \begin{aligned}& 6.17 \times 3.9 \\= & \frac{617}{100} \times \frac{39}{10} \\= & \frac{617 \times 39}{100 \times 10}=\frac{24063}{1000} \\= & 24.063

\end{aligned}$

iii. $0.57 \times 2$

$\begin{aligned}& =\frac{57}{100} \times \frac{2}{1} \\& =\frac{57 \times 2}{100 \times 1}=\frac{114}{100} \\& =1.14\end{aligned}$

iv. $5.04 \times 0.7$

$\begin{aligned}& =\frac{504}{100} \times \frac{7}{10} \\& =\frac{504 \times 7}{100 \times 10}=\frac{3528}{1000} \\& =3.528\end{aligned}$

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Question 64 Marks
Convert the common fractions into decimal fractions:

i. $\frac{36}{40}$

iv. $\frac{7}{25}$

iii. $\frac{19}{200}$

iv. $\frac{17}{20}$

Answer
$\begin{aligned} & \text { i. } \frac{36}{40} \\ & \frac{36}{40}=\frac{9}{10}=0.9\end{aligned}$

$\begin{aligned} & \text { ii. } \frac{7}{25} \\ & \frac{7}{25}=\frac{7 \times 4}{25 \times 4}=\frac{28}{100}=\mathbf{0 . 2 8}\end{aligned}$

$\begin{aligned} & \text { iii. } \frac{19}{200} \\ & \frac{19}{200}=\frac{19 \times 5}{200 \times 5}=\frac{95}{1000}=\mathbf{0 . 0 9 5}\end{aligned}$

$\begin{aligned} & \text { iv. } \frac{17}{20} \\ & \frac{17}{20}=\frac{17 \times 5}{20 \times 5}=\frac{85}{100}=\mathbf{0 . 8 5}\end{aligned}$

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Question 74 Marks
Convert the decimal fractions into common fractions:
i. 27.5
ii. 0.007
iii. 90.8
iv. 39.15
Answer
$\begin{aligned}& \text { i. } 27.5 \\& =\frac{275}{10}\end{aligned}$

ii. 0.007

$=\frac{7}{1000}$

iii. 90.8

$=\frac{908}{10}$

iv. 39.15

$=\frac{3915}{100}$

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Question 84 Marks
Convert the common fractions into decimal fractions:

i. $\frac{3}{4}$

ii. $\frac{4}{5}$

iii. $\frac{9}{8}$

iv. $\frac{17}{20}$

Answer
i. $\frac{3}{4}$
$\frac{3}{4}=\frac{3 \times 25}{4 \times 25}=\frac{75}{100}=0.75$

$\begin{aligned} & \text { ii. } \frac{4}{5} \\ & \frac{4}{5}=\frac{4 \times 2}{5 \times 2}=\frac{8}{10}=0.8\end{aligned}$

iii. $\frac{9}{8}$
$\frac{9}{8}=\frac{9 \times 125}{8 \times 125}=\frac{1125}{1000}=1.125$

$\begin{aligned} & \text { iv. } \frac{17}{20} \\ & \frac{17}{20}=\frac{17 \times 5}{20 \times 5}=\frac{85}{100}=\mathbf{0 . 8 5}\end{aligned}$

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