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SCERT Class 7 Maths Chapter 2 Solutions Fractions
Class 7 Maths Chapter 2 Fractions Questions and Answers Kerala State Syllabus
Fractions Class 7 Questions and Answers Kerala Syllabus
Page 24
Do the following problems mentally. Write each as how many times and also as a product.
Question 1.
Each piece of a pumpkin weighs a quarter kilogram. What is the weight of two pieces together? What is the weight of four such pieces? Six pieces?
Answer:
Two times quarter kilogram is half kilogram.
Four times quarter kilogram is one kilogram.
Six times quarter kilogram is one and a half kilogram.
Mathematically,
Each piece of a pumpkin weighs \(\frac{1}{4}\) kilogram.
The weight of two pieces is two times \(\frac{1}{4}\), which is \(\frac{1}{2}\) kilogram.
The weight of four pieces is 4 times \(\frac{1}{4}\) which is 1 kilogram.
The weight of six pieces is 6 times \(\frac{1}{4}\) which is 1\(\frac{1}{2}\) kilogram.
Using products,
The weight of two pieces = 2 × \(\frac{1}{4}=\frac{2}{4}\) = \(\frac{1}{2}\) kilogram
The weight of four pieces= 4 × \(\frac{1}{4}=\frac{4}{4}\) = 1 kilogram
The weight of six pieces = 6 × \(\frac{1}{4}\) = 1\(\frac{1}{2}\) kilogram.
Question 2.
We can fill a cup with one-third of a litre of milk. How much milk is needed to fill two cups? Four cups?
Answer:
Two times one-third of a litre is two-third of a litre.
Four times one-third of a litre is four-third of a litre. Mathematically,
Each cup contains one-third of a litre of milk.
So, milk needed to fill two cups is 2 times \(\frac{1}{3}\) which is \(\frac{2}{3}\) litre.
Milk needed to fill four cups is 4 times \(\frac{1}{3}\), which is 1\(\frac{1}{3}\) litre.
Using products,
Milk needed to fill two cups = 2 × \(\frac{1}{3}=\frac{2}{3}\) litre
Milk needed to fill four cups = 4 × \(\frac{1}{3}\) = 1\(\frac{1}{3}\) litre.
Question 3.
What is the total length of four pieces of ribbons, each of length three fourths of a metre? What about five pieces?
Answer:
Four times three fourth of a metre is three metre.
Five times three fourth of a metre is three and three-fourth of a metre.
Mathematically,
Length of each piece is three-fourth of a metre.
So, total length of four pieces of ribbon is 4 times \(\frac{3}{4}\), which is 3 metre.
Total length of five pieces of ribbon is 5 times \(\frac{3}{4}\), which is 3\(\frac{3}{4}\) metre.
Using products,
Total length of four pieces of ribbon = 4 × \(\frac{3}{4}\) = 3 metre
Total length of five pieces of ribbon = 5 × \(\frac{1}{2}\) = 3\(\frac{3}{4}\) metre
Question 4.
It takes hour to walk around a play ground once.
(i) How much time does it take to walk 4 times around at this speed?
(ii) What about 7 times?
Answer:
(i) 4 times \(\frac{1}{4}\) is 1 hour.
Using products,
Time taken to walk 4 time around = 4 × \(\frac{1}{4}\) = 1 hour
(ii) 7 times \(\frac{1}{4}\) is 1\(\frac{3}{4}\) hour.
Using products,
Time taken to walk 7 times around = 7 × \(\frac{1}{4}\) = 1\(\frac{3}{4}\)hour.
Page – 25,26
Question 1.
The weight of an iron block is kilogram.
(i) What is the total weight of such 15 blocks?
(ii) 16 blocks?
Answer:
(i) Weight of one block = \(\frac{1}{4}\) kilogram.
Weight of 15 blocks = 15 × \(\frac{1}{4}=\frac{15 \times 1}{4}\)
= \(\frac{15}{4}=\frac{12+3}{4}\)
= \(\frac{12}{4}+\frac{3}{4}\)
= 3\(\frac{3}{4}\)
(ii) Weight of 16 blocks = 16 × \(\frac{1}{4}=\frac{16}{4}\) = 4 kilogram.
Question 2.
Some 2 metre long rods are cut into 5 pieces of equal length.
(i) What is the length of each piece?
(ii) What is the total length of 4 pieces?
(iii) of 10 pieces?
Answer:
(i) Total length of the rod = 2 metre.
Length of each piece = \(\frac{2}{5}\) metre
(ii) Total length of 4 pieces = 4 × \(\frac{2}{5}=\frac{4 \times 2}{5}=\frac{8}{5}\)
= \(\frac{5+3}{5}=\frac{5}{5}+\frac{3}{5}\)
= 1\(\frac{1}{5}\) metre
Question 3.
5 litres of milk is filled in 6 bottles of the same size.
(i) How many litres of milk does each bottle hold?
(ii) How many litres in 3 bottles together?
(iii) In 4 bottles?
