7th Grade > Mathematics
FRACTIONS AND DECIMALS MCQs
Fractions, Decimals
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Steps: 1 Mark
Calculation: 2 Marks
Time taken by Lipika to read a book =134 hours
She reads the entire book in 6 days.
Now, total number of hours she took to read the entire book
=134×6=74×6=212=1012 hours
Now if she reads for 12 hours daily, time required by her to complete the book
=1012÷ 12=212÷12=21
Hence, if she reads for half an hour daily she will finish reading the book in 21 days.
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Steps: [3 Marks]
Answer: [1 Mark]
Let the length and breadth of the bigger rectangle be a meters and b meters respectively
As per the question.
The length of the shaded rectangle is (110) of the bigger rectangle.
The length of the shaded rectangle is 0.1×a meters.
The breadth of the shaded rectangle is 0.001 times the bigger rectangle.
The breadth of the shaded rectangle is 0.001×b meters.
Area of the given bigger rectangle =a×b metres =10000m2
Area of the shaded rectangle =(0.1a)×(0.001b)
=(0.0001)×(ab)
=(0.0001)×(10000)
=1 m2
So, the area of the shaded rectangle is 1 m2.
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Steps: [2 Marks]
Application: [1 Mark]
Answer: [1 Mark]
Let the total volume of the bottle be Vm3
Volume filled in the first minute is V2
Volume of the bottle remaining=V−V2=V2
Volume filled in the second minute is (34)×(V2) m3
Volume filled in the third minute is V−(V2)−(34)×(V2)
=(V8) m3
Then the remaining volume =7 m3
(V8)=7
V=56 m3
The volume of the bottle is 56 m3
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Steps: 3 Marks
Result: 1 Mark
Given that
Ram purchased 1.5 kgs of tomato for 35 rupees.
Also, 5.6 kg of tomato is required to prepare 5 kg of tomato pickle.
The first step is to find per kg cost of tomato.
Now, cost of 1 kg of tomato = 351.5 rupees = 35×21.5×2 = 703 rupees
Given that 5.6 kg of tomato is required to prepare 5 kg tomato pickle
Then tomatoes required for making of 1 kg of pickle = 5.65 kgs = 1.12 kgs
Cost of 1kg of tomato pickle =(1.12)×703 = 26.133 rupees
Look at the figure above. This is a staircase consisting of 5 steps. The height of each in-step(green area) is 6 cms.
(i) What is the total length of the pink line if the breadth of each step is 32 cms.
(ii) Write the ratio of the height of the instep to its total length of the pink line in the form of a fraction.
[4 MARKS]
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(i) Formula: 1 Mark
Result: 1 Mark
(ii) Formula: 1 Mark
Result: 1 Mark
(i) Given: The height of the staircase = 6 cms
The breadth of the staircase = 32 cms
So, length of the pink line will be = (breadth + height) of five steps.
⇒5 (6 cms) + 5 (32 cms)
⇒5[6+32] cms
⇒5[38] cms
⇒190 cms
(ii) The total length of the in−stepThe total length of the pink line
⇒5(6) cms190 cms
⇒30190⇒319
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Steps: 2 Marks
Answers: 2 Marks
Given the length of the train is 322 m
Let x metres be the length that was found off the track. Then using unitary method we have
Or, x×1414=322×1114
Or, 14x=322×11
∴x=322×1114
=32214×11
=23×11
=253 metres
The total length of the train = 322 m
Total length of the train off the track = 253 m
So, the length of the train which was still on track = 322 - 253 = 69 m.
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B
Shifting the decimal point 3 places to the right of the decimal number 0.89345, we have
0.89345×1000=893.45
∴(0.89345×1000)+8.9345−893.45
=893.45+8.9345−893.45
=0+8.9345
=8.9345
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B
(12.4+9.6)×(0.1 +0.001)
=22.0×0.101
=2.222
And, (1.24×10.96)×0.2
=13.59×0.2
=2.718
2.718 is greater than 2.222
Therefore, (12.4+9.6)×(0.1 +0.001) < (1.24×10.96)×0.2
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A
(60×0.06×6)−(0.0006×600×0.6)
=(21.6)−(0.216)
=21.384