Teach Kids Easy: June 2021

Monday 28 June 2021

Olympiad : Grade 4 : Chapter 1 : Number system

Number System

Sample Questions

a)10 tens = 10 * 10

= 100

= 1hundred

b) 100 tens = 100 * 10

= 1000

= 1 thousand

c) 1000 ones = 1000 * 1

= 1000

= 1 thousand

2) Using digits 5 , 0 , 3 , 8 , 1 each only once

a) Smallest 3 digit number

First, we have to check the smallest number

the smallest number among the given numbers 5, 0, 3, 8, 1 is 0

but if we write 0 in the first place then the three-digit number will become a two-digit number.

so the next smallest number is 1

write1 in the first place

now for the second place, we can write 0

for the third place, the next smallest number is 3

hence the smallest three-digit number among the given numbers is 103

b) Smallest five-digit number having 1 at hundreds place

given 1 at hundreds place

so, TTh Th H T O

at TTh place, 0 is not possible (if we write 0 then it will become 4 digit number)

1 is also not possible because given that it must be in the hundred place

the next smallest is 3

TTh Th H T O

3 1

TTh Th H T O

3 0 1

TTh Th H T O

3 0 1 5

TTh Th H T O

3 0 1 5 8

Hence the smallest 5 digit number among the given number and 1 at hundred places is 30158

3) Using the digits 0 , 3 , 9 , 2 , 4 each only once

a) largest 4 digit number

here, we have to write from the largest number

Th H T O

9 4

Th H T O

9 4 3

Th H T O

9 4 3 2

hence the largest four-digit number among given numbers is 9432

b) largest 5 digit number having 9 at tens place

given, 9 at tens place

so TTh Th H T O

TTh Th H T O

4 9

TTh Th H T O

4 3 9

TTh Th H T O

4 3 2 9

TTh Th H T O

4 3 2 9 0

Hence the largest 5 digit number having 9 at tens place is 43290

4) Write in words

a) 78609 = Seventy eight thousand six hundred and nine

b) 65079 = Sixty five thousand seventy nine

a) The greatest 5 digit number with all digits different and 4 at tens place is

TTh Th H T O

9 8 7 4 6

hence the greatest 5 digit number is 98746

b) The smallest 5 digit number with all digits different and 8 at hundred places is

TTh Th H T O

9 7 8 6 5

Hence the smallest 5 digit number with all digits different and 8 at hundred places is 97865

6) Expanded form of 38092 is 30000 + 8000 + 0 + 90 + 2

7) Compare

a) DCCCLXXXIX _____ CMLIX

I - 1 : V - 5 : X - 10 : L - 50 : C - 100 : D - 500 : M - 1000

D C C C L X X X IX

500 + 100 + 100 + 100 + 50 + 10 + 10 + 10 + 9 = 889

CM L IX

900 + 50 + 9 = 959

DCCCLXXXIX ( 889 ) < CMLIX ( 959)

b) CDXXIV _____ CCCXXIV

CD X X IV

400 + 10 + 10 + 4 = 424

C C C X X IV

100 + 100 + 100 + 10 + 10 + 4 = 324

CDXXIV (424) > CCCXXIV (324)

8) Place Value : Place value is the value of each digit in a number

Face value : Face value of a number is the value of the number itself

a) In number 35687 the place and face value of 6 is

place value of 6 is 600

face value of 6 is 6

b) In number 87312, which digit has same place value and face value?

the place value of any number in the units place is the number itself

hence place value = face value = 2

9) Arrange in Ascending and descending order

38790, 39087 , 37908 , 30789 , 38079

Ascending order : Small to big

30789 , 37908 , 38079 , 38790 , 39087

Descending order : big to small

39087, 38790, 38079 , 37908 , 30789

10 ) Seventy five thousand five hundred is same as 75500

Wednesday 9 June 2021

Square

Find the Length of a side when the area of a square is given

a) 81cm^2

Solution

Given,

Area of a square = 81cm^2

Formula

Area of a square = a^2 square units ( 'a' is the length of a side )

here, a^2 = 81cm^2

to find a, we have to take sqrt on both the sides

sqrt(a^2) = sqrt(81cm^2)

a = 9cm ( sqrt(81) = +/-9, but length of a side is always positive )

Hence the length of a side = 9cm

b) 0.25 dm^2

Solution

Given,

Area of a square = 0.25 dm^2

Formula

Area of a square = a^2 square units ( 'a' is the length of a side )

here, a^2 = 0.25 dm^2

to find a, we have to take sqrt on both the sides

sqrt(a^2) = sqrt(0.25 dm^2)

a = 0.5 dm

Hence the length of a side = 0.25 dm

c) 1.44 km^2

Solution

Given,

Area of a square = 1.44 km^2

Formula

Area of a square = a^2 square units ( 'a' is the length of a side )

here, a^2 = 1.44 km^2

to find a, we have to take sqrt on both the sides

sqrt(a^2) = sqrt(1.44 km^2)

a = 1.2 km

Hence the length of a side = 1.2 km

d) 2.25 ha

Given,

Area of a square = 2.25 ha

we know that , 1 ha = 1000 m^2 (ha - hectare)

2.25 ha = 2.25 * 1000 m^2

= 2250 m^2

so, now area of a square = 2250 m^2

Formula

Area of a square = a^2 square units ( 'a' is the length of a side )

a^2 = 2250 m^2

sqrt(a^2) = sqrt(2250 m^2)

a = 15sqrt(10) m

Note

sqrt(2250) = sqrt(225*10)

= sqrt(225) * sqrt(10)

= 15 sqrt(10)

Hence the length of a side = 15 sqrt(10) m

Solve the Quadratic Equation

Solve for x

1) x^2 = 0.64

Solution

We have to solve for 'x'

but here we are having x^2, so to make this x^2 as x,

we have to take square root on both the sides

sqrt(x^2) = sqrt(0.64)

x = +/- 0.8

2) x^2 - 50 = 50

Solution

We have to solve for x

so first let's move -50 to another side

to move -50, we have to add 50 on both sides

x^2 -50 +50 = 50 +50

x^2 +0 = 100

x^2 = 100

Now to make x^2 as x, Take square root on both sides

sqrt(x^2) = sqrt(100)

x = +/- 10

3) 2 - x^2 = 1.51

Solution

We have to solve for x

so first let's move 2 to another side

to move 2, we have to subtract 2 on both sides

2 - x^2-2 = 1.51-2

-x^2 = -0.49

to make -x^2 as x^2, we have to multiply by -1 on both sides
(- * - = + )

x^2 = 0.49

Take sqrt on both sides

sqrt(x^2) = sqrt(0.49)

x = +/- 0.7

4) 3x - x^2 = -144 + 3x

Solution

3x present on both sides

if we subtract 3x on both sides then 3x gets vanished (3x-3x=0)

so, -x^2 = -144

multiply by -1 on both the sides

x^2 = 144

take sqrt on both sides

sqrt(x^2) = sqrt(144)

x = +/-12

5) -x^2 -4 = 0

Solution

To move -4 to another side, add 4 on both the sides

-x^2 -4 +4 = 0+4

-x^2 + 0 = 4

-x^2 = 4

To make -x^2 as x^2, multiply by -1 on both sides

-x^2 * -1 = 4* -1

x^2 = -4

Take sqrt on both sides

sqrt(x^2) = sqrt(-4)

x = +/- 2i

Note :
sqrt(-1) = i ( imaginary value )
so, sqrt(-4) = sqrt(-1*4)
= sqrt(-1) * sqrt(4)
= +/- i * 2 or +/-2i

6) 3y^2 = 48

Solution

To make 3y^2 as y^2, we have to divide by 3 on both the sides

3y^2 / 3 = 48 / 3

y^2 = 16

Take sqrt on both the sides

sqrt(y^2) = sqrt(16)

y = +/- 4

7) 6x^2 - x = 216 - x

Solution

-x is present on both the sides, so if we add x on the sides, x gets vanished

6x^2 ~~- x~~ = 216 ~~- x~~

6x^2 = 216

take make 6x^2 as x^2, divide both the sides by 6

6x^2 / 6 = 216 / 6

x^2 = 36

Take sqrt on both the sides

sqrt(x^2) = sqrt(36)

x = +/- 6

8) 10+4y^2 = 115 -y^2

Solution

First, let us move 10 to the right side, so subtract 10 on both sides

10+4y^2 - 10 = 115 -y^2 -10

4y^2 = 105 -y^2

now to move -y^2 to the left side, add y^2 on both sides

4y^2 + y^2 = 105 -y^2 + y^2

5y^2 = 105

to make 5y^2 as y^2, divide both the sides by 5

5y^2 / 5 = 105 / 5

y^2 = 21

y= +/-sqrt(21)

Tuesday 1 June 2021

Examples on finding Square root using Long Division method

1) Find the square root of 322624

Hence the square root of 322624 is +/- 568.

2) Find the square root of 10435

Hence the square root of 10435 is approximate +/- 102.1

3) Find the square root of 62150.49

Hence the square root of 62150.49 is +/- 249.9