NCERT Exemplar Problems Class 7 Maths – Fractions and Decimals

NCERT Exemplar Problems Class 7 Maths – Fractions and Decimals

Multiple Choice Questions (MCQs)

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In questions 21 to 44, fill in the blanks to make the statements true.

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True / False

In questions 45 to 54, State whether the statements are True or False.

Question 45:
The reciprocal of a proper fraction is a proper fraction.
Solution:
False
The reciprocal of a proper fraction is always an improper fraction.
e.g. 5/6   —> Proper fraction
Its reciprocal is 5/6 , i.e. improper fraction.

Question 46:
The reciprocal of an improper fraction is an improper fraction.
Solution:
False
The reciprocal of an improper fraction is a proper fraction, e.g. 7/6  —> Improper fraction
Its reciprocal is 7/6, i.e. proper fraction.

Question 47:
 

Solution:
False
Two fractions are multiplied by multiplying their numerators and denominators separately and writing the product as,

Question 48:
The product of two improper fractions are less than both the fractions.
Solution:
False
The product of two improper fractions are greater than both the fractions.

Question 49:
A reciprocal of a fraction, is obtained by inverting it upside down.
Solution:
True
Let a/b be the fraction. Then, for obtaining its reciprocal, numerator and denominator are interchanged.
∴ Reciprocal of a/b = b/a

Question 50:
To multiply a decimal number by 1000, we move the decimal point in the number to the right by three places.
Solution:
True
e.g. 2.732 x 1000= 2732 (moving the decimal to right by three places)

Question 51:
To divide a decimal number by 100, we move the decimal point in the number to the left by two places.
Solution:
True
e.g. 273.2/100 = 2.732 (moving decimal point to the left by two places.

Question 52:
1 is the only number which is its own reciprocal.
Solution:
True
For obtaining the reciprocal of a number, we simply interchange the numerator and denominator.
Hence, reciprocal of 1 will be 1/1, i.e. 1

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Question 56:
What happens to the value of a fraction, if the denominator of the fraction is decreased while numerator is kept unchanged?
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Question 66:
Animals: The label on a bottle of pet vitamins lists dosage guidelines. What dosage would you give to each of these animals?
(a) a 18 kg adult dog
(b) a 6 kg cat
(c) a 18 kg pregnant dog

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Question 68:
Anvi is making bookmarker like the one shown in the given figure. How many bookmarker can she make from a 15 m long ribbon?

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Question 69:
A rule for finding the approximate length of diagonal of a square is to multiply the length of a side of the square by 1.414.
Find the length of the diagonal when:
(a) the length of a side of the square is 8.3 cm.
(b) the length of a side of the square is exactly 7.875 cm.
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Question 70:

The largest square that can be drawn in a circle has a side whose length is 0.707 times the diameter of the circle. By this rule, find the length of the side of such a square, when the diameter of the circle is
(a) 14.35 cm
(b) 8.63 cm

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Question 71:
To find the distance around a circular disc, multiply the diameter of the disc by 3.14.
What is the distance around the disc, when
(a) the diameter is 18.7cm?
(b) the radius is 6.45cm?
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Question 72:
What is the cost of 27.5 m of cloth at Rs. 53.50 per metre ?
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Question 80:
Heena’s father paid an electric bill of Rs. 385.70 out of a Rs. 500 note. How much change should he have received?
Solution:
Given, total rupees = Rs. 500
and money paid = Rs. 385.70
∴ Change he received = Rs. (500 – 385.70) = Rs. 114.30

Question 81:
The normal body temperature is 98.6°F. When Savitri was ill, her temperature rose to 103.1°F. How many degrees above normal was that?
Solution:
Given, normal body temperature = 98.6° F
and temperature rise to = 103.1° F
∴Rise in temperature = (103.1 – 98.6)° F = 4.5° F

Question 82:
Meteorology One measure of average global temperature shows how each year varies from a base measure.The table shows results for several years.

See the table and answer the following:
(a) Order the five years from coldest to warmest.
(b) In 1946, the average temperature varied by – 0.03°C from the base measure. Between which two years should 1946 fall, when the years are ordered from coldest to warmest?
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Science Application

Question 83:
In her Science class, Jyoti learned that the atomic weight of Helium is 4.0030; of Hydrogen is 1.0080; and of Oxygen is 16.0000. Find the difference between the atomic weights of:
(a) Oxygen and Hydrogen
(b) Oxygen and Helium
(c) Helium and Hydrogen.
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Question 84:
Measurement made in Science lab must be as accurate as possible. Ravi measured the length of an iron rod and said, it was 19.34 cm long; Kamal said 19.25 cm; and Tabish said 19.27 cm. The correct length was 19.33 cm. How much of error was made by each of the boys?
Solution:
The actual length of an iron rod = 19.33 cm
Measured Ravi = 19.34 cm
Error = Measured value – Actual value
= (19.34-19.33) cm = 0.01 cm
Kamal measured = 19.25 cm
Error = (19.25- 19.33) cm = – 0.08 cm
Tabish measured = 19.27 cm
Error = (19 27 -19.33) cm = – 0.06 cm

Question 85:
When 0.02964 is divided by 0.004, What will be the quotient?
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Question 86:
What number divided by 520 gives the same quotient as 85 divided by 0.625 ?
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Question 87:
A floor is 4.5 m long and 3.6 m wide. A 6 cm square tile costs ?Rs. 23.25. What will be the cost to cover the floor with these tiles?
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Question 89:
A flower garden is 22.50 m long. Sheela wants to make a border along one side using bricks that are 0.25 m long. How many bricks will be needed?
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Question 92:
For the celebrating children’s day, students of Class VII bought sweets for Rs. 740.25 and cold drink for Rs. 70. If 35 students contributed equally what amount was contributed by each student?
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Question 93:
The time taken by Rohan in five different races to run a distance of 500 m was 3.20 minutes, 3.37 minutes, 3.29 minutes, 3.17 minutes and 3.32 minutes. Find the average time taken by him in the races.
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Question 96:
In a survey, 200 students were asked what influenced them most to buy their latest CD. The results are shown in the circle graph

(a) How many students said radio influenced them most?
(b) How many students were influenced by radio than by a music video channel?
(c) How many said a friend or relative influenced them or they heard the CD in a shop?
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Question 98:
Anuradha can do a piece of work in 6hours. What part of the work can she do in 1 hour, in 5 hours and in 6 hours?
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Question 103:
Raj travels 360 km on three-fifth of his petrol tank. How far would he travel at the same rate with a full tank of petrol?
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Question 107:
Some pictures (a) to (f) are given below. Tell which of them show:

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Question 108:
Evaluate: (0.3) x (0.3)-(0.2) x (0.2)
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Question 116:
Sports: Reaction time measures, how quickly a runner reacts to the starter pistol? In the 100 m dash at the 2004 Olympic Games, Lauryn Williams had a reaction time of 0.214 second. Her total race time, including reaction time, was 11.03 seconds. How Long did it take her to run the actual distance?
Solution:
Time taken to run the actual distance =Total race time – Reaction time
=(11.03-0.214) s
= 10.816 s

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In questions 119 to 122, replace ‘?’ with appropriate fraction.

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Given sequence is 0.05, 0.5, 5, 50, ?.
We observe that, each number is multiplied by 10 to get next number.
?= 50 x 10 = 500

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What is the error in each of questions 123 to 125 ?

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If the numbers are negative, then the numbers whose absolute value is greater, will be smaller.
Hence, -0.25 is greater than -0.3.
So, the student made the error that (- 0.3)> – (0.25)

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