Answer:
Total milk = 5 litre
Number of bottles = 6
(i) Milk in each bottle = \(\frac{5}{6}\) litre
(ii) Milk in 3 bottles together = 3 × \(\frac{5}{6}=\frac{3 \times 5}{6}=\frac{15}{6}\)
= \(\frac{12+3}{6}=\frac{12}{6}+\frac{3}{6}\)
= 2\(\frac{1}{2}\) litre.
(iii) Milk in 4 bottles = 4 × \(\frac{5}{6}=\frac{4 \times 5}{6}=\frac{20}{6}\)
= \(\frac{18+2}{6}=\frac{18}{6}+\frac{2}{6}\)
= 3\(\frac{1}{3}\) litre
Page – 28
Do these problems in head. Then write each as a part and also as a product of numbers.
Question 1.
Nine litres of milk is divided equally among three children. How many litres will each get? What if there are four children?
Answer:
Each will get a third of nine litres, that is three litres.
As a part,
Each will get \(\frac{1}{3}\) of 9, which is 3 litres.
As a product,
Each will get \(\frac{1}{3}\) × 9 = \(\frac{9}{3}\) = 3 litres.
If there are four children,
Each will get a fourth of nine litres. A fourth of 8 litre is 2 litre and then a fourth of the remaining one litre. So, two and one-fourth of a litre.
As a part,
Each will get \(\frac{1}{4}\) of 9, which is 2\(\frac{1}{4}\) litres.
As a product,
Each will get \(\frac{1}{4}\) × 9 = \(\frac{9}{4}\) = 2\(\frac{1}{4}\) litres.
Question 2.
Six kilograms of rice was packed in five bags of the same size. How many kilograms of rice in each bag? What if it is packed in four bags?
Answer:
Each bag has one fifth of six kilograms. One fifth of 5 kilogram is 1 kilogram and then one fifth of remaining one kilogram. So, one and one-fifth of a kilogram.
As a part,
Each bag has \(\frac{1}{5}\) of 6, which is 1\(\frac{1}{5}\) kilograms.
As a product,
Each bag has \(\frac{1}{4}\) × 6 = \(\frac{6}{5}\) = 1\(\frac{1}{5}\) kilograms.
If it is packed in four bags,
Each bag has one-fourth of six kilograms. One-fourth of four kilograms is 1 kilogram and then one- fourth of remaining two kilograms. So, one and a half kilograms.
As a part,
Each bag has \(\frac{1}{4}\) of 6, which is 1\(\frac{1}{2}\) kilograms.
As a product,
Each bag has \(\frac{1}{4}\) × 6 = \(\frac{6}{4}\) = 1\(\frac{1}{2}\) kilograms.
Question 3.
A seven metre long string is divided into six equal pieces. What is the length of each piece? What if it is divided into three equal pieces?
Answer:
Each piece is one-sixth of seven metres. One-sixth of six metres is 1 metre and then one-sixth of the remaining one metre. So, one and one-sixth of a metre.
As a part,
Length of each piece is \(\frac{1}{6}\) of 7, which is 1\(\frac{1}{6}\) metres.
As a product,
Length of each piece = \(\frac{1}{6}\) × 7 = \(\frac{7}{6}\) = 1 \(\frac{1}{6}\) metres.
If it is divided into three equal pieces,
Each piece is one-third of seven metres. One-third of six metres is 2 metres and one-third of remaining one metre. So, two and one-third of a metre.
As a part,
Length of each piece is \(\frac{1}{3}\) of 7, which is 2\(\frac{1}{3}\) metres.
As a product,
Length of each piece \(\frac{1}{3}\) × 7 = \(\frac{7}{3}\) = 2\(\frac{1}{3}\) metres.
The calculations of the types of problems above can be done as follows:
Question 4.
We have to cut off \(\frac{3}{5}\) of a 7 metre long string. How long is this piece?
Answer:
Here we have to calculate \(\frac{3}{5}\) of 7.
\(\frac{3}{5}\) x 7 = \(\frac{3 \times 7}{5}=\frac{21}{5}=\frac{20+1}{5}\)
\(\frac{20}{5}+\frac{1}{5}\) = 4 + \(\frac{1}{5}\)
= 4\(\frac{1}{5}\)
So, we need to cut off 4\(\frac{1}{5}\) metres.
Page – 29
Question 1.
There are 35 children in a class. of them are girls. How many girls are there in the class?
Answer:
Number of girls = \(\frac{3}{5}\) × 35
= 3 × \(\frac{35}{5}\)
= 3 × 7
= 21
Or,
Number of girls = \(\frac{3}{5}\) × 35
= \(\frac{3 \times 35}{5}\)
= \(\frac{105}{5}\)
= 21
Question 2.
10 kilograms of rice is filled equally in 8 bags. If the rice in 3 such bags are taken together, how many kilograms would that be?
Answer:
Rice in 3 bags are taken together.
That is, we have to find- of 10 kilograms.
So, amount of rice = \(\frac{3}{8}\) × 10
= \(\frac{30}{8}=\frac{24+6}{8}\)
= \(\frac{24}{8}+\frac{6}{8}\)
= 3\(\frac{3}{4}\) kilograms.
Question 3.
The area of the rectangle in the figure is 27 square centimetres. It is divided into 9 equal parts.
What is the area of the darker part in square centimetres?
Answer:
5 of the 9 equal parts are darker.
So, we have to find \(\frac{5}{9}\) of 27 square centimetres.
Area of darker part = \(\frac{5}{9}\) × 27 = 5 × \(\frac{27}{9}\)
= 5 × 3 = 15 square centimeres.
Area of darker part = \(\frac{5}{9}\) × 27 = \(\frac{5 \times 27}{9}=\frac{135}{9}\)
= 15 square centimetres.
Page – 32
Question 1.
Draw rectangles and find these products.
(i) \(\frac{1}{2} \times \frac{1}{4}\)
(ii) \(\frac{1}{3} \times \frac{1}{6}\)
(iii) \(\frac{1}{5} \times \frac{1}{8}\)
Answer:
(i) \(\frac{1}{2} \times \frac{1}{4}\)
Draw a rectangle a divide it into 4 equal parts. Then divide one part into half.
Now extend the horizontal line.
So, \(\frac{1}{2} \times \frac{1}{4}\) = \(\frac{1}{8}\)
(ii) \(\frac{1}{3} \times \frac{1}{6}\)
Draw a rectangle and divide it into 6 equal parts. Then divide each part into 3 equal parts.
Now extend the horizontal line.
So, \(\frac{1}{3} \times \frac{1}{6}=\frac{1}{18}\)
(iii) \(\frac{1}{5} \times \frac{1}{8}\)
Draw a rectangle a divide it into 8 equal parts. Then divide one part into 5 equal parts.
Now extend the horizontal line.
So, \(\frac{1}{5} \times \frac{1}{8}=\frac{1}{40}\)
Question 2.
A one metre long string is divided into five equal parts. How long is half of each part in metres? In centimetres?
Answer:
When one metre long string divided into five equal parts each part is one- fifth of one metre.
Now half of each part is \(\frac{1}{2}\) of \(\frac{1}{5}\)of one metre.
∴ Length of each part = \(\frac{1}{2} \times \frac{1}{5}\) = \(\frac{1}{10}\) metre
= \(\frac{1}{10}\) × 100
= 10 centimetre.
Question 3.
One litre of milk is filled in two bottles of equal size. A quarter of the milk in one bottle was used to make tea. How many litres of milk were used for tea? In millilitres?
Answer:
When one litre of milk is filled in two bottles of equal size, each bottle contain half of a litre.
A quarter of the milk in one bottle was used to make tea, which is of of one litre.
Milk used for tea \(\frac{1}{4}\) of \(\frac{1}{2}\) one litre
= \(\frac{1}{4} \times \frac{1}{2}=\frac{1}{8}\) litre
= \(\frac{1}{8}\) × 1000 = 125 millilitre.
Consider another type of problem:
Find of \(\frac{4}{5}\) of \(\frac{2}{3}\).
Answer:
Page – 34
Question 1.
A rope 2 metres long is cut into 5 equal pieces. What is the length of three quarters of one of the pieces in metres? In centimetres?
Answer:
When 2 metre long rope cut into 5 equal pieces, length of each piece is \(\frac{1}{5}\) of 2 metre, which is \(\frac{2}{5}\) metre.
Length of three quarters of one of the pieces is \(\frac{3}{4}\) of \(\frac{2}{5}\)
Required length of the piece = \(\frac{3}{4} \times \frac{2}{5}\)
= 3 × \(\frac{1}{4} \times \frac{1}{5}\) × 2
= 3 × \(\frac{1}{20}\) × 2
= \(\frac{6}{20}=\frac{3}{10}\)
Question 2.
4 bottles of the same size were filled with 3 litres of water. One of these was used to fill 5 cups of the same size. How much water is there in one such cup, in litres? And in millilitres?
Answer:
When 4 bottles of the same size were filled with 3 litres of water, each bottle has of 3 litre, which is \(\frac{3}{4}\) litre.
One of these was used to fill 5 cups of the same size. Then, amount of water in one cup is \(\frac{1}{5}\) of \(\frac{3}{4}\).
Amount of water in one cup = \(\frac{1}{5} \times \frac{3}{4}\)
= \(\frac{1}{5} \times \frac{1}{4}\) × 3
= \(\frac{1}{20}\) × 3
= \(\frac{3}{20}\)
Question 3.
A watermelon weighing four kilograms was cut into five equal pieces. One piece was again halved. What is the weight of each of these two pieces in kilograms? And in grams?
Answer:
When watermelon weighing 4 kg cut into five equal pieces, weight of each piece is \(\frac{1}{5}\) of 4 kg, which is \(\frac{4}{5}\)kg.
Each piece is again halved.
Then weight of each of these two pieces is \(\frac{1}{2}\) of \(\frac{4}{5}\)
Required weight = \(=\frac{1}{2} \times \frac{4}{5}\)
= \(=\frac{1}{2} \times \frac{1}{5}\) × 4
= \(\frac{1}{10}\) × 4
= \(\frac{4}{10}=\frac{2}{5}\) kilograms
Question 4.
A vessel full of milk is used to fill three bottles of the same size. Then the milk in each bottle was used to fill four cups of the same size. What fraction of the milk in the first vessel does each cup contain?
Answer:
When a vessel full of milk used to fill three bottles of same size, each bottle has one-third of milk.
When milk in each bottle was used to fill four cups of same size, each cup has \(\frac{1}{4}\) of \(\frac{1}{3}\) of the milk.
∴ fraction of milk in each cup = \(\frac{1}{4} \times \frac{1}{3}=\frac{1}{12}\)
Question 5.
Draw a line AB of length 12 centimetres. Mark AC as \(\frac{2}{3}\) of AB. Mark AD as \(\frac{1}{4}\) of AC. What part of AB is AD?
Answer:
AD = \(\frac{1}{4}\) of AC
= \(\frac{1}{4}\) of \(\frac{2}{3}\) of AB
= \(\frac{1}{4} \times \frac{2}{3}\) of AB
= \(\frac{1}{4} \times \frac{1}{3}\) × 2 of AB
= \(\frac{1}{12}\) × 2 of AB
= \(\frac{2}{12}=\frac{1}{6}\) of AB
Question 6.
Calculate the following using multiplication:
(i) \(\frac{3}{7}\) of \(\frac{2}{5}\)
Answer:
\(\frac{3}{7}\) of \(\frac{2}{5}\) = \(\frac{3}{7} \times \frac{2}{5}\)
= 3 × \(\frac{1}{7} \times \frac{1}{5}\) × 2
= 3 × \(\frac{1}{35}\) × 2
= \(\frac{6}{35}\)
(ii) \(\frac{2}{3}\) of \(\frac{3}{4}\)
Answer:
\(\frac{2}{3}\) of \(\frac{3}{4}\) = \(\frac{2}{3} \times \frac{3}{4}\)
= 2 × \(\frac{1}{3} \times \frac{1}{4}\) × 3
= 2 × \(\frac{1}{12}\) × 3
= 6 × \(\frac{1}{12}=\frac{6}{12}=\frac{1}{2}\)
(iii) \(\frac{3}{5}\) of \(\frac{2}{7}\)
Answer:
\(\frac{3}{5}\) of \(\frac{2}{7}\) = \(\frac{3}{5} \times \frac{2}{7}\)
= 3 × \(\frac{1}{5} \times \frac{1}{7}\) × 2
= 3 × \(\frac{1}{35}\) × 2
= \(\frac{6}{35}\)
(iv) \(\frac{5}{6}\) of \(\frac{3}{10}\)
Answer:
\(\frac{5}{6}\) of \(\frac{3}{10}\) = \(\frac{5}{6} \times \frac{3}{10}\)
= 5 × \(\frac{1}{6} \times \frac{1}{10}\) × 3
= 5 × \(\frac{1}{60}\) × 3
= 15 × \(\frac{1}{60}=\frac{15}{60}=\frac{1}{4}\)
Page – 37
Question 1.
One and a half metres of cloth is needed for a shirt. How much cloth is required for five such shirts?
Answer:
Cloth needed for a shirt = 1 metres
Cloth needed for 5 shirts = 5 × 1\(\frac{1}{2}\)
= 5 × (1 + \(\frac{1}{2}\))
= (5 × 1) + (5 × \(\frac{1}{2}\))
= 5 + 2\(\frac{1}{2}\)
= 7\(\frac{1}{2}\) metres.
Or,
5 × 1\(\frac{1}{2}\) = 5 × \(\frac{3}{2}\)
= \(\frac{15}{2}\) = 7\(\frac{1}{2}\)
Question 2.
The price of one kilogram of okra is thirty rupees. What is the price of two and a half kilograms?
Answer:
Price of one kilogram of okra = 30 rupees
Price of two and a half kilograms of okra = 30 × 2\(\frac{1}{2}\)
= 30 × (2 + \(\frac{1}{2}\))
= (30 × 2) + (30 × \(\frac{1}{2}\))
= 60 + 15
= 75 rupees
Or,
30 × 2\(\frac{1}{2}\) = 30 × \(\frac{5}{2}\)
= \(\frac{30}{2}\) × 5
= 15 × 575 rupees
Question 3.
A person walks two and a half kilometres in an hour. At the same speed, how far will he walk in one and a half hours?
Answer:
Distance he walks in one hour = 2 \(\frac{1}{2}\) km
Distance he walks in one and a half hours = 1 \(\frac{1}{2}\) x 2\(\frac{1}{2}\)
= \(\frac{3}{2} \times \frac{5}{2}\)
= \(\frac{3 \times 5}{2 \times 2}=\frac{15}{4}\)
= 3 \(\frac{3}{4}\) km
Question 4.
Roni has 36 stamps with her. Sahira says she has 2 times this. How many stamps does Sahira have?
Answer:
Number of stamps with Roni = 36
Number of stamps with Sahira = 2\(\frac{1}{2}\) × 36
= (2 + \(\frac{1}{2}\)) × 36
= (2 × 36) +(\(\frac{1}{2}\) × 36)
= 72 + 18
= 90
Or
2\(\frac{1}{2}\) × 36 = \(\frac{5}{2}\) × 36
= 5 × \(\frac{36}{2}\)
= 5 × 18
= 90
Question 5.
Joji works 4\(\frac{1}{2}\) hours each day. How many hours does he work in 6 days?
Answer:
Number of hours Joji works each day = 4 hours
Number of hours Joji work in 6 days = 6 × 4\(\frac{1}{2}\)
= 6 × (4 + \(\frac{1}{2}\))
= (6 × 4) + (6 × \(\frac{1}{2}\))
= 24 + 3
= 27 hours
Question 6.
Calculate the following:
(i) 4 times 5\(\frac{1}{3}\)
Answer:
4 times 5\(\frac{1}{3}\) = 4 × 5\(\frac{1}{3}\)
= 4 × (5 + \(\frac{1}{3}\))
= (4 × 5) + (4 × \(\frac{1}{3}\))
= 20 + 1\(\frac{1}{3}\)
= 21 \(\frac{1}{3}\)
(ii) 4\(\frac{1}{3}\) times 5
Answer:
4\(\frac{1}{3}\) times 5 = 4\(\frac{1}{3}\) × 5
= (4 + \(\frac{1}{3}\)) × 5
= (4 × 5) + (\(\frac{1}{3}\) × 5)
= 20 + 1\(\frac{2}{3}\)
= 21\(\frac{2}{3}\)
(iii) 1\(\frac{1}{2}\) times \(\frac{2}{3}\)
Answer:
1\(\frac{1}{2}\) times \(\frac{2}{3}\) = 1\(\frac{1}{2}\) × \(\frac{2}{3}\)
= \(\frac{3}{2} \times \frac{2}{3}\)
= \(\frac{3 \times 2}{2 \times 3}\)
= 1
(iv) \(\frac{2}{5}\) times 2\(\frac{1}{2}\)
Answer:
\(\frac{2}{5}\) times 2\(\frac{1}{2}\) = \(\frac{2}{5}\) × 2\(\frac{1}{2}\)
= \(\frac{3}{2} \times \frac{2}{3}\)
= \(\frac{3 \times 2}{2 \times 3}\)
= 1
(v) 2\(\frac{1}{2}\) times 5\(\frac{1}{2}\)
Answer:
2\(\frac{1}{2}\) times 5\(\frac{1}{2}\) = 2\(\frac{1}{2}\) × 5\(\frac{1}{2}\)
= \(\frac{5}{2} \times \frac{11}{2}\)
= \(\frac{5 \times 11}{2 \times 2}\)
= \(\frac{55}{4}\)
= 13 \(\frac{3}{4}\)
Page – 42
Question 1.
The length and breadth of some rectangles are given below. Find the area of each:
(i) 3\(\frac{1}{4}\) centimetres, 4\(\frac{1}{2}\) centimetres
Answer:
3\(\frac{1}{4}\) centimetres, 4\(\frac{1}{2}\) centimetres
Area of the rectangle = 3\(\frac{1}{4}\) × 4\(\frac{1}{2}\)
= \(\frac{13}{4} \times \frac{9}{2}\)
= \(\frac{13 \times 9}{4 \times 2}\)
= \(\frac{117}{8}\)
= 14\(\frac{5}{8}\) square centimetres
(ii) 5\(\frac{1}{3}\) metres, 6\(\frac{3}{4}\) metres
Answer:
5\(\frac{1}{3}\) metres, 6\(\frac{3}{4}\) metres
Area of the rectangle = 5\(\frac{1}{3}\) × 6\(\frac{3}{4}\)
= \(\frac{16}{3} \times \frac{27}{4}\)
= \(\frac{16}{4} \times \frac{27}{3}\)
= 4 × 3 = 12
Question 2.
What is the area of a square of side 1 metres?
Answer:
Area of the square = 1\(\frac{1}{2}\) × 1\(\frac{1}{2}\)
= \(\frac{3}{2} \times \frac{3}{2}\)
= \(\frac{3 \times 3}{2 \times 2}\)
= \(\frac{9}{4}\)
= 2\(\frac{1}{4}\) square metre
Question 3.
The perimeter of a square is 14 metres. What is its area?
Answer:
Perimeter of the square = 14 metres
4 × side = 14
∴ Side = \(\frac{14}{4}\)= 3\(\frac{1}{2}\) metre
Area = 3\(\frac{1}{2}\) × 3\(\frac{1}{2}\)
= \(\frac{7}{2} \times \frac{7}{2}\)
= \(\frac{7 \times 7}{2 \times 2}\)
= \(\frac{49}{4}\)
= 12\(\frac{1}{4}\) square metres
Intext Questions and Answers
Question 1.
A bottle holds a quarter litre of water. How much water is needed to fill three such bottles?
Answer:
Each bottle holds a quarter litre of water. So, water needed to fill three such bottles is three times a quarter litre, which is three-quarter litres.
This can be calculated as,
3 times \(\frac{1}{4}\) is \(\frac{3}{4}\) is \(\frac{3}{4}\)
As a product,
3 × \(\frac{1}{4}=\frac{3}{4}\)
Question 2.
The calculations in the type of problems above can be done easily as follows:
\(\frac{3}{4}\) litres of milk in a bottle; how many litres in 7 such bottles?
Answer:
Amount of milk in one bottle = \(\frac{3}{4}\) litres
Amount of milk in 7 such bottles = 7 times \(\frac{3}{4}\)
7 × \(\frac{3}{4}=\frac{7 \times 3}{4}=\frac{21}{4}\)
Split 21 as a multiple of 4.
\(\frac{21}{4}=\frac{20+1}{4}=\frac{20}{4}+\frac{1}{4}\)
= 5 + \(\frac{1}{4}\)
= 5\(\frac{1}{4}\)
Question 3.
A five metre long string is cut into three equal pieces. What is the length of each piece?
Answer:
3 metres cut into three equal pieces, each piece is 1 metre. The remaining 2 metre cut into three equal pieces, each piece must be two-third of a metre. So, the length of each piece is 1 metres.
In terms of number alone,
\(\frac{1}{3}\) of 5 is 1\(\frac{2}{3}\)
Writing it as a product,
\(\frac{1}{3}\) × 5 = \(\frac{5}{3}\) = 1\(\frac{2}{3}\)
Question 4.
Draw rectangle and find \(\frac{1}{3} \times \frac{1}{2}\)
Answer:
First, draw a rectangle and divide it into two equal part. Then each part is \(\frac{1}{2}\)
Then divide one part into three equal parts. Here, each part is \(\frac{1}{3} \times \frac{1}{2}\)
Now extend the horizontal line.
The rectangle is divided into 6 equal parts and so each part is
Hence, \(\frac{1}{3} \times \frac{1}{2}\) = \(\frac{1}{6}\)
Question 5.
Find 3 × 2\(\frac{1}{4}\)
Answer:
3 × 2\(\frac{1}{4}\) = 3 × (2 + \(\frac{1}{4}\))
= (3 × 2) + (3 × \(\frac{1}{4}\))
= 6 + \(\frac{3}{4}\)
= 6\(\frac{3}{4}\)
Another way,
3 × 2\(\frac{1}{4}\) = 3 × \(\frac{9}{4}\)
= \(\frac{27}{4}\)
= 6\(\frac{3}{4}\)
Consider another problem.
Question 6.
Find 3\(\frac{1}{2}\) × 2\(\frac{1}{4}\)
Answer:
3\(\frac{1}{2}\) × 2\(\frac{1}{4}\)
= \(\frac{7}{2} \times \frac{9}{4}\)
= \(\frac{7 \times 9}{2 \times 4}\)
= \(\frac{63}{8}=\frac{56+7}{8}=\frac{56}{8}+\frac{7}{8}\)
= 7\(\frac{7}{8}\)
Question 7.
Find the area of the rectangle having length 5\(\frac{1}{2}\) cm and breadth 3\(\frac{1}{3}\) cm.
Answer:
Now, divide the length 5\(\frac{1}{2}\) cm into 11 equal parts of length \(\frac{1}{2}\) cm.
Divide the breadth 3\(\frac{1}{3}\) cm into 10 equal parts of length \(\frac{1}{3}\) cm.
So, 11 × 10 = 110 rectangles in all, each of area \(\frac{1}{6}\) square centimetres.
∴ Area of rectangle = 110 × \(\frac{1}{6}\) = 18\(\frac{1}{3}\)
Now, 5\(\frac{1}{2}\) × 3\(\frac{1}{3}\)
= \(\frac{11}{2} \times \frac{10}{3}\)
= 11 × \(\frac{1}{2}\) × 10 × \(\frac{1}{3}\)
= 110 × \(\frac{1}{6}\)
= 18\(\frac{1}{3}\)
So, even if the lengths are in fractions, the area of a rectangle is still the product of the lengths of sides.
Class 7 Maths Chapter 2 Kerala Syllabus Fractions Questions and Answers
Question 1.
Calculate the following:
(i) \(\frac{2}{3}\) of 16
Answer:
\(\frac{2}{3}\) of 16
= \(\frac{2}{3}\) × 16
= \(\frac{2 \times 16}{3}=\frac{32}{3}\)
= 10\(\frac{2}{3}\)
(ii) \(\frac{4}{7}\) of 25
Answer:
\(\frac{4}{7}\) of 25
= \(\frac{4}{7}\) × 25
= \(\frac{4 \times 25}{7}=\frac{100}{7}\)
= 14\(\frac{2}{3}\)
(iii) \(\frac{2}{7}\) of \(\frac{1}{4}\)
Answer:
\(\frac{2}{7}\) of \(\frac{1}{4}\)
= \(\frac{2}{7}\) × \(\frac{1}{4}\)
= \(\frac{2}{7} \times \frac{1}{4}\)
= \(\frac{2 \times 1}{7 \times 4}=\frac{2}{28}\)
= \(\frac{1}{14}\)
(iv) 1\(\frac{1}{2}\) × 6\(\frac{2}{3}\)
Answer:
1\(\frac{1}{2}\) × 6\(\frac{2}{3}\)
= \(\frac{3}{2} \times \frac{20}{3}=\frac{3 \times 20}{2 \times 3}\)
= \(\frac{60}{6}\)
= 10
(v) 2\(\frac{3}{4}\) × \(\frac{5}{8}\)
Answer:
2\(\frac{3}{4}\) × \(\frac{5}{8}\)
= \(\frac{11}{4} \times \frac{5}{8}\)
= \(\frac{11 \times 5}{4 \times 8}=\frac{55}{32}\)
= 1\(\frac{23}{32}\)
(vi) \(\frac{4}{7}\) of \(\frac{3}{5}\)
Answer:
\(\frac{4}{7}\) of \(\frac{3}{5}\)
= \(\frac{4}{7}\) × \(\frac{3}{5}\)
= \(\frac{4 \times 3}{7 \times 5}\)
= \(\frac{12}{35}\)
Question 2.
12 metre long rope cut into 4 equal pieces.
(i) What is the length of each piece?
(ii) What if it is cut into 5 equal pieces?
Answer:
(i) Length of each piece = \(\frac{12}{4}\) = 3 metres
(ii) If it is cut into 5 equal pieces,
Length of each piece = \(\frac{12}{5}\) = 2\(\frac{2}{5}\) metres
Question 3.
Each piece of rope is \(\frac{7}{4}\) metres long. What is the total length of 8 such pieces?
Answer:
Lenth of each piece = \(\frac{7}{4}\) metres
Length of 8 pieces = \(\frac{7}{4}\) × 8 = 7 × \(\frac{8}{4}\)
= 7 × 2
= 14 metres
Question 4.
If 4 strings of length \(\frac{1}{3}\) metre were laid end to end, what would be the total length?
Answer:
Total length = \(\frac{1}{3}\) × 4 = \(\frac{4}{3}\)
= 1\(\frac{1}{3}\) metres
Question 5.
Suhara has 1 metre long silk ribbon. She gave half of it to Soumya. She in turn gave half of this to Reena. What is the length of the piece Reena got?
Answer:
Length of the piece Reena got = \(\frac{1}{2}\) of \(\frac{1}{2}\) of 1 metre
= \(\frac{1}{2}\) × \(\frac{1}{2}\)
= \(\frac{1}{4}\) metre
Question 6.
Half the children in a class are girls. A third of them are in the Math Club. What fraction of the total children are they?
Answer:
Number of girls in Math club = \(\frac{1}{3}\) of \(\frac{1}{2}\) of total children
= \(\frac{1}{3} \times \frac{1}{2}\) of total children
= \(\frac{1}{6}\) of total children
Question 7.
The length and breadth of some rectangles are given below. Calculate their areas.
(i) 4\(\frac{1}{2}\) cm, 3\(\frac{1}{4}\) cm
Answer:
Area = 4\(\frac{1}{2}\) × 3\(\frac{1}{4}\)
= \(\frac{9}{2} \times \frac{13}{4}=\frac{9 \times 13}{2 \times 4}\)
= \(\frac{117}{8}\)
= 14\(\frac{5}{8}\) cm²
(ii) 6\(\frac{3}{4}\) cm, 5\(\frac{1}{3}\) cm
Answer:
Area = 6\(\frac{3}{4}\) × 5\(\frac{1}{3}\)
= \(\frac{27}{4} \times \frac{16}{3}\)
= \(\frac{27}{3} \times \frac{16}{4}\)
= 9 × 4
= 36 cm²
Question 8.
What is the area of a square of side 1 metre?
Answer:
Area 1\(\frac{1}{2}\) x 1\(\frac{1}{2}\)
= \(\frac{3}{2} \times \frac{3}{2}\)
= \(\frac{9}{4}\)
= 2\(\frac{1}{4}\) m²
Practice Questions
Question 1.
Each bottle has \(\frac{3}{4}\) litres of water. What is the quantity of water in 14 such bottles?
Answer:
\(\frac{21}{2}\) = 10\(\frac{1}{2}\) litres
Question 2.
A farmer plants the sapling of a plant at a uniform distance of cm. If he plants 27 such saplings in a row, find the total distance between the first and the last sapling.
Answer:
45 cm
Question 3.
In a class of 60 students, two-thirds are boys. How many girls are there in the class?
Answer:
20
Question 4.
The weight of an iron block is \(\frac{3}{4}\) kilogram. What is the total weight of such 17 blocks?
Answer:
\(\frac{51}{4}\) = 12\(\frac{3}{4}\) kilogram
Question 5.
There are some cans, each containing 3 litres of milk. The milk in each vessel is used to fill 5 identical bottles.
(i) How much milk is there in each bottle?
Answer:
\(\frac{3}{5}\) litres
(ii) How much milk in 3 such bottles?
Answer:
\(\frac{9}{5}\) = 1 \(\frac{4}{5}\) litres
(iii) In 10 bottles?
Answer:
6 litres
Question 6.
Calculate the following:
(i) \(\frac{1}{8} \times \frac{1}{5}\)
Answer:
\(\frac{1}{40}\)
(ii) \(\frac{1}{6} \times \frac{1}{7}\)
Answer:
\(\frac{1}{42}\)
(iii) \(\frac{2}{5} \times \frac{7}{9}\)
Answer:
\(\frac{14}{45}\)
(iv) \(\frac{4}{5}\) of \(\frac{2}{3}\)
Answer:
\(\frac{8}{15}\)
(v) \(\frac{2}{9}\) of \(\frac{3}{2}\)
Answer:
\(\frac{1}{3}\)
(vi) 1\(\frac{3}{4}\) of 4
Answer:
7
(vii) \(\frac{3}{8}\) of 2\(\frac{1}{2}\)
Answer:
\(\frac{15}{16}\)
(viii) 3\(\frac{1}{4}\) × 5\(\frac{2}{9}\)
Answer:
\(\frac{611}{36}\)
(ix) 4\(\frac{1}{7}\) × 3\(\frac{1}{8}\)
Answer:
\(\frac{725}{56}\)
Question 7.
If three litres of milk is equally divided among four persons, how much would each get?
Answer:
\(\frac{3}{4}\) litres
Question 8.
Six kilogram of rice is packed into four identical bags.
(i) How much rice is in each bag?
Answer:
\(\frac{3}{2}\) Kilograms
(ii) What if it is packed into two bags?
Answer:
3 Kilograms
Class 7 Maths Chapter 2 Notes Kerala Syllabus Fractions
Fractions are a way to represent parts of a whole. A fraction consists of a numerator and a denominator. The numerator is the number written above the fraction line, which tells how many equal parts you consider, and the denominator is the number written below the fraction line, which tells the total number of equal parts the whole thing has been cut into.
Multifold multiplication
If we have to find 4 times three-quarter, we calculate it in following way:
\(\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}\) = 3
This can be easily calculated as:
4 × \(\frac{3}{4}=\frac{12}{4}\) = 3
Part and multiplication
If three litres of milk divided among four people, each will get \(\frac{1}{4}\) of 3 litres.
i.e, \(\frac{1}{4}\) of 3 = \(\frac{1}{4}\) × 3 = \(\frac{3}{4}\) litres.
Part of part
If we have to calculate \(\frac{1}{5}\) of \(\frac{1}{4}\), it can be done as as follows:
\(\frac{1}{5} \times \frac{1}{4}=\frac{1}{5 \times 4}=\frac{1}{20}\)
Now, if have to calculate \(\frac{3}{5}\) of \(\frac{2}{7}\),
\(\frac{3}{5} \times \frac{2}{7}=3 \times \frac{1}{5} \times \frac{1}{7} \times 2=\frac{3 \times 2}{5 \times 7}=\frac{6}{35}\)
To calculate 2\(\frac{1}{4}\) × 5,
2\(\frac{1}{4}\) × 5 = (2 + \(\frac{1}{4}\)) × 5
= (2 × 5) + (\(\frac{1}{4}\) × 5)
= 10 + 1\(\frac{1}{4}\)
= 11\(\frac{1}{4}\)
To calculate 1\(\frac{1}{2}\) × 3\(\frac{3}{4}\)
1\(\frac{1}{2}\) × 3\(\frac{3}{4}\) = \(\frac{3}{2} \times \frac{15}{4}\)
= \(\frac{3 \times 15}{2 \times 4}\)
= \(\frac{45}{8}=\frac{40+5}{8}=\frac{40}{8}+\frac{5}{8}\)
= 5 \(\frac{5}{8}\)
Even if the lengths are in fractions, the area of a rectangle is still the product of the lengths of sides.
Share And Fraction
If 4 litres of milk is divided equally among 3 persons, how much milk will each one get? First give 1 litre to each one. If the remaining 1 litre is divided among 3 persons, each will get \(\frac{1}{3}\) litre. So, in total each get 1\(\frac{1}{3}\) litres.
Numerically,
4 ÷ 3 = \(\frac{4}{3}\) = 1\(\frac{1}{3}\)