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Selina Concise Mathematics Class 6 ICSE Solutions Chapter 6 Negative Numbers and Integers

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 6 Negative Numbers and Integers

Negative Numbers and Integers Exercise 6 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) Negative of -20 is ……….
(ii) Negative of 0 is …………
(iii) Negative of 8 is ………..
(iv) If 10 represents gain of ₹ 10, then -10 represents …………..
(v) If going south is negative then going north is …………
(vi) Because 5 < 7, therefore -5 ……….. -7. (vii) If 3 > -2, then 3 is on the ………….. of -2.
(viii) If -8 < -6, then -8 is on the …………. of-6.
Solution:

Question 2.
Use a number line to write the following integers in ascending (increasing) order :
(i) -5, 8, 0, -9, 4, -14 and 12
(ii) -6, 7, 0, -9, 5 and 9
Solution:

Question 3.
Use a number line to write the following integers in descending (decreasing) order :
(i) -10, 0, 3, -4, 12, 11, -1 and 5
(ii) -4, 3, -8, -12, -7 and 6.
Solution:

Question 4.
Add:
(i) 13 and 15
(ii) -13 and 15
(iii) 13 and -15
(iv) -13 and -15
Solution:

Question 5.
Add:
(i) 259 from 214
(ii) -528 and -243
(iii) -623 and 326
(iv) 258 and -473
(v) -622 and -254
(vi) 257 and -254
Solution:

Question 6.
Subtract :
(i) 5 from 8
(ii) -5 from 8
(iii) 4 from -7
(iv) -8 from -2
(v) -3 from 12
(vi) -6 from -3
Solution:

Question 7.
Subtract:
(i) -123 from 453
(ii) -78 from -12
(iii) 329 and -124
(iv) -222 from 0
Solution:

Question 8.
Using a number line, find the integer which is :
(i) 3 more than -1
(ii) 5 less than 2
(iii) 5 more than -9
(iv) 4 less than -4
(v) 7 more than 0
(vi) 7 less than -8
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers (Including Patterns)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 5 Natural Numbers and Whole Numbers (Including Patterns)

Natural Numbers and Whole Numbers Exercise 5A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) Smallest natural number is …………..
(ii) Smallest whole number is …………
(iii) Largest natural number is …………
(iv) Largest whole number is ………..
(v) All natural numbers are …………
(vi) All whole numbers are not …………
(vii) Successor of 4099 is …………..
(viii) Predecessor of 4330 is …………….
Solution:

Question 2.
Represent the following whole numbers on a number line :
0, 3, 5, 8, 10
Solution:

Question 3.
State, true or false :
(i) Whole number are closed for addition.
(ii) If a and b are any two whole numbers, then a + b is not a whole number.
(iii) If a and b are any two whole numbers, then a + b = b + a
(iv) 0 + 18= 18 + 0
(v) Addition of whole numbers is associative.
(vi) 10 + 12 + 16 = (10 + 12) + 16 = 10 + (12 + 16)
Solution:

Question 4.
Fill in the blanks :
(i) 54 + 234 = 234 + …………
(ii) 332 + 497 = ………… + 332
(iii) 286 + 0 = ………..
(iv) 286 x 1 = ……….
(v) a + (b + c) = (a + ………) + c
Solution:

Question 5.
By re-arranging the given numbers, evaluate :
(i) 237 + 308 + 163
(ii) 162 + 253 +338 + 47
(iii) 21 + 22 + 23 + 24 + 25 + 75 + 76 + 77 + 78 + 79
(iv) 1 + 2 + 3 + 4 + 596 + 597 + 598 + 599
Solution:

Question 6.
Is a + b + c = a + (b + c) = (b + a) + c ?
Solution:

Question 7.
Which property of addition is satisfied by :
(i) 8 + 7 = 15
(ii) 3+ (5 + 4) = (3 + 5)+ 4
(iii) 8 x (8 + 0) = 8 x 8 + 8 x 0
(iv) (7 + 6) x 10 = 7 x 10 + 6 x 10
(v) (15 – 12) x 18 = 15 x 18 – 12 x 18
(vi) 16 + 0= 16
(vii) 23 + (-23) = 0
Solution:

Question 8.
State, True or False :
(i) The sum of two odd numbers is an odd number.
(ii) The sum of two odd numbers is an even number.
(iii) The sum of two even numbers is an even number.
(iv) The sum of two even numbers is an odd number.
(v) The sum of an even number and an odd number is odd number.
(vi) Every whole number is a natural number.
(vii) Every natural number is a whole number.
(viii) Every whole number + 0 = The whole number itself.
(ix) Every whole number x 1 = The whole number itself.
(x) Commutativity and associativity are properties of natural numbers and whole numbers both.
(xi) Commutativity and associativity are properties of addition for natural numbers and whole numbers both.
(xii) If x is a whole number then -x is also a whole number.
Solution:

Natural Numbers and Whole Numbers Exercise 5B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Consider two whole numbers a and b such that a is greater than b.
(i) Is a – b a whole number? Is this result always true?
(ii) b – a a whole number? Is this result always true?
Solution:

Question 2.
Fill in the blanks :
(i) 8 – 0 = ……….. and 0 – 8 = ……….
8 – 0 ≠ 0 – 8, this shows subtraction of whole numbers is not ………..
(ii) 5 – 10 = ………., which is not a …………
⇒ Subtraction of ……….. is not closed.
(iii) 7 – 18 = ……….. and (7 – 18) – 5 = …………..
18 – 5 = …………. and (7 – 18) – 5 = ………….
Is (7 – 18) – 5 = 7 – (18 – 5) ?
⇒ Subtraction of whose numbers is not ………….
Solution:

Question 3.
Write the identify number, if possible for subtraction.
Solution:

Question 4.
Write the inverse, if possible for subtraction of whole numbers ?
Solution:

Question 5.
12 × (9 – 6) = ………….. = ………….
12 × 9 – 12 × 6 = …………. = …………….
Is 12 × (9 – 6) = 12 × 9 – 12 × 6 ? ………….
Is this type of result always true ? ……………
Name the property used here …………..
Solution:

Question 6.
(16 – 8) × 24 = ………….. = …………..
16 × 24 – 8 × 24 = …….. – ……….. = ………..
Is (16 – 8) × 24 = 16 × 24 – 8 × 24 ? …………..
Is the type of result always true? ………….
Name the property used here ………………
Solution:

Natural Numbers and Whole Numbers Exercise 5C – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) 42 × o = ……….
(ii) 592 × 1 = ………..
(iii) 328 × 573 = ……….. × 328
(iv) 229 × ………… = 578 × 229
(v) 32 × 15 = 32 × 6 + 32 × 7 + 32 × ……….
(vi) 23 × 56 = 20 × 56 + ……… × 56
(vii) 83 × 54 + 83 × 16 = 83 × ( ……….. ) = 83 × ………….. = …………
(viii) 98 × 273 – 75 × 273 = ( …………. ) × 273 = ………… × 273
Solution:

Question 2.
By re-arranging the given numbers, evaluate :
(i) 2 × 487 × 50
(ii) 25 × 444 × 4
(iii) 225 × 20 × 50 × 4
Solution:

Question 3.
Use distributive law to evaluate :
(i) 984 × 102
(ii) 385 × 1004
(iii) 446 × 10002
Solution:

Question 4.
Evaluate using properties :
(i) 548 × 98
(ii) 924 × 988
(iii) 3023 × 723
Solution:

Question 5.
Evaluate using properties :
(i) 679 × 8 + 679 × 2
(ii) 284 × 12 – 284 × 2
(iii) 55873 × 94 + 55873 × 6
(iv) 7984 × 15 – 7984 × 5
(v) 8324 × 1945 – 8324 × 945
(vi) 3333 × 987 + 13 × 3333
Solution:

Question 6.
Find the product of the :
(i) greatest number of three digits and smallest number of five digits.
(ii) greatest number of four digits and the greatest number of three digits.
Solution:

Question 7.
Fill in the blanks :
(i) (437 + 3) × (400 – 3) = 397 × ……….
(ii) 66 + 44 + 22 = 11 × (………..) = 11 × ……….
Solution:

Question 8.
Evaluate :
(i) 355 × 18
(ii) 6214 × 12
(iii) 15 × 49372
(iv) 9999 × 8
Solution:

Natural Numbers and Whole Numbers Exercise 5D – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Show that :
(i) division of whole numbers is not closed
(ii) any whole number divided by 1, always gives the number itself.
(iii) every non-zero whole number divided by itself gives 1 (one).
(iv) zero divided by any non-zero number is zero only.
(v) a whole number divided by 0 is not defined.
For each part, given above, give an example.
Solution:

Question 2.
If x is a whole number such that x ÷ x = x, state the value of x.
Solution:

Question 3.
Fill in the blanks :
(i) 987 + 1 = …………
(ii) 0 + 987 = ……….
(iii) 336 – (888 + 888) = ……….
(iv) (23 + 23) – (437 + 437) = ………
Solution:

Question 4.
Which of the following statements are true ?
(i) 12 ÷ (6 × 2) = (12 ÷ 6) × (12 ÷ 2)
(ii) a ÷ (b – c) = \(\frac { a }{ b } -\frac { a }{ c }\)
(iii) (a – b) ÷ c = \(\frac { a }{ c } -\frac { b }{ c }\)
(vi) (15 – 13) ÷ 8 = (15 ÷ 8) – (13 ÷ 8)
(v) 8 ÷ (15 – 13) = \(\frac { 8 }{ 15 } -\frac { 8 }{ 13 }\)
Solution:

Natural Numbers and Whole Numbers Exercise 5E – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Find the difference between the largest number of four digits and the smallest number of six digits.
Solution:

Question 2.
Find the difference between the smallest number of eight digits and the largest number of five digits.
Solution:

Question 3.
The product of two numbers is 528. If the product of their unit’s digits is 8 and the product of their ten’s digits is 4 ; find the numbers.
Solution:

Question 4.
Does there exist a number a such that a ÷ a = a?
Solution:

Question 5.
Divide 5936 by 43 to find the quotient and remainder. Also, check your division by using the formula,
dividend = divisor × quotient + remainder.
Solution:

Natural Numbers and Whole Numbers Exercise 5F – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
(i) 1 × 9 + 1 = 10
12 × 9 + 2 = 110
123 × 9 + 3 = 1110
(ii) 9 × 9 + 7 = 88
98 × 9 + 6 = 888
987 × 9 + 5 = 8888
(iii) 1 × 8 + 1 = 9
12 × 8 + 2 = 98
123 × 8 + 3 = 987
(iv) 111 ÷ 3 = 37
222 ÷ 6 = 37
333 ÷ 9 = 37
Solution:

Question 2.
Complete each of the following magic squares :

Solution:

Question 3.
See the following pattern carefully :

(i) If n denotes the number of figure and S denotes the number of matches ; find S in terms of n.
(ii) Find how many matches are required to make the :
(1) 15th figure
(2) 40th figure
(iii) Write a discretion of the pattern in words.
Solution:

Question 4.
(i) In the following pattern, draw the next two figures.

(ii) Construct a table to describe the figures in the above pattern.
(iii) If n denotes the number of figure and L denotes the number of matches, find L in terms of n.
(iv) Find how may matches are required to make the :
(1) 12th figure
(2) 20th figure
Solution:

Question 5.
In each of the following patterns, construct next figure.
(i) In each case, if n denotes the number of figure and F denotes the number of matchsticks used, find F in terms of n.
(ii) Also find, in each case, how many matches are required to make the : 16th figure and 30th figure.


Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 4 Place Value

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 4 Place Value

Place Value Exercise 4A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) In 20 kg, the unit is ………….., which is taken …………. times.
(ii) In 80 m, the unit is …………., which is taken …………. times.
(iii) If a unit cm (centimetre) is taken 5 times, the corresponding quantity is …………….
(iv) If a unit km (kilometre) is taken 24 times, the corresponding quantity is ……………
(v)

Solution:

Question 2.
Fill in the blanks :
(i) In 24,673 ; the place value of 6 is ………..
(ii) In 8,039 ; the place value of 8 is …………..
(iii) In 3,25,648; the local value of 5 is ……………
(iv) In 6,439 ; the local value of 6 is ……….
Solution:

Question 3.
Find the difference between the place values of 3 and 5 in the number 3945.
Solution:

Question 4.
In the number 40562
(i) the local value of 5 = …………..
(ii) the place value of 6 = ………..
(iii) the sum of the place value of 5 and the place value of 6 = …………
Solution:

Question 5.
Read and write the following numbers in words and also in expanded form :
(i) 35,000 = …………
(ii) 76,000 = ……………
(iii) 6,23,000 = ………….
(iv) 40,075 = …………….
(v) 50,004 = ………..
Solution:

Question 6.
Find the difference in the place values of two sevens in the number 8, 72, 574.
Solution:

Place Value Exercise 4B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Fill in the blanks :
(i) 999 + 1 = …………
(ii) 10,000 – 1 = …………
(iii) 10 coins – one coin = …………
(iv) ₹ 99 + ₹ 1 = ………..
(v) 10,000 boys – 1 boy = ………..
(vi) 1000 toys – 1 toy = ……….
Solution:

Question 2.
Would the number of students in your school be a 3-digit number or a 4-digit number or a 5-digit number ?
Solution:

Question 3.
Write the smallest number which is just more than 9, 99, 999.
Solution:

Question 4.
Starting from the greatest 5-digit number, write the previous five numbers in descending order.
Solution:

Question 5.
Starting from the smallest 7-digit number, write the next four numbers in ascending order.
Solution:

Question 6.
How many numbers lie between the largest 3-digit number and the smallest 4-digit number ?
Solution:

Question 7.
How many 5-digit numbers are there in all?
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 3 Numbers in India and International System (With Comparison)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 3 Numbers in India and International System (With Comparison)

Numbers in India and International System Exercise 3 – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write the following numerals using Indian System words or International system (as required in words) :
(i) 4, 35, 342 = …………..
(ii) 36, 71, 430 = …………..
(iii) 4, 28, 30, 004 = …………..
(iv) 75, 132, 684 = ……………
(v) 815, 906 = …………….
(vi) 5, 420, 700 = ……………..
Solution:

Question 2.
Write the following numbers, placing the commas, according to Indian system :
(i) 835629 = …………
(ii) 35640254 = …………
(iii) 2826040 = ………
Solution:

Question 3.
Write the following numbers, by placing the commas, according to International system :
(i) 6509820 = ………..
(ii) 428140584 = …………
(iii) 63560981 = ……….
Solution:

Question 4.
Fill in the blanks :
(i) Four lakh sixty seven thousand three hundred six.
= ……………… (In numeral form)
= …………… (In International System)
= ……………. (In International numeration)
(ii) Thirteen lakh forty five.
= ……………. (In numeral form)
= ……………. (In International System)
= ……………. (In International numerals)
Solution:

Question 5.
Fill in the blanks :
(i) Six hundred four thousand eight hundred forty seven.
= ……………. (In numeral form)
= ……………. (In Indian System)
= ……………… (Number name in Indian System)
(ii) Two million three hundred ten thousand one hundred four
= …………….. (In numeral form)
= …………… (In Indian System)
= ……………. (In Indian numeration)
= …………….. (In international numerals)
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions

Selina Concise Mathematics Class 6 ICSE Solutions Chapter 2 Estimation

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 2 Estimation

Estimation Exercise 2A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Round off each of the following to the nearest ten :
(i) 62
(ii) 265
(iii) 543
(iv) 8261
(v) 6294
(vi) 3008
(vii) 72326
Solution:

Question 2.
Round off each of the following to the nearest hundred :
(i) 748
(ii) 784
(iii) 2667
(iv) 5432
(v) 6388
(vi) 59237
Solution:

Question 3.
Round off each of the following to the nearest thousand :
(i) 6475
(ii) 6732
(iii) 5352
(iv) 32568
(v) 9248
(vi) 83294
Solution:

Question 4.
Round off
(i) 578 to the nearest ten.
(ii) 578 to the nearest hundred.
(iii) 4327 to the nearest thousand.
(iv) 32974 to the nearest ten-thousand.
(v) 27487 to the nearest ten-thousand.
Solution:

Question 5.
Round off each of the following to the nearest tens, hundreds and thousands.
(i) 864
(ii) 1249
(iii) 54, 547
(iv) 68, 076
(v) 56, 293
(vi) 7, 293
(vii) 89, 24, 379
Solution:

Question 6.
Round off the following to the nearest tens ;
(i) ₹ 562
(ii) 837 m
(iii) 545 cm
(iv) ₹ 27
Solution:

Question 7.
List all the numbers which can be round off to 30.
Solution:

Question 8.
List all the numbers which can be rounded off to 50.
Solution:

Question 9.
Write the smallest and the largest numbers which are rounded off to 80.
Solution:

Question 10.
Write the smallest and the largest numbers which are rounded off to 130.
Solution:

Estimation Exercise 2B – Selina Concise Mathematics Class 8 ICSE Solutions

Question 1.
Estimate the sum of each pair of numbers to the nearest ten :
(i) 67 and 44
(ii) 34 and 87
(iii) 23 and 66
(iv) 78 and 18
(v) 96 and 55
(vi) 76 and 62
(vii) 457 and 175
(viii) 474 and 173
(ix) 527 and 267
Solution:

Question 2.
Estimate the sum of each pair of numbers to the nearest hundred :
(i) 336 and 782
(ii) 546 and 342
(iii) 270 and 495
(iv) 4280 and 5295
(v) 4230 and 2410
(vi) 30047 and 39287
Solution:

Question 3.
Estimate the sum of the following pair of numbers to the nearest thousand:
(i) 53826 and 36455
(ii) 56802 and 22475
Solution:

Question 4.
Estimate the following differences correct to nearest ten :
(i) 82 – 27
(ii) 96 – 36
(iii) 508 – 248
Solution:

Question 5.
Estimate each difference to the nearest hundred :
(i) 769 – 314
(ii) 856 – 687
(iii) 6352 – 2086
Solution:

Question 6.
Estimate each difference to the nearest thousand :
(i) 45974 – 38766
(ii) 76003 – 48399
Solution:

Question 7.
Estimate each of the following products by rounding of each number to the nearest ten :
(i) 49 x 52
(ii) 63 x 38
(iii) 27 x 54
(iv) 53 x 85
(v) 74 x 67
(vi) 25 x 33
Solution:

Question 8.
Estimate each of the following products by rounding off each number to the nearest hundred :
(i) 477 x 213
(ii) 624 x 236
(iii) 333 x 247
(iv) 537 x 283
(v) 382 x 127
(vi) 427 x 328
Solution:

Question 9.
Estimate each of the following products by rounding off the first number correct to nearest ten and the other number correct to nearest hundred :
(i) 28 x 287
(ii) 432 x 128
(iii) 48 x 165
(iv) 72 x 258
(v) 83 x 664
(vi) 44 x 250
Solution:

Question 10.
Estimate each of the following quotients by converting each number to the nearest ten :
(i) 87 ÷ 28
(ii) 84 ÷ 23
(iii) 77 ÷ 22
(iv) 198 ÷ 24
(v) 355 ÷ 26
(vi) 444 ÷ 42
(vii) 843 ÷ 33
Solution:

Selina Concise Mathematics Class 6 ICSE Solutions