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Selina Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 18 Fundamental Concepts

Fundamental Concepts Exercise 18A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following statements in algebraic form :
(i) The sum of 8 and x is equal to y.
(ii) x decreased by 5 is equal to y.
(iii) The sum of 2 and x is greater than y.
(iv) The sum of x and y is less than 24.
(v) 15 multiplied by m gives 3n.
(vi) Product of 8 and y is equal to 3x.
(vii) 30 divided by b is equal to p.
(viii) z decreased by 3x is equal to y.
(ix) 12 times of x is equal to 5z.
(x) 12 times of x is greater than 5z.
(xi) 12 times of x is less than 5z.
(xii) 3z subtracted from 45 is equal to y.
(xiii) 8x divided by y is equal to 2z.
(xiv) 7y subtracted from 5x gives 8z.
(xv) 7y decreased by 5x gives 8z.
Solution:

Question 2.
For each of the following algebraic expressions, write a suitable statement in words:
(i) 3x + 8=15
(ii) 7 – y > x
(iii) 2y – x < 12
(iv) 5 ÷ z = 5
(v) a + 2b > 18
(vi) 2x – 3y= 16
(vii) 3a – 4b > 14
(viii) b + 7a < 21
(ix) (16 + 2a) – x > 25
(x) (3x + 12) – y < 3a
Solution:

Fundamental Concepts Exercise 18B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Separate the constants and the variables from each of the following:

Solution:

Question 2.
Group the like terms together :

Solution:

Question 3.
State whether true or false :
(i) 16 is a constant and y is a variable but 16y is variable.
(ii) 5x has two terms 5 and x.
(iii) The expression 5 + x has two terms 5 and x
(iv) The expression 2x² + x is a trinomial.
(v) ax² + bx + c is a trinomial.
(vi) 8 x ab is a binomial.
(vii) 8 + ab is a binomial.
(viii) x³ – 5xy + 6x + 7 is a polynomial.
(ix) x³ – 5xy + 6x + 7 is a multinomial.
(x) The coefficient of x in 5x is 5x.
(xi) The coefficient of ab in – ab is – 1.
(xii) The coefficient of y in – 3xy is – 3
Solution:

Question 4.
State the number of terms in each of the following expressions :

Solution:

Question 5.
State whether true or false:
(i) xy and – yx are like terms.
(ii) x²y and – y²x are like terms.
(iii) a and – a are like terms.
(iv) – ba and 2ab are unlike terms.
(v) 5 and 5x are like terms.
(vi) 3xy and 4xyz are unlike terms.
Solution:

Question 6.
For each expression, given below, state whether it is a monomial, or a binomial or a trinomial.

Solution:

Question 7.
Write down the coefficient of x in the following monomial :

Solution:

Question 8.
Write the coefficient of :

Solution:

Question 9.
State the numeral coefficient of the following monomials :

(vii) – 7x ÷ y
(viii) – 3x ÷ (2y)
Solution:

Question 10.
Write the degree of each of the following polynomials :

Solution:

Fundamental Concepts Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following statements in algebraic form :
(i) The sum of 3x and 4y is 8.
(ii) 5x decreased by 7 gives y.
(iii) 31 added to 4x gives 6x.
(iv) 3x subtracted from 89 gives 44.
Solution:

Question 2.
Group the like terms :

Solution:

Question 3.
Write the number of terms in each of the following polynomials :

Solution:

Question 4.
For each expression, given below, state whether it is a monomial, or a binomial or a trinomial:
(i) x + y
(ii) 5x – 4y
(iii) 7x² + 5x + 8
(iv) 64 + 3 ÷ 6
(v) 9 ÷ a x b
(vi) 8a ÷ b
Solution:

Question 5.
Write the coefficient of x2y in :
(i) -7x²yz
(ii) 8abx²y
(iii) – x²y
Solution:

Question 6.
Write the coefficient of :
(i) x² in – 8x²y
(ii) y in -4y
(iii) x in – xy²
Solution:

Question 7.
Write the numeral coefficient in :

Solution:

Question 8.
Write the degree of each of the following polynomials :

Solution:

Question 9.
Write each statement, given below in algebraic form :
(i) 28 more than twice of x is equal to 45.
(ii) 3y reduced by 5z is greater than 8x.
(iii) 6x divided by 13y is less than 17.
(iv) 9 multiplied by 5x is equal to 2y.
Solution:

Question 10.
State whether true or false :
(i) If 23 is a constant and x is a variable, 23 + x is constant.
(ii) If 23 is a constant and x is a variable, 23x is a variable.
(iii) If y is a variable and 57 is a constant, y – 57 is a variable.
(iv) If 3x and 2y are variable; each of 3x + 2y, 3x – 2y, 3x ÷ 2y and 3x x 2y is a variable.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 17 Idea of Speed, Distance and Time

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 17 Idea of Speed, Distance and Time

Idea of Speed, Distance and Time Exercise 17A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
A train covers 51 km in 3 hours. Calculate its speed. How far does the train go in 30 minutes?
Solution:

Question 2.
A motorist travelled the distance between two towns, which is 65 km, in 2 hours and 10 minutes. Find his speed in metre per minute.
Solution:

Question 3.
A train travels 700 metres in 35 seconds. What is its speed in km/h?
Solution:

Question 4.
A racing car covered 600 km in 3 hours 20 minutes. Find its speed in metre per second. How much distance will the car cover in 50 sec?
Solution:

Question 5.
Rohit goes 350 km in 5 hours. Find :
(i) his speed
(ii) the distance covered by Rohit in 6.2 hours
(iii) the time taken by him to cover 210 km.
Solution:

Question 6.
A boy drives his scooter with a uniform speed of 45 km/h. Find :
(i) the distance covered by him in 1 hour 20 min.
(ii) the time taken by him to cover 108 km.
(iii) the time taken to cover 900 m.
Solution:

Question 7.
I travel a distance of 10 km and come back in 2\(\frac { 1 }{ 2 }\) hours. What is my speed?
Solution:

Question 8.
A man walks a distance of 5 km in 2 hours. Then he goes in a bus to a nearby town, which is 40 km, in further 2 hours. From there, he goes to his office in an autorickshaw, a distance of 5 km, in \(\frac { 1 }{ 2 }\) hour. What was his average speed during the whole journey?
Solution:

Question 9.
Jagan went to another town such that he covered 240 km by a car going at 60 kmh^-1. Then he covered 80 km by a train, going at 100 kmh^-1 and the rest 200 km, he covered by a bus, going at 50 kmh^-1. What was his average speed during the whole journey?
Solution:

Question 10.
The speed of sound in air is about 330 ms^-1. Express this speed in kmh^-1. How long will the sound take to travel 99 km?
Solution:

Idea of Speed, Distance and Time Exercise 17B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
A train 180 m long is running at a speed of 90 km/h. How long will it take to pass a railway signal?
Solution:

Question 2.
A train whose length is 150 m, passes a telegraph pole in 10 sec. Find the speed of the train in km/h.
Solution:

Question 3.
A train 120 m long passes a railway platform 160 m long in 14 sec. How long will it take to pass another platform which is 100 m long?
Solution:

Question 4.
Mr. Amit can walk 8 km in 1 hour 20 minutes.
(a) How far does he go in :
(i) 10 minutes?
(ii) 30 seconds?
(b) How long will it take him to walk :
(i) 2500 m?
(ii) 6.5 km?
Solution:

Question 5.
Which is greater : a speed of 45 km/h or a speed of 12.25 m/sec?
How much is the distance travelled by each in 2 seconds?
Solution:

Question 6.
A and B start from the same point and at the same time with speeds 15 km/h and 12 km/h respectively, find the distance between A and B after 6 hours if both move in :
(i) same direction
(ii) the opposite directions.
Solution:

Question 7.
A and B start from the same place, in the same direction and at the same time with speeds 6 km/h and 2 m/sec respectively. After 5 hours who will be ahead and by how much?
Solution:

Question 8.
Mohit covers a certain distance in 6 hrs by his scooter at a speed of 40 kmh^-1.
(i) Find the time taken by Manjoor to cover the same distance by his car at the speed of 60 kmh^-1.
(ii) Find the speed of Joseph, if he takes 8 hrs to complete the same distance.
Solution:

Question 9.
A boy swims 200 m in still water and then returns back to the point of start in total 10 minutes. Find the speed of his swim in
(i) ms^-1
(ii) kmh^-1.
Solution:

Question 10.
A distance of 14.4 km is covered in 2 horus 40 minutes. Find the speed in ms^-1. With this speed Sakshi goes to her school, 240 m away from her house and then returns back. How much time, in all, will Sakshi take?
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 16 Percent (Percentage)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 16 Percent (Percentage)

Percent Exercise 16A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express each of the following statements in the percentage form :
(i) 13 out of 20
(ii) 21 eggs out of 30 are good
Solution:

Question 2.
Express the following fractions as percent :

Solution:

Question 3.
Express as percent:
(i) 0.10
(ii) 0.02
(iii) 0.7
(iv) 0.15
(v) 0.032
Solution:

Question 4.
Convert into fractions in their lowest terms:
(i) 8%
(ii) 20%
(iii) 85%
(iv) 250%
(v) 12\(\frac { 1 }{ 2 }\) %
Solution:

Question 5.
Express as decimal fractions :
(i) 25%
(ii) 108%
(iii) 95%
(iv) 4.5%
(v) 29.2%
Solution:

Question 6.
Express each of the following natural numbers as percent :
(i) 7
(ii) 2
(iii) 19.5
(iv) 5.37
Solution:

Percent Exercise 16B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express :
(i) Rs 5 as a percentage of Rs 25.
(ii) 80 paise as a percent of Rs 4.
(iii) 700 gm as a percentage of 2.8 kg.
(iv) 90 cm as a percent of 4.5 m.
Solution:

Question 2.
Express the first quantity as a percent of the second :
(i)) 40 P, ₹ 2
(ii) 500 gm, 6 kg
(iii) 42 seconds, 6 minutes
Solution:

Question 3.
Find the value of each of the following:
(i) 20% of ₹ 150
(ii) 90% of 130
(iii) 15% of 2 minutes
(iv) 7.5 % of 500 kg.
Solution:

Question 4.
If a man spends 70% of his income, what percent does he save ?
Solution:

Question 5.
A girl gets 65 marks out of 80. What percent marks did she get?
Solution:

Question 6.
A class contains 25 children, of which 6 are girls. What percentage of the class are the boys.
Solution:

Question 7.
A tin contains 20 litres of petrol. Due to leakage, 3 litres of petrol is lost. What percent is still present in the tin?
Solution:

Question 8.
An alloy of copper and zinc contains 45% copper and the rest is zinc. Find the weight of zinc in 20 kg of the alloy.
Solution:

Question 9.
A boy got 60 out of 80 in Hindi, 75 out of 100 in English and 65 out of 70 in Arithmetic. In which subject his percentage of marks the best ? Also, find his overall percentage.
Solution:

Question 10.
In a camp, there were 500 soldiers. 60 more soldiers joined them. What percent of the earlier (original) number have joined the camp.
Solution:

Question 11.
In a plot of ground of area 6000 sq. m, only 4500 sq. m is allowed for construction. What percent is to be left without construction?
Solution:

Question 12.
Mr. Sharma has a monthly salary of ₹ 8,000. If he spends ₹ 6,400 every month; find :
(i) his monthly expenditure as percent.
(ii) his monthly savings as percent.
Solution:

Question 13.
The monthly salary of Rohit is ₹ 24,000. If his salary increases by 12%, find his new monthly salary
Solution:

Question 14.
In a sale, the price of an article is reduced by 30%. If the original price of the article is ₹ 1,800, find :
(i) the reduction in the price of the article
(ii) reduced price of the article.
Solution:

Question 15.
Evaluate :
(i) 30% of 200 + 20% of 450 – 25% of 600
(ii) 10% of ₹ 450 – 12% of ₹ 500 + 8% of ₹ 500.
Solution:

Percent Exercise 16C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The price of rice rises from Rs. 30 per kg to Rs. 36 per kg. Find the percentage rise in the price of rice.
Solution:

Question 2.
The population of a small locality was 4000 in 1979 and 4500 in 1981, By what percent had the population increase ?
Solution:

Question 3.
The price of a scooter was ₹ 8000 in 1975. It came down to ₹ 6000 in 1980. By what percent had the price of the scooter came down?
Solution:

Question 4.
Find the resulting quantity when :
(i) ₹ 400 is decreased by 8%.
(ii) 25 km is increased by 5%.
(iii) a speed of 600 km/h is increased by 12\(\frac { 1 }{ 2 }\) %
(iv) there is 2.5% increase in a salary of ₹ 62, 500.
Solution:

Question 5.
The population of a village decreased by 12%. If the original population was 25,000, find the population after decrease?
Solution:

Question 6.
Out of a salary of Rs. 13,500,1 keep 1/3 as savings. Of the remaining money, I spend 50% on food and 20% on house rent. How much do I spend on food and house rent?
Solution:

Question 7.
A tank can hold 50 litres of water. At present, it is only 30% full. How many litres of water shall I put into the tank so that it becomes 50% full?
Solution:

Question 8.
In an election, there are a total of 80,000 voters and two candidates, A and B. 80% of the voters go to the polls out of which 60% vote for A. How many votes does B get.
Solution:

Question 9.
70% of our body weight is made up of water. Find the weight of water in the body of a person whose body weight is 56 kg.
Solution:

Question 10.
Only one-fifth of water is available in liquid form. This limited amount of water is replenished and used by man recurrently. Express this information as percent, showing :
(i) water available in liquid form.
(ii) water available in frozen form.
Solution:
<

Question 11.
By weight, 90% of tomato and 78% of potato is water. Find :
(i) the weight of water in 25 kg of tomato.
(ii) the total quantity, by weight, of water in 90 kg of potato and 30 kg of tomato
(iii) the weight of potato which contains 39 kg of water.
Solution:

Percent Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Rohit’s age is 12 years and Geeta’s age is 15 years. Express :
(i) Rohit’s age as a percent of Geeta’s age.
(ii) Geeta’s age as a percent of Rohit’s age.
Solution:

Question 2.
A class has 30 boys and 20 girls. Find:
(i) the percentage of girls in the class
(ii) the percentage of boys in the class
(iii) percentage of number of boys as compared with number of girls.
Solution:

Question 3.
Mrs. Sharma went to the market with ₹ 800 in her purse. When she returned to her home, ₹ 240 were still left in her purse. What percent of her money did she spend in the market?
Solution:

Question 4.
In a mixture of two liquids A and B, 35% is liquid B. If the total quantity of the mixture is 20 kg, find the quantity of A, by weight.
Solution:

Question 5.
A girl got 375 marks out of 500 in the first term examination, 560 marks out of 800 in the second term examination and 840 marks out of 1200 in the third term examination. Find:
(i) her percentage score in the first term examination.
(ii) her percentage score in the second term examination.
(iii) her percentage score in the third term examination.
(iv) the total marks secured in all the three examinations.
(v) the total marks scored in all the three examinations.
(vi) her percentage score on the whole in all the three examinations.
Solution:

Question 6.
Out of his monthly income of ₹ 2,500; a man spends ₹ 1,750. What percent of his income does he save every month?
Solution:

Question 7.
Mr. Singh’s monthly salary is ₹ 15,000. This month he was promoted with an increment of ₹ 3,000 in his salary. Express his increment as a percent of his original salary.
Solution:

Question 8.
(i) The price of an article increased from ₹ 16 to ₹ 20 ; find the percentage increase.
(ii) The price of an article decreased from Rs 20 to Rs 16 ; find the percentage decrease.
Solution:

Question 9.
(i)) The salary of a man is ₹ 7,200 per month, which is now increased by 8%. Find his new salary per month.
(ii) The salary of Mr. Sahni is ₹ 8,400 per month, which is now decreased by 8%. Find his new salary per month.
Solution:

Question 10.
Find the percentage change from the first quantity to the second :
(i) ₹ 80, ₹ 120
(ii) 75 kg, 60 kg
(iii) 50 cm, 45 cm
Solution:

Question 11.
The original price of an article is ₹ 640. Find its new price when its price is :
(i) increased by 30%
(ii) decreased by 20%
Solution:

Question 12.
Find the number that is :
(i) 50% more than 48
(ii) 30% less than 70
Solution:

Question 13.
Evaluate :
(i) 8% of 900 – 12% of 750 + 20% of 165.
(ii) 70% of 70 + 90% of 90 – 120% of 120.
Solution:

Question 14.
Approximately 97.3% water on the earth is not fit for drinking. Find :
(i) the percentage of water on the earth that is fit for drinking.
(ii) The total volume of water available in certain part of the earth where there is 21,600 m3 of drinking water.
Solution:

Question 15.
Air is an important inexhaustible natural resource. It is essential for the survival of human beings, microbes, plants and animals. The following table shows the percentage of various gases in air.

(i) In 800 m3 of air, calculate the approximate quantities of nitrogen, oxygen and other gases.
(ii) If a certain quantity (by volume) of air contains 4,200 litres of oxygen, find the total quantity of air taken and the amount of nitrogen in it.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 3 Fractions (Including Problems)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 3 Fractions (Including Problems)

Fractions Exercise 3A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Classify, each fraction given below, as decimal or vulgar fraction, proper or improper fraction and mixed fraction :

Solution:

Question 2.
Express the following improper fractions as mixed fractions :

Solution:

Question 3.
Express the following mixed fractions as improper fractions :

Solution:

Question 4.
Reduce the given fractions to lowest terms

Solution:

Question 5.
State : true or false

Solution:

Question 6.
Distinguish each of the following fractions, given below, as a simple fraction or a complex fraction :

Solution:

Fractions Exercise 3B – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
For each pair, given below, state whether it forms like fractions or unlike fractions :

Solution:

Question 2.
Convert given fractions into fractions with equal denominators :

Solution:

Question 3.
Convert given fractions into fractions with equal numerators :

Solution:

Question 4.
Put the given fractions in ascending order by making denominators equal :

Solution:

Question 5.
Arrange the given fractions in descending order by making numerators equal :

Solution:

Question 6.
Find the greater fraction :


Solution:

Question 7.
Insert one fraction between :

Solution:

Question 8.
Insert three fractions between

Solution:

Question 9.
Insert two fractions between

Solution:

Fractions Exercise 3C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Reduce to a single fraction :


Solution:

Question 2.
Simplify :

Solution:

Question 3.
Subtract :

Solution:

Question 4.
Find the value of

Solution:

Question 5.
Simplify and reduce to a simple fraction :


Solution:

Question 6.
A bought 3 \(\frac { 3 }{ 4 }\) kg of wheat and 2 \(\frac { 1 }{ 2 }\) kg of rice. Find the total weight of wheat and rice bought.
Solution:

Question 7.
Which is greater,\(\frac { 3 }{ 5 }\) or \(\frac { 7 }{ 10 }\) and by how much?
Solution:

Question 8.
What number should be added to 8 \(\frac { 2 }{ 3 }\) to 12 \(\frac { 5 }{ 6 }\)
Solution:

Question 9.
What should be subtracted from 8\(\frac { 3 }{ 4 }\) to get 2 \(\frac { 2 }{ 3 }\)
Solution:

Question 10.
A field is 16 \(\frac { 1 }{ 2 }\) m long and 12 \(\frac { 2 }{ 5 }\) m wide. Find the perimeter of the field.
Solution:

Question 11.
Sugar costs ₹37 \(\frac { 1 }{ 2 }\)per kg. Find the cost of 8\(\frac { 3 }{ 4 }\) kg sugar.
Solution:

Question 12.
A motor cycle runs 31\(\frac { 1 }{ 4 }\) km consuming 1 litre of petrol. How much distance will it run consuming 1\(\frac { 3 }{ 5 }\) liter of petrol?
Solution:

Question 13.
A rectangular park has length = 23 \(\frac { 2 }{ 3 }\) m and breadth = 16 \(\frac { 2 }{ 3 }\) m. Find the area of the park.
Solution:

Question 14.
Each of 40 identical boxes weighs 4 \(\frac { 4 }{ 5 }\) kg Find the total weight of all the boxes.
Solution:

Question 15.
Out of 24 kg of wheat, \(\frac { 5 }{ 6 }\) th of wheat is consumed. Find, how much wheat is still left?
Solution:

Question 16.
A rod of length 2 \(\frac { 2 }{ 5 }\) metre is divided into five equal parts. Find the length of each part so obtained.
Solution:

Question 17.
IfA = 3\(\frac { 3 }{ 8 }\) and B = 6\(\frac { 5 }{ 8 }\) find :
(i) A+B
(ii) B A
Solution:

Question 18.
Cost of 3 \(\frac { 5 }{ 7 }\) litres of oil is ₹83 \(\frac { 1 }{ 2 }\). Find the
cost of one litre oil.
Solution:

Question 19.
The product of two numbers is 20 \(\frac { 5 }{ 7 }\). If one of these numbers is 6 \(\frac { 2 }{ 3 }\), find the other.
Solution:

Question 20.
By what number should 5 \(\frac { 5 }{ 6 }\) be multiplied 1 to get 3\(\frac { 1 }{ 3 }\) ?
Solution:

Fractions Exercise 3D – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Simplify
Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Fractions Exercise 3E – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
A line AB is of length 6 cm. Another line CD is of length 15 cm. What fraction is :
(i) The length of AB to that of CD ?
(ii) \(\frac { 1 }{ 2 }\) the length of AB to that of \(\frac { 1 }{ 3 }\) of CD ?
(iii) \(\frac { 1 }{ 5 }\) of CD to that of AB ?
Solution:

Question 2.
Subtract \(\frac { 2 }{ 7 }\) – \(\frac { 5 }{ 21 }\) from the sum of \(\frac { 3 }{ 4 }\) , \(\frac { 5 }{ 7 }\) and \(\frac { 7 }{ 12 }\)
Solution:

Question 3.
From a sack of potatoes weighing 120 kg, a merchant sells portions weighing 6 kg, 5\(\frac { 1 }{ 4 }\) kg, 9\(\frac { 1 }{ 2 }\) kg and 9\(\frac { 3 }{ 4 }\) kg respectively.
(i) How many kg did he sell ?
(ii) How many kg are still left in the sack ?
Solution:

Question 4.
If a boy works for six consecutive days for 8 hours, 7\(\frac { 1 }{ 2 }\) hours, 8\(\frac { 1 }{ 4 }\) hours, 6 \(\frac { 1 }{ 4 }\)4 3hours, 6\(\frac { 3 }{ 4 }\) hours and 7 hours respectively. How much money will he earn at the rate of Rs. 36 per hour ?
Solution:

Question 5.
A student bought 4 \(\frac { 1 }{ 3 }\) m of yellow ribbon, 6 \(\frac { 1 }{ 6 }\) m of red ribbon and 3\(\frac { 2 }{ 9 }\) m of blue ribbon for decorating a room. How many metres of ribbon did he buy ?
Solution:

Question 6.
In a business, Ram and Deepak invest \(\frac { 3 }{ 5 }\) and \(\frac { 2 }{ 5 }\) of the total investment. IfRs. 40,000 is the total investment, calculate the amount invested by each ?
Solution:

Question 7.
Geeta had 30 problems for home work. She worked out \(\frac { 2 }{ 5 }\) of them. How many problems were still left to be worked out by her ?
Solution:

Question 8.
A picture was marked at Rs. 90. It was sold at \(\frac { 3 }{ 4 }\) of its marked price. What was the sale price ?
Solution:

Question 9.
Mani had sent fifteen parcels of oranges. What was the total weight of the parcels, if each weighed 10\(\frac { 1 }{ 2 }\) kg ?Solution:

Question 10.
A rope is 25\(\frac { 1 }{ 2 }\) m long. How many pieces , 1 \(\frac { 1 }{ 2 }\) each of length can be cut out from it?Solution:

Question 11.
The heights of two vertical poles, above the earth’s surface, are 14 \(\frac { 1 }{ 4 }\) m and 22 \(\frac { 1 }{ 3 }\) respectively. How much higher is the second pole as compared with the height of the first pole ?
Solution:

Question 12.
Vijay weighed 65\(\frac { 1 }{ 2 }\) kg. He gained 1\(\frac { 2 }{ 5 }\) kg during the first week, 1 \(\frac { 1 }{ 4 }\) kg during the second week, but lost \(\frac { 5 }{ 16 }\) kg during the 16 third week. What was his weight after the third week ?
Solution:

Question 13.
A man spends \(\frac { 2 }{ 5 }\) of his salary on food and \(\frac { 3 }{ 10 }\) on house rent, electricity, etc. What fraction of his salary is still left with him ?
Solution:

Question 14.
A man spends \(\frac { 2 }{ 5 }\) of his salary on food and \(\frac { 3 }{ 10 }\) of the remaining on house rent, electricity, etc. What fraction of his salary is still left with him ?
Solution:

Question 15.
Shyam bought a refrigerator for Rs. 5000. He paid \(\frac { 1 }{ 10 }\) of the price in cash and the rest in 12 equal monthly instalments. How much had he to pay each month ?
Solution:

Question 16.
A lamp post has half of its length in mud, and \(\frac { 1 }{ 3 }\) of its length in water.
(i) What fraction of its length is above the water ?
(ii) If 3\(\frac { 1 }{ 3 }\) m of the lamp post is above the water, find the whole length of the lamp post.
Solution:

Question 17.
I spent \(\frac { 3 }{ 5 }\) of my savings and still have Rs. 2,000 left. What were my savings ?
Solution:

Question 18.
In a school, \(\frac { 4 }{ 5 }\) of the children are boys. If the number of girls is 200, find the number of boys.
Solution:

Question 19.
If \(\frac { 4 }{ 5 }\) of an estate is worth Rs. 42,000, find the worth of whole estate. Also, find the value of \(\frac { 3 }{ 7 }\) of it.
Solution:

Question 20.
After going \(\frac { 3 }{ 4 }\) of my journey, I find that I have covered 16 km. How much Journey is still left ?
Solution:

Question 21.
When Krishna travelled 25 km, he found that \(\frac { 3 }{ 5 }\) of his journey was still left. What was the length of the whole journey.
Solution:

Question 22.
From a piece of land, one-third is bought by Rajesh and one-third of remaining is bought by Manoj. If 600 m² land is still left unsold, find the total area of the piece of land.
Solution:

Question 23.
A boy spent \(\frac { 3 }{ 5 }\) of his money on buying 1 cloth and \(\frac { 1 }{ 4 }\) of the remaining on buying shoes. If initially he has ?2,400; how much did he spend on shoes?
Solution:

Question 24.
A boy spent \(\frac { 3 }{ 5 }\) of his money on buying cloth and \(\frac { 1 }{ 4 }\) of his money on buying shoes. If initially he has ?2,400; how much did he spend on shoes?
Solution:

Selina Concise Mathematics Class 7 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 15 Decimal Fractions

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 15 Decimal Fractions

Decimal Fractions Exercise 15A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write the number of decimal places in each of the following :
(i) 7.03
(ii) 0.509
(iii) 146.2
(iv) 0.0065
(v) 8.03207
Solution:

Question 2.
Convert the given unlike decimal fractions into like decimal fractions:
(i) 1.36, 239.8 and 47.008
(ii) 507.0752, 8.52073 and 0.808
(iii) 459.22, 7.03093 and 0.200037
Solution:

Question 3.
Change each of following fractions to a decimal fraction :

Solution:

Question 4.
Convert into a decimal fraction :

Solution:

Question 5.
Change the given decimals fractions to fractions in their lowest terms :
(i) 0.05
(ii) 3.95
(iii) 4.005
(iv) 0.876
(v) 50.06
(vi) 0.01075
(vii) 4.8806
Solution:

Decimal Fractions Exercise 15B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Add the following :
(i) 0.243, 2.47 and 3.009
(ii) 0.0736, 0.6095 and 0.9107
(iii) 1.01, 257 and 0.200
(iv) 18, 200.35, 11.72 and 2.3
(v) 0.586, 0.0586 and 0.00586
Solution:

Question 2.
Find the value of :
(i) 6.8 – 2.64
(ii) 2 – 1.0304
(iii) 0.1 – 0.08
(iv) 0.83 – 0.342
Solution:

Question 3.
Subtract :
(i) 0.43 from 0.97
(ii) 2.008 from 22.1058
(iii) 0.18 from 0.6
(iv) 1.002 from 17
(v) 83 from 92.05
Solution:

Question 4.
Simplify :
(i) 3.5 – 2.43 + 0.075
(ii) 7.84 + 0.3 – 4.016
(iii) 2.987 – 1.25 – 0.54
(iv) 52.9 – 231.666 + 204
(v) 8.57 – 6.4432 – 1.70 + 0.683
Solution:

Question 5.
From the sum of 75.75 and 4.9 subtract 28.465.
Solution:

Question 6.
Subtract the sum of 8.14 and 12.9 from 32.7.
Solution:

Question 7.
Subtract the sum of 34.27 and 159.8 from the sum of 20.937 and 200.6.
Solution:

Question 8.
From the sum of 2.43 and 4.349 subtract the sum of 0.8 and 3.15.
Solution:

Question 9.
By how much does the sum of 18.0495 and 34.9644 exceed the sum of 7.6752 and 24.876?
Solution:

Question 10.
What least number must be added to 89.376 to get 1000?
Solution:

Decimal Fractions Exercise 15C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Multiply :
(i) 5.6 and 8
(ii) 38.46 and 9
(iii) 0.943 and 62
(iv) 0.0453 and 35
(v) 7.5 and 2.5
(vi) 4.23 and 0.8
(vii) 83.54 and 0.07
(viii) 0.636 and 1.83
(ix) 6.4564 and 1000
(x) 0.076 and 100
Solution:

Question 2.
Evaluate :
(i) 0.0008 x 26
(ii) 0.038 x 95
(iii) 1.2 x 2.4 x 3.6
(iv) 0.9 x 1.8 x 0.27
(v) 1.5 x 1.5 x 1.5
(vi) 0.025 x 0.025
(vii) 0.2 x 0.002 x 0.001
Solution:

Question 3.
Multiply each of the following numbers by 10, 100 and 1000 :
(i) 3.9
(ii) 2.89
(in) 0.0829
(iv) 40.3
(v) 0.3725
Solution:

Question 4.
Evaluate :
(i) 8.64 ÷ 8
(ii) 0.0072 ÷ 6
(iii) 20.64 ÷ 16
(iv) 1.602 ÷ 15
(v) 13.08 ÷ 4
(vi) 3.204 ÷ 9
(vii) 3.024 ÷ 12
(viii) 5.15 ÷ 5
(ix) 3 ÷ 5
Solution:

Question 5.
Divide each of the following numbers by 10,100 and 1000 :
(i) 49.79
(ii) 0.923
(iii) 0.0704
Solution:

Question 6.
Evaluate :
(i) 9.4 ÷ 0.47
(ii) 6.3 ÷ 0.09
(iii) 2.88 ÷ 1.2
(iv) 8.64 ÷ 1.6
(v) 37.188 ÷ 3.6
(vi) 16.5 ÷ 0.15
(vii) 3.2 ÷ 0.005
(viii) 3.24 ÷ 0.0016
Solution:

Question 7.
Fill in the blanks with 10,100,1000, or 10000 etc.:
(i) 7.85 x ………….. = 78.5
(ii) 0.442 x ………. = 442
(in) 0.0924 x ………… = 9.24
(iv) 0.00187 x …………. = 18-7
(v) 2.6 x …………. = 2600
(vi) 0.08 x ………… = 80
(vii) 96.7 ÷ ………….. = 0.967
(viii) 5.2 ÷ ……………. = 0.52
(ix) 33.15 ÷ ……………….. = 0.03315
(x) 0.7 ÷ ………… = 0.007
(xi) 0.00672 x ……… = 67.2
Solution:

Question 8.
Evaluate :
(i) 9.32 – 28.54 ÷ 10
(ii) 0.234 x 10 + 62.8
(iii) 3.06 x 100 – 889.4 ÷ 100
(iv) 2.86 x 7.5 + 45.4 ÷ 0.2
(v) 97.82 x 0.03 – 0.54 ÷ 0.3
Solution:

Decimal Fractions Exercise 15D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Express in paise :
(i) Rs. 8.40
(ii) Rs. 0.97
(iii) Rs. 0.09
(iv) Rs. 62.35
Solution:

Question 2.
Express in rupees :
(i) 55 P
(ii) 8 P
(iii) 695 P
(iv) 3279 P
Solution:

Question 3.
Express in centimetre (cm) :
(i) 6 m
(ii) 8.54 m
(iii) 3.08 m
(iv) 0.87 m
(v) 0.03 m
(vi) 25.04 m
Solution:

Question 4.
Express in metre (m) :
(i) 250 cm
(ii) 2328 cm
(iii) 86 cm
(iv) 4 cm
(v) 107 cm
Solution:

Question 5.
Express in gramme (gm) :
(i) 6 kg
(ii) 5.543 kg
(iii) 0.078 kg
(iv) 3.62 kg
(v) 4.5 kg
Solution:

Question 6.
Express in kilogramme (kg) :
(i) 7000 gm
(ii) 6839 gm
(iii) 445 gm
(iv) 8 gm
(iv) 93 gm
(vi) 13545 gm
Solution:

Question 7.
Add (giving answer in rupees) :
(i) Rs. 5.37 and Rs. 12
(ii) Rs. 24.03 and 532 paise
(iii) 73 paise and Rs. 208
(iv) 8 paise and Rs. 1536
Solution:

Question 8.
Subtract :
(i) Rs. 35.74 from Rs. 63.22
(ii) 286 paise from Rs. 7.02
(iii) Rs. 0.55 from 121 paise
Solution:

Question 9.
Add (giving answer in metre) :
(i) 2.4 m and 1.78 m
(ii) 848 cm and 2.9 m
(iii) 0.93 m and 64 cm
Solution:

Question 10.
Subtract (giving answer in metre) :
(i) 5.03 m from 19.6 m
(ii) 428 cm from 1033 m
(iii) 0.84 m from 122 cm
Solution:

Question 11.
Add (giving answer in kg) :
(i) 2.06 kg and 57.864 kg
(ii) 778 gm and 1.939 kg
(iii) 0.065 kg and 4023 gm
Solution:

Question 12.
Subtract (giving answer in kg) :
(i) 9.462 kg from 15.6 kg
(ii) 4317 gm from 23 kg
(iii) 0.798 kg from 4169 gm
Solution:

Decimal Fractions Exercise 15E – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
The cost of a fountain pen is Rs. 13.25. Find the cost of 8 such pens.
Solution:

Question 2.
The cost of 25 identical articles is Rs. 218.25. Find the cost of one article.
Solution:

Question 3.
The length of an iron rod is 10.32 m. The rod is divided into 4 pieces of equal lengths. Find the length of each piece.
Solution:

Question 4.
What will be the total length of cloth required to make 5 shirts, if 2.15 m of cloth is needed for each shirt?
Solution:

Question 5.
Find the distance walked by a boy in 1\(\frac { 1 }{ 2 }\) hours, if he walks at 2.150 km every hour.
Solution:

Question 6.
83 note-books are sold at Rs. 15.25 each. Find the total money (in rupees) obtained by selling these note-books.
Solution:

Question 7.
If length of one bed-cover is 2.1 m, find the total length of 17 bed-covers.
Solution:

Question 8.
A piece of rope is 10 m 67 cm long. Another rope is 16 m 32 cm long. By how much is the second rope longer than the first one?
Solution:

Question 9.
12 cakes of soap together weigh 5 kg and 604 gm. Find the weight of
(i) One cake in both kg and gramme
(ii) 5 cakes in kg.
Solution:

Question 10.
Three strings of lengths 50 m 75 cm; 68 m 58 cm and 121 m 3 cm, respectively, are joined together to get a single string of greatest length, And the length of the single string obtained.
If this single string is then divided into 12 equal pieces ; find the length of each piece.
Solution:

Decimal Fractions Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write th& following decimal numbers in ascending order of value
(i) 5.054, 5.250, 5.245 and 5.0543
(ii) 62.443, 62.434, 62.344 and 62.444
Solution:

Question 2.
What number added to 0.805 gives 1?
Solution:

Question 3.
What must be subtracted from 3 to get 2.462?
Solution:

Question 4.
By how much should 83.407 be decreased to get 27.78?
Solution:

Question 5.
Two articles weigh 32.674 kg and 40.038 kg respectively. Find :
(i) the total weight of both the articles.
(ii) the difference in the weights of both the articles.
Solution:

Question 6.
By how much does the sum of 34.07 and 15.239 exceed the sum of 16.40 and 27.08?
Solution:

Question 7.
The cost of 1 kg of fruit is Rs. 27.50. What is the cost of 3.6 kg of fruit?
Solution:

Question 8.
Evaluate :
(i) 0.8 x 0.8 x 0.8
(ii) 0.8 ÷ 0.8 x 0.8
(iii) 0.8 x 0.8 ÷ 0.8
(iv) 0.8 ÷ 0.8 of 0.8
(v) 0.8 of 0.8 ÷ 0.8
Solution:

Question 9.
Evaluate :
(i) 3.5 x (4.2 + 2.6)
(ii) 3.5 x 4.2 + 3.5 x 2.6
Are (i) and (ii) equal ?
Solution:

Question 10.
Evaluate :
(i) (3.87 – 2.09) x 2.4
(ii) 3.87 x 2.4 – 2.09 x 2.4
Are (i) and (ii) equal ?
Solution:

Question 11.
A 4.85 m long pole is divided into 5 equal parts. Find the length of each part.
Solution:

Question 12.
A car can run 16.8 km consuming one litre of petrol. How many kilometres will it run on 3.7 litres of petrol ?
Solution:

Question 13.
A certain amount of money is distributed among 28 persons. If each person gets Rs. 62.45 and Rs. 5.78 is left, find the original amount of money.
Solution:

Question 14.
Complete the following table :

Solution:

Question 15.
The difference between two numbers is 47.364. If the smaller number is 31.855 ; find the bigger one.
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions