NCERT Exemplar Solutions
Class 7 - Mathematics

Unit 2: Fractions and Decimals

Rani ate \(\dfrac{2}{7}\) part of a cake while her brother Ravi ate \(\dfrac{4}{5}\) of the remaining. Part of the cake left is ________

The reciprocal of \(\dfrac{3}{7}\) is ________

\(\dfrac{2}{3}\) of \(27\) is ________

\(\dfrac{4}{5}\) of \(45\) is ______

\(4 \times 6\dfrac{1}{3}\) is equal to ______

\(\dfrac{1}{2}\) of \(4\dfrac{2}{7}\) is ______

\(\dfrac{1}{9}\) of \(\dfrac{6}{5}\) is ______

The lowest form of the product \(2\dfrac{3}{7}\times\dfrac{7}{9}\) is ______

\(\dfrac{4}{5}\div4\) is equal to ______

\(\dfrac{2}{5}\) of \(25\) is ______

\(\dfrac{1}{5} \div \dfrac{5}{6} = (\dfrac{1}{5})\, \_\_\_\_\, \dfrac{6}{5}\)

\(3.2 \times 10 =\) ______

\(25.4 \times 1000 =\) ______

\(93.5 \times 100 =\) ______

\(4.7 \div 10 =\) ______

\(4.7 \div 100 =\) ______

\(4.7 \div 1000 =\) ______

The product of two proper fractions is ______ than each of the fractions that are multiplied.

While dividing a fraction by another fraction, we ______ the first fraction by the ______ of the other fraction.

\(8.4 \div\) ______ \(= 2.1\)

\(52.7 \div\) ______ \(= 0.527\)

\(0.5\) _____ \(0.7 = 0.35\)

\(2\) ____ \(\dfrac{5}{3} = \dfrac{10}{3}\)

\(2.001 \div 0.003 =\) __________

The reciprocal of a proper fraction is a proper fraction.

The reciprocal of an improper fraction is an improper fraction.

Product of two fractions =
\(\dfrac{\text{Product of their denominators}}{\text{Product of their numerators}}\)

The product of two improper fractions is less than both the fractions.

A reciprocal of a fraction is obtained by inverting it upside down.

To multiply a decimal number by 1000, we move the decimal point in the number to the right by three places.

To divide a decimal number by 100, we move the decimal point in the number to the left by two places.

1 is the only number which is its own reciprocal.

\(\dfrac{2}{3}\) of 8 is same as \(\dfrac{2}{3}\div8\).

The reciprocal of \(\dfrac{4}{7}\) is \(\dfrac{4}{7}\).

If 5 is added to both the numerator and the denominator of the fraction \(\dfrac{5}{9}\), will the value of the fraction be changed? If so, will the value increase or decrease?

What happens to the value of a fraction if the denominator of the fraction is decreased while numerator is kept unchanged?

Which letter comes \(\dfrac{2}{5}\) of the way among A and J?

If \(\dfrac{2}{3}\) of a number is \(10\), then what is \(1.75\) times that number?

In a class of 40 students, \(\dfrac{1}{5}\) of the total number of students like to eat rice only, \(\dfrac{2}{5}\) of the total number of students like to eat chapati only and the remaining students like to eat both. What fraction of the total number of students like to eat both?

Renu completed \(\dfrac{2}{3}\) part of her home work in 2 hours. How much part of her home work had she completed in \(1\dfrac{1}{4}\) hours?

Reemu read \(\dfrac{1}{5}\)th pages of a book. If she reads further 40 pages, she would have read \(\dfrac{7}{10}\)th pages of the book. How many pages are left to be read?

Write the number in the box \([\;]\) such that \(\dfrac{3}{7}\times[\;]=\dfrac{15}{98}\).

Will the quotient \(7\dfrac{1}{6} \div 3\dfrac{2}{3}\) be a fraction greater than \(1.5\) or less than \(1.5\)? Explain.

Describe two methods to compare \(\dfrac{13}{17}\) and \(0.82\). Which do you think is easier and why?

65. Health: The directions for a pain reliever recommend that an adult of 60 kg and over take 4 tablets every 4 hours as needed, and an adult who weighs between 40 and 50 kg take only \(2\dfrac{1}{2}\) tablets every 4 hours as needed. Each tablet weighs \(\dfrac{4}{25}\) gram.

(a) If a 72 kg adult takes 4 tablets, how many grams of pain reliever is he or she receiving?

(b) How many grams of pain reliever is the recommended dose for an adult weighing 46 kg?

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

How many \(\dfrac{1}{16}\) kg boxes of chocolates can be made with \(1\dfrac{1}{2}\) kg chocolates?

Anvi is making bookmarker like the one shown in Fig. 2.6. How many bookmarker can she make from a 15 m long ribbon?

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.

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

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 18.7 cm?

(b) the radius is 6.45 cm?

What is the cost of 27.5 m of cloth at ₹ 53.50 per metre?

In a hurdle race, Nidhi is over hurdle B and \(\dfrac{2}{6}\) of the way through the race, as shown in Fig. 2.7.

Then, answer the following:

(a) Where will Nidhi be, when she is \(\dfrac{4}{6}\) of the way through the race?

(b) Where will Nidhi be when she is \(\dfrac{5}{6}\) of the way through the race?

(c) Give two fractions to tell what part of the race Nidhi has finished when she is over hurdle C.

Diameter of Earth is 12,756 km. In 1996, a new planet was discovered whose diameter is \(\dfrac{5}{86}\) of the diameter of Earth. Find the diameter of this planet in km.

What is the product of \(\dfrac{5}{129}\) and its reciprocal?

Simplify: \(\dfrac{2\tfrac{1}{2}+\tfrac{1}{5}}{2\tfrac{1}{2}\div\tfrac{1}{5}}\)

Simplify: \(\dfrac{\tfrac{1}{4}+\tfrac{1}{5}}{1-\tfrac{3}{8}\times\tfrac{3}{5}}\)

Divide \(\dfrac{3}{10}\) by \(\dfrac{1}{4}\) of \(\dfrac{3}{5}\).

\(\dfrac{1}{8}\) of a number equals \(\dfrac{2}{5}\div\dfrac{1}{20}\). What is the number?

Heena’s father paid an electric bill of ₹385.70 out of a 500 rupee note. How much change should he have received?

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?

82. Meteorology: See the table and answer:

(a) Order the five years from coldest to warmest.

(b) In 1946, the average temperature varied by −0.03°C. Between which two years should 1946 fall when the years are ordered?

Atomic weights: Helium = 4.0030, Hydrogen = 1.0080, Oxygen = 16.0000. Find the differences:

(a) Oxygen – Hydrogen

(b) Oxygen – Helium

(c) Helium – Hydrogen

Correct length = 19.33 cm. Errors made:

Ravi = 19.34 cm, Kamal = 19.25 cm, Tabish = 19.27 cm.

When 0.02964 is divided by 0.004, what will be the quotient?

What number divided by 520 gives the same quotient as 85 divided by 0.625?

A floor is 4.5 m long and 3.6 m wide. A 6 cm square tile costs ₹23.25. What will be the cost to cover the floor?

Sunita has \(\tfrac{3}{4}\) m cloth, gives \(\tfrac{1}{3}\) to Rehana. How much did Rehana have?

Garden length = 22.50 m. Bricks length = 0.25 m. How many bricks?

6 shirts, each requires \(2\tfrac{1}{4}\,m\) cloth + \(\tfrac{1}{8}\,m\) waste. How much cloth total?

Hall = 820 seats. Ticket sales = 648. One usher said ¾ full, another ⅔. Whose guess is better?

Sweets ₹740.25, drinks ₹70. 35 students share equally. Contribution per student?

Rohan’s race times: 3.20, 3.37, 3.29, 3.17, 3.32 min. Find average.

Sewer line length = 80¼ m. Completed per day = 7.5 m. How many days?

Weight on moon = 1/6 of Earth. If Earth weight = 5⅗ kg, weight on moon?

In a survey of 200 students, fractions shown in circle graph.

(a) Radio?

(b) How many more than Music Video?

(c) Friend/Relative or Heard in Shop?

A milkman filled \(5\tfrac{1}{2}\) L milk. Sold: 3×\(\tfrac{3}{4}\) L, Shadma \(\tfrac{7}{8}\) L, Jassi \(1\tfrac{1}{2}\) L. How much is left?

Anuradha can finish work in 6 h. Part of work in:

(a) 1 h (b) 5 h (c) 6 h

Rehana paints 1 saree in 5 h. Portion in:

(a) 1 h (b) 4\tfrac{3}{5} h (c) 3\tfrac{1}{2} h

Rama has 6\tfrac{1}{4} kg wool. 1 pillow needs 1\tfrac{1}{4} kg. How many pillows?

Shirt needs 2\tfrac{1}{3} m cloth. From 9\tfrac{1}{3} m, how many shirts?

Ravi walks 3\tfrac{1}{3} km/h. Distance 10 km. Time?

Raj travels 360 km on 3/5 tank. How far on full tank?

Kajol has ₹75, which is 3/8 of earning. Find total earning.

17 trees = 1 tonne paper. Forest has 221 trees. (i) Fraction for:

(a) 5 t (b) 10 t

(ii) To save 7/13 forest, paper?

Simplify: \((1÷2/9)+(1÷3 1/5)+(1÷2 2/3)\).

Match diagrams (a)–(f) with expressions.

Evaluate: (0.3×0.3)−(0.2×0.2).

Evaluate: 0.6/0.3+0.16/0.4.

Value of (0.2×0.14 + 0.5×0.91)/(0.1×0.2).

Square & equilateral triangle share side 4/3 cm. Find perimeter of figure.

Carpet=4×6 2/3=26.67 m². Room=3 1/3×5 1/3=17.78 m². Fraction cut?

Photograph length=14 2/5, breadth=10 2/5, border=2 3/5. Find area.

Burger=₹20¾, Macpuff=₹15½. Cost for 4 burgers, 14 macpuffs?

Hill=101 1/3 m. 1/4 under water. Visible?

Runner total time=11.03 s. Reaction=0.214 s. Actual run?

Mark whether answer is greater or less than 1.

Smallest container height=7/25 x=10.5 cm. Find largest (x).

Replace ? with appropriate fraction.

Replace ? with appropriate fraction.

Replace ? in diagram.

Replace ? in diagram.

A student compared −1/4 and −0.3 wrongly. Error?

Student multiplied 2 4/7 × 3 1/4 = 6 1/7. Error?

In pattern 1/3+1/4+1/5+..., which term first makes sum >1?