ICSE

ML Aggarwal Class 6 Solutions Chapter 8 Ratio and Proportion Ex 8.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 8 Ratio and Proportion Ex 8.1

Question 1.
Express the following ratios in simplest form:
(i) 20 : 40
(ii) 40 : 20
(iii) 81 : 108
(iv) 98 : 63
Solution:

Question 2.
Fill in the missing numbers in the following equivalent ratios:

Solution:

Question 3.
Find the ratio of each of the following in simplest form :
(i) 2.1 m to 1.2 m
(ii) 91 cm to 1.04m
(iii) 3.5 kg to 250gm
(iv) 60 paise to 4 rupees
(v) 1 minute to 15 seconds
(vi) 15 mm to 2 cm
Solution:

Question 4.
The length and the breadth of a rectangular park are 125 m and 60 m respectively. What is the ratio of the length to the breadth of the park?
Solution:

Question 5.
The population of village is 4800. If the numbers of females is 2160, find the ratio of males to that of females.
Solution:

Question 6.
In a class, there are 30 boys and 25 girls. Find the ratio of the numbers of
(i) boys to that of girls.
(ii) girls to that of total number of students.
(iii) boys to that of total numbers of students.
Solution:

Question 7.
In a year, Reena earns ₹ 1,50,000 and saves ₹ 50,000. Find the ratio of
(i) money she earns to the money she saves.
(ii) money that she saves to the money she spends.
Solution:

Question 8.
The monthly expenses of a student have increased from ₹350 to ₹500. Find the ratio of
(i) increase in expenses and original expenses.
(ii) original expenses to increased expenses.
(iii) increased expenses to increased in expenses.
Solution:

Question 9.
Mr Mahajan and his wife are both school teachers and earn ₹20900 and ₹ 18700 per month respectively. Find the ratio of
(i) Mr Mahajan’s income to his wife’s income.
(ii) Mrs Mahajan’s income to the total income of both.
Solution:

Question 10.
Out of 30 students in a class, 6 like football, 12 like cricket and remaining like tennis. Find the ratio of
(a) Number of students liking football to number of students liking tennis.
(b) Number of students liking cricket to total number of students.
Solution:

Question 11.
Divide ₹ 560 between Ramu and Munni in the ratio 3 : 2.
Solution:

Question 12.
Two people invested ₹ 15000 and ₹25000 respectively to start a business. They decided to share the profits in the ratio of their investments. If their profit is ₹ 12000, how much does each get?
Solution:

Question 13.
The ratio of Ankur’s money to Roma’s money is 9 : 11. if Ankur has ₹540, how much money does Roma have?
Solution:

Question 14.
The ratio of weights of tin and zinc in on alloy is 2 : 5. How much zinc is there in 31.5g of alloy?
Solution:

ML Aggarwal Class 6 Solutions Chapter 7 Decimals Check Your Progress for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 7 Decimals Check Your Progress

Question 1.
Convert the following decimal numbers into fractions (in lowest terms).
(i) 6.015
(ii) 0.876
(iii) 23.375
Solution:

Question 2.
Write the following fractions as decimals numbers:

Solution:

Question 3.
Arrange the following decimal numbers in ascending order:
(i) 123.8, 74.205, 74.209, 7.4209
(ii) 85.01, 85.1, 85.001, 85.103
Solution:

Question 4.
Arrange the following decimal numbers in desending order:
(i) 6.45, 4.65, 6.405, 64.5, 6.54
(ii) 73.5, 35.7, 7.35, 7.53, 7.035
Solution:

Question 5.
If the school bags of Garima and Nakul weigh 5.2 kg and 4.832 kg respectively, find
(i) the total weight.
(ii) the difference in weight of the bags.
Solution:

Question 6.
Evaluate the following:
(i) 31.42 – 17.853 -6.43
(ii) 13.01 – 5.428 – 3.703 + 2.99.
Solution:

Question 7.
By how much does the sum of 15.453 and 31.647 exceed the sum of 18.47 and 19.506?
Solution:

Question 8.
Namita travels 20 km 50 m every day. Out of this she travels 10 km 200 m by bus and the rest by auto. How much distance does she travel by auto?
Solution:

Question 9.
Ravi purchased 5 kg 400 g rice, 2 kg 20 g sugar and 10 kg 850 g flour (aata). Find the total weight of his purchases.
Solution:

Question 10.
1 kg of pure milk contains 0.263 kg of fat. How much fat is there 15.5 kg of milk?
Solution:

Question 11.
The product of two numbers is 15.275. If one number is 4.7, find the other.
Solution:

ML Aggarwal Class 6 Solutions Chapter 7 Decimals Objective Type Questions for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 7 Decimals Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) The decimal point in a decimal number is placed between ones digit and ……….. digit.
(ii) The place value of the digit 3 in the decimal number 15.437 is ………
(iii) The decimal number 27.025 has ………. decimal places.
(iv) The decimal number 5.06 is read as five point
(v) If an object is divided into 1000 equal parts, then its 27 parts are represented by ………
(vi) Two decimal numbers having different number of …………. are called unlike decimal numbers.
(vii) 4 tens, 3 ones, 2 tenths, 0 hundredths and 5 thousandths in decimal form is written as ……
(viii)The smallest decimal number upto three decimal places is ……….
Solution:

Question 2.
State whether the following statements are true (T) or false (F):
(i) Every decimal number can be represented by a point on a number line.
(ii) Fractions with denominator 10, 100, 1000, are called decimal fractions.
(iii) A decimal number having 3 decimal places can be written as a fraction with denominator 1000.
(iv) The value of a decimal number remains the same if any number of extra zeros are written at the end of a decimal number.
(v) If a decimal number is multiplied by 10, then the decimal point moves by one place to the left.
Solution:

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 23):
Question 3.
Five and seven hundredths is equal to
(a) 5.7
(b) 5.07
(c) 5.70
(d) 0.57
Solution:

Question 4.
Sicty three thousandths is equal to
(a) 0.63
(b) 0.603
(c) 0.063
(d) 0.630
Solution:

Question 5.
\(3 \frac{7}{100}\) is equal to :
(a) 3.07
(b) 3.7
(c) 3.70
(d) 3.007
Solution:

Question 6.
\(5 \frac{3}{1000}\) is equal to
(a) 5.03
(b) 5.3
(c) 5.003
(d) 5.0003
Solution:

Question 7.
The place value of the digit 7 in the decimal number 5.0378 is

Solution:

Question 8.
The place value of the digit 0 in the decimal number 13.405 is

Solution:

Question 9.
The value of \(5+\frac{7}{10}+\frac{3}{1000}\) is
(a) 5.73
(b) 5.703
(c) 5.073
(d) 0.753
Solution:

Question 10.
The value of \(\frac{3}{25}\) is
(a) 1.2
(b) 0.012
(c) 0.12
(d) none of these
Solution:

Question 11.
The value of \(5 \frac{1}{25}\) is
(a) 5.4
(b) 5.25
(c) 5.04
(d) 5.004
Solution:

Question 12.
The decimal number not equivalent to 5.7 is
(a) 5.70
(b) 5.07
(c) 5.700
(d) 5.7000
Solution:

Question 13.
1 g is equal to
(a) 0.1 kg
(b) 0.01 kg
(c) 0.001 kg
(d) 0.0001 kg
Solution:

Question 14.
2 km 7 m is equal to
(a) 2.7 km
(b) 2.07 km
(c) 2.007 km
(d) 2.0007 km
Solution:

Question 15.
Among 2.34, 2 .43, 2.344 and 2.4, the greatest number is
(a) 2.34
(b) 2.43
(c) 2.344
(d) 2.4
Solution:

Question 16.
5.2 – 3.6 is equal to
(a) 0.16
(b) 2.6
(c) 0.26
(d) 1.6
Solution:

Question 17.
A decimal number lying between 2.2 and 2.22 is
(a) 2.12
(b) 2.23
(c) 2.219
(d) 2.3
Solution:

Question 18.
0.023 lies between
(a) 0.2 and 0.3
(b) 0.02 and 0.03
(c) 0.029 and 0.03
(d) 0.026 and 0.024
Solution:

Question 19.
0.7499 lies between
(a) 0.7 and 0.74
(b) 0.759 and 0.799
(c) 0.749 and 0.75
(d) 0.74992 and 0.75
Solution:

Question 20.
Which of the following decimal numbers is the greatest?
(a) 0.182
(b) 0.038
(c) 0.219
(d) 0.291
Solution:

Question 21.
Which of the following decimal numbers is the smallest?
(a) 0.108
(b) 1.08
(c) 0.801
(d) 0.81
Solution:

Question 22.
0.003 × 0.2 is equal to
(a) 0.6
(b) 0.06
(c) 0.006
(d) 0.0006
Solution:

Question 23.
0.45 + 0.9 is equal to
(a) 50
(b) 5
(c) 0.5
(d) 0.05
Solution:

Higher Order Thinking Skills(Hots)
Question 1.
On her birthday, Ayushi is taking her 5 friends to a movie and treats them with cold costs. The cost of a ticket is ₹150 and a cold drink cost ₹28.50. How much Ayushi has to spend?
Solution:

Question 2.
Write digits in the boxes of the number : \(3 \square 6 \square .8 \square \square\) to obtain
(i) greatest possible number
(ii) smallest possible number. Repetition of digits in a number is not allowed.
Solution:

ML Aggarwal Class 6 Solutions Chapter 7 Decimals Ex 7.5 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 7 Decimals Ex 7.5

Question 1.
Express as rupees using decimals:
(i) 75 paise
(ii) 1025 paise
(ii) 63 rupees 9 paise
Solution:

Question 2.
Express as cm using decimals:
(i) 8 mm
(ii) 263 mm
(iii) 13 cm 3 mm
Solution:

Question 3.
Express as metres using decimals:
(i) 6 cm
(ii) 528 cm
(iii) 7 m 55 cm
Solution:

Question 4.
Express as km using decimals:
(i) 5 m
(ii) 888 m
(iii) 15 km 88 m
Solution:

Question 5.
Express as kg using decimals:
(i) 37 g
(ii) 100 g
(iii) 5 kg 8 g
Solution:

Question 6.
Anita bought 2 m 70 cm cloth for her shirt and 2 m 85 cm cloth for her trouser. Find the total length of the cloth bought by her.
Solution:

Question 7.
Sunita travelled 15 km 268 m by bus, 7 km 7 m by car and 500 m on foot in order to reach her school. How far is her school from her residence?
Solution:

Question 8.
Rahul bought 4 kg 90 g apples, 2 kg 60 g grapes and 5 kg 300 g mangoes. Find the total weight of all the fruits he bought.
Solution:

Question 9.
Rani had ₹18.50. She bought one ice¬cream for ₹11.75. How much money does she have now?
Solution:

Question 10.
Tina had 20 m 5 cm long cloth. She cuts 4m 50 cm length of cloth from this for making a curtain. How much cloth is left with her?
Solution:

Question 11.
Ruby bought a watermelon weighing 5 kg 300 g. Out of which she gave 2 kg 680 g to her neighbour. What is the weight of the watermelon left with Ruby?
Solution:

Question 12.
The cost of 1 metre of cloth is ₹35.80. What will be cost of 9.8 metres of cloth?
Solution:

Question 13.
Farida bought some bags of cement, each weighing 49.8 kg. If the total weight of all the bags is 1792.8 kg, how many bags did she buy?
Solution:

ML Aggarwal Class 6 Solutions Chapter 7 Decimals Ex 7.4 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 6 Solutions for ICSE Maths Chapter 7 Decimals Ex 7.4

Question 1.
Evaluate the following:
(i) 3.7 × 4.5
(ii) 12.08 × 9.3
(iii) 238.06 × 7.5
(iv) 0.79 × 32.4
(v) 3.6 × 1.4 × 0.7
(vi) 9.01 × 2.5 × 1.6
Solution:

Question 2.
Work out the following:
(i) 70.756 ÷ 4
(ii) 2.46 ÷ 6
(iii) 3.016 ÷ 8
(iv) 8.64 ÷ 3.6
(v) 72.8 ÷ 0.04
(vi) 0.144 ÷ 0.02
Solution:

Question 3.
Multiply each of the following numbers by 10, 100 and 1000 orally ;
(i) 4.7
(ii) 3.45
(iii) 23.01
Solution:

Question 4.
Divide each of the following numbers by 10, 100 and 1000 (orally):
(i) 4.7
(ii) 3.45
(iii) 23.01
Solution